Panel unit root test with structural breaks. A problem with the code

Question

Hi Everyone,

I am a Masters student currently constructing econometric models for my dissertation topic of environmental degradation. While researching I came across the test mentioned in the subject bar which originally came from the below reference.

Carrion-i-Silvestre, J. Ll., del Barrio, T. and López-Bazo, E. (2005): “Breaking the Panels: An Application to GDP per capita”, Econometrics Journal, 8, 159-175.

Thankfully I was sent the code but there seem to be errors when I run the file at the point where it creates the bootstrap critical values. The problems seem to start the point where it says "do until in". I think there should be some sort of inequality sign between the i and n but I'm not sure whether it would be >, <, => or <=.

When I put one of those in the error message then moves on to

{kpsstest,num,den} = pankpss(yb[.,i],dd_tb,model,kernel);

but I have not worked out what the issue is here and therefore cannot tell if more problems follow once this has been fixed.

The deadline is fast approaching and I'm stuck as to what is wrong with the code so if anyone can fix it I would be extremely grateful. Thank you for your time.

Kind regards,

James

The code is as follows:

/*
/*
Lectura de la base de dades de PIB per capita
de Maddison.

Període: 1980-2013 per a 19 països (primera columna amb els anys).
*/

new;
cls;

output file=c:\Disscode\carrion.out reset;
outwidth 256;

load odata[35,20]=c:\gauss16\gdp.prn;

aut=ln(odata[.,2]);
bel=ln(odata[.,3]);
bul=ln(odata[.,4]);
den=ln(odata[.,5]);
fin=ln(odata[.,6]);
fra=ln(odata[.,7]);
deu=ln(odata[.,8]);
gre=ln(odata[.,9]);
hun=ln(odata[.,10]);
ire=ln(odata[.,11]);
ita=ln(odata[.,12]);
net=ln(odata[.,13]);
pol=ln(odata[.,14]);
por=ln(odata[.,15]);
rom=ln(odata[.,16]);
slo=ln(odata[.,17]);
esp=ln(odata[.,18]);

swe=ln(odata[.,19]);

uk=ln(odata[.,20]);

print "
    /*********************************************************************/
    /* Anàlisi */
    /*********************************************************************/ " ;

/*data=aust~bel~can~den~fra~jap~usa; @ Data set that RHo at the 1% in Ben-David and Papell (1995) @*/
/*data=aust~bel~can~den~fra~jap~swe~uk~usa; @ Data set that RHo at the 1% and 2.5% in Ben-David and Papell (1995) @*/
/*data=aust~bel~can~den~fin~fra~ger~jap~swe~uk~usa; @ Data set that RHo at the 1, 2.5 and 10% in Ben-David and Papell (1995) @*/
/*data=aus~aust~bel~can~den~fin~fra~ger~ita~jap~ned~nze~nor~swe~swi~uk~usa; @ The Whole data set @*/
data=aut~bel~bul~den~fin~fra~deu~gre~hun~ire~ita~net~pol~por~rom~slo~esp~swe~uk; @ Countries with complete time series 1870-... @

k=cols(data); @ Number of countries (individuals) @
bigt=rows(data); @ Number of time periods @
kernel=0|5;

m=5; @maximum number of structural changes allowed@

model0=2; @ Model quan no hi ha canvis. Segon model: efectes individuals + tendència @
model = 4; @ Model quan hi ha canvis. Canvis en la mitjana i en el pendent @

/*
model0=1; @ Model quan no hi ha canvis. Primer model: efectes individuals @
model = 3; @ Model quan hi ha canvis. Canvis en la mitjana @
*/

/**********************************************************************************************/
/**********************************************************************************************/

eps1=.15; @Value of the trimming (in percentage) for the construction
and critical values of the supF ype tests (used in the
supF test, the Dmax, the supF(l+1|l) and the sequential
procedure). if these test are used, h below should be set
at int(eps1*bigt). But if the tests are not required, estimation
can be done with an arbitrary h.
There are five options: eps1 = .05, .10, .15, .20 or .25.
for each option, the maximal value of m above is: 10 for eps1 = .05;
8 for eps1 = .10, 5 for eps1 = .15, 3 for eps1 = .20 and 2 for eps1 = .25.@
h=int(eps1*bigt); @minimal length of a segment (h >= q). Note: if
robust=1, h should be set at a larger value.@
/* the following are options if p > 0.
----------------------------------- */
fixb=0; @set to 1 if use fixed initial values for beta@
betaini=0; @if fixb=1, load the initial value of beta.@
maxi=20; @maximum number of iterations for the nonlinear
procedure to obtain global minimizers.@
printd=1; @set to 1 if want the output from the iterations
to be printed.@
eps=0.0001; @criterion for the convergence.@
/*--------------------------------- */

robust=0; @set to 1 if want to allow for heterogeneity
and autocorrelation the in residuals, 0 otherwise.
The method used is Andrews(1991) automatic
bandwidth with AR(1) approximation and the
quadratic quernel. Note: Do not set to 1 if
lagged dependent variables are included as
regressors.@
prewhit=0; @set to 1 if want to apply AR(1) prewhitening
prior to estimating the long run covariance
matrix@
hetdat=1; @Option for the construction of the F-tests.
Set to 1 if want to allow different moment matrices of the
regressors accross segments. if hetdat = 0, the same
moment matrices are assumed for each segment and estimated
from the full sample. It is recommended to set hetdat=1. if p > 0
set hetdat = 1.@
hetvar=1; @Option for the construction of the F-tests.
Set to 1 if want to allow for the variance of the residuals
to be different across segments. if hetvar=0, the variance
of the residuals is assumed constant across segments
and constructed from the full sample. This option is not available
when robust = 1.@
hetomega=1; @Used in the construction of the confidence
intervals for the break dates. if hetomega=0,
the long run covariance matrix of zu is assumed
identical accross segments (the variance of the
errors u if robust = 0).@
hetq=1; @Used in the construction of the confidence
intervals for the break dates. if hetq=0,
the moment matrix of the data is assumed
identical accross segments.@
doglobal=1; @set to 1 if want to call the procedure
to obtain global minimizers.@
dotest=1; @set to 1 if want to construct the sup F,
UDmax and WDmax tests. doglobal must be set
to 1 to run this procedure.@
dospflp1=1; @set to 1 if want to construct the sup(l+1|l)
tests where under the null the l breaks are
obtained using global minimizers. doglobal
must be set to 1 to run this procedure.@
doorder=1; @set to 1 if want to call the procedure that
selects the number of breaks using information
criteria. doglobal must be set to 1 to run
this procedure.@
dosequa=1; @set to 1 if want to estimate the breaks
sequentially and estimate the number of
breaks using the supF(l+1|l) test.@
dorepart=1; @set to 1 if want to modify the
break dates obtained from the sequential
method using the repartition method of
Bai (1995), Estimating breaks one at a time.
This is needed for the confidence intervals
obtained with estim below to be valid.@
estimbic=1; @set to 1 if want to estimate the model with
the number of breaks selected by BIC.@
estimlwz=0; @set to 1 if want to estimate the model with
the number of breaks selected by LWZ.@
estimseq=0; @set to 1 if want to estimate the model with
the number of breaks selected using the
sequential procedure.@
estimrep=0; @set to 1 if want to esimate the model with
the breaks selected using the repartition
method.@
estimfix=0; @set to 1 if want to estimate the model with
a prespecified number of breaks equal to fixn
set below.@
fixn=0;

/*****************************************************************************/
/*****************************************************************************/

if model == 3;
    z=ones(bigt,1); @ Matrix conformeb by the elements that are allowed to change @
    q=cols(z); @ Number of regressors z @
    x=0;
    p=0;
elseif model == 4;
    z=ones(bigt,1)~seqa(1,1,bigt); @ Matrix conformeb by the elements that are allowed to change @
    q=cols(z); @ Number of regressors z @
    x=0;
    p=0;
endif;

@ Matrices of results @
numkpss=zeros(k,1);
denkpss=zeros(k,1);
m_lee_est=zeros(k,4);
m_tb=zeros(1,m);
m_tb2=zeros(1,m);

m_deter=zeros(bigt,k);

j=1;
do until j > k;
    
    {datevec,nbreak,mbic,mlwz,supfl,dateseq,ftest,wftest,reparv}=pbreak(bigt,data[.,j],z,q,m,h,eps1,robust,prewhit,hetomega,
        hetq,doglobal,dotest,dospflp1,doorder,dosequa,dorepart,estimbic,estimlwz,
        estimseq,estimrep,estimfix,fixb,x,q,eps,maxi,fixb,betaini,printd,hetdat,hetvar,fixn);
    
    nbr=nbreak[2]; @ Numero de canvis detectats pel procediment sequencial al 5% de significacio @
    
    /*nbr=mbic;*/
    
    nbr=mlwz;
    
    if nbr > 0;
        tb=selif(datevec[.,nbr],datevec[.,nbr] .gt 0);
        {kpsstest,num,den} = pankpss(data[.,j],tb,model,kernel);
        
        deter=dekpss(model,bigt,tb);
        beta=data[.,j]/deter;
        m_deter[.,j] =deter*beta;
        
    elseif nbr == 0;
        {kpsstest,num,den} = pankpss(data[.,j],0,model0,kernel);
        
        z=dekpss(model0,bigt,0);
        beta=data[.,j]/z;
        m_deter[.,j] =z*beta;
        
    endif;
    
    numkpss[j]=num;
    denkpss[j]=den;
    m_lee_est[j,.]=kpsstest~nbr~mbic~mlwz;
    
    m_tb=m_tb|datevec;
    m_tb2=m_tb2|reparv;
    
    j=j+1;
endo;

test_hom=meanc(numkpss)./meanc(denkpss); @ Assuming homogeneous long-run variance @
test_het=meanc(m_lee_est[.,1]); @ Assuming heterogeneous long-run variance @

m_tb=m_tb[2:rows(m_tb),.];

test_mean=zeros(k,1);
test_var=zeros(k,1);

j=1;
do until j > k;
    if m_lee_est[j,2] > 0;
        temp1=m_tb[(j*m)-m+1:(j*m),.];
        temp2=calcdem(model,temp1[.,m_lee_est[j,2]],bigt); @ Computes the mean and variance @
        test_mean[j]=temp2[1];
        test_var[j]=temp2[2];
    elseif m_lee_est[j,2] == 0;
        temp2=calcdem(model0,0,bigt); @ Computes the mean and variance @
        test_mean[j]=temp2[1];
        test_var[j]=temp2[2];
    endif;
    j=j+1;
endo;

test_mean=meanc(test_mean);
test_var=meanc(test_var);

testd_hom=sqrt(k)*(test_hom-test_mean)./sqrt(test_var);
testd_het=sqrt(k)*(test_het-test_mean)./sqrt(test_var);

print "************************************";
print "Results for the PANKPSS test ";
print "************************************";

print "Stationarity test with structural breaks (homogeneous): " testd_hom "with p-val: " cdfnc(testd_hom);
print "Stationarity test with structural breaks (heterogeneous): " testd_het "with p-val: " cdfnc(testd_het);

print "Nombre de breaks permesos com a maxim" m;
print "Matriu de tests individuals" m_lee_est;
print "Nombre d'observacions" rows(data);
print "Punts de trencament estimats" m_tb;

@++++++++++++@
@ Bootstrap @
@++++++++++++@

n=cols(data);
t=rows(data);
m_res=zeros(t,n); @ Matriu per deixar els residus @

i=1;
do until i > n; @ Residuals @
    m_res[.,i]=data[.,i]-m_deter[.,i];
    i=i+1;
endo;

re=2000; @ Nombre de rèpliques del Bootstrap @
m_kpss_hom=zeros(re,1);
m_kpss_het=zeros(re,1);
m_had_test=zeros(n,3);

j=1;
do while j <= re;
    tt=rows(m_res);
    m_resb=zeros(t+30,n);
    
    i=1;
    do while in;
        yb[.,i]=m_deter[.,i]+m_resb[.,i];
        i=i+1;
    endo;
    
    i=1;
    do until in;
        
        temp1=m_tb[(i*m)-m+1:(i*m),.]; @ Matrix of Breaks @
        dd_tb=temp1[.,m_lee_est[i,2]];
        
        if nbr > 0;
            dd_tb=selif(dd_tb,dd_tb .gt 0);
            {kpsstest,num,den} = pankpss(yb[.,i],dd_tb,model,kernel);
        elseif nbr == 0;
            {kpsstest,num,den} = pankpss(yb[.,i],0,model0,kernel);
        endif;
        
        numkpss[i]=num;
        denkpss[i]=den;
        m_lee_est[i,.]=kpsstest~nbr~mbic~mlwz;
        
        i=i+1;
    endo;
    
    test_hom=meanc(numkpss)./meanc(denkpss); @ Assuming homogeneous long-run variance @
    test_het=meanc(m_lee_est[.,1]); @ Assuming heterogeneous long-run variance @
    
    m_kpss_hom[j,.]=sqrt(n)*(test_hom-test_mean)./sqrt(test_var);
    m_kpss_het[j,.]=sqrt(n)*(test_het-test_mean)./sqrt(test_var);
    
    j=j+1;
endo;

e=0.01|0.025|0.05|0.1|0.9|0.95|0.975|0.99;

print "Homogeneous";
q=quantile(m_kpss_hom,e);
e~q;

print "Heterogeneous";
q=quantile(m_kpss_het,e);
e~q;

/****************************************/
/****************************************/

#include c:\Gauss16\brcode2.src;
#include c:\Gauss16\granada.src;

5 Answers

Your Answer

aptech · Answer 1

In the code, we see that both n and k are assigned to be the number of columns in the variable data. In the loop in which you have the question:

i=1;
    do while in;
        yb[.,i]=m_deter[.,i]+m_resb[.,i];
        i=i+1;
    endo;

the code is using columns from m_deter and m_resb. These variables are assigned with the following lines:

m_resb=zeros(t+30,n);
m_deter=zeros(bigt,k);

Since both variables have the same number of columns and the loop counter starts at 1 and ends in reference to n, I think it is safe to assume that the do while statement should be:

do while i <= n;

which would make the loop use all columns of m_deter and all columns of m_resb.

link

aptech

1,773

013179 · Answer 2

Thank you! That seems to have done the trick, although I'm struggling to find where the Break dates and Bootstrap critical values appear in the output. Could you possibly point me in the right direction? Thank you for your time.

The output is as follows:
/*********************************************************************/
/* Anàlisi */
/*********************************************************************/
The options chosen are:
h = 18.000000
eps1 = 0.15000000
hetdat = 1.0000000
hetvar = 1.0000000
hetomega = 1.0000000
hetq = 1.0000000
robust = 0.00000000 (prewhit = 0.00000000 )
The maximum number of breaks is: 5.0000000
********************************************************
Output from the global optimization
********************************************************
The model with 1.0000000 breaks has SSR : 0.63788477
The dates of the breaks are: 60.000000
The model with 2.0000000 breaks has SSR : 0.38171908
The dates of the breaks are:
22.000000
59.000000
The model with 3.0000000 breaks has SSR : 0.31905432
The dates of the breaks are:
22.000000
42.000000
60.000000
The model with 4.0000000 breaks has SSR : 0.27477778
The dates of the breaks are:
22.000000
42.000000
60.000000
98.000000
The model with 5.0000000 breaks has SSR : 0.24255780
The dates of the breaks are:
22.000000
40.000000
59.000000
77.000000
98.000000
********************************************************
Output from the testing procedures
********************************************************
a) supF tests against a fixed number of breaks
--------------------------------------------------------------
The supF test for 0 versus 1.0000000 breaks (scaled by q) is: 744.56580
The supF test for 0 versus 2.0000000 breaks (scaled by q) is: 569.58163
The supF test for 0 versus 3.0000000 breaks (scaled by q) is: 406.45509
The supF test for 0 versus 4.0000000 breaks (scaled by q) is: 383.65621
The supF test for 0 versus 5.0000000 breaks (scaled by q) is: 481.52066
-------------------------
The critical values at the 10.000000 % level are (for k=1 to 5.0000000 ):
9.8100000 8.6300000 7.5400000 6.5100000 5.2700000
The critical values at the 5.0000000 % level are (for k=1 to 5.0000000 ):
11.470000 9.7500000 8.3600000 7.1900000 5.8500000
The critical values at the 2.5000000 % level are (for k=1 to 5.0000000 ):
12.960000 10.750000 9.1500000 7.8100000 6.3800000
The critical values at the 1.0000000 % level are (for k=1 to 5.0000000 ):
15.370000 12.150000 10.270000 8.6500000 7.0000000
--------------------------------------------------------------
b) Dmax tests against an unknown number of breaks
--------------------------------------------------------------
The UDmax test is: 744.56580
(the critical value at the 10.000000 % level is: 10.160000 )
(the critical value at the 5.0000000 % level is: 11.700000 )
(the critical value at the 2.5000000 % level is: 13.180000 )
(the critical value at the 1.0000000 % level is: 15.410000 )
********************************************************
---------------------
The WDmax test at the 10.000000 % level is: 896.34112
(The critical value is: 11.150000 )
---------------------
The WDmax test at the 5.0000000 % level is: 944.10974
(The critical value is: 12.810000 )
---------------------
The WDmax test at the 2.5000000 % level is: 978.13602
(The critical value is: 14.580000 )
---------------------
The WDmax test at the 1.0000000 % level is: 1057.2818
(The critical value is: 17.010000 )
********************************************************
supF(l+1|l) tests using global otimizers under the null
--------------------------------------------------------------
The supF( 2.0000000 | 1.0000000 ) test is : 78.670792
It corresponds to a new break at: 22.000000
The supF( 3.0000000 | 2.0000000 ) test is : 65.729190
It corresponds to a new break at: 98.000000
The supF( 4.0000000 | 3.0000000 ) test is : 66.650554
It corresponds to a new break at: 98.000000
The supF( 5.0000000 | 4.0000000 ) test is : 8.9555079
It corresponds to a new break at: 78.000000
********************************************************
The critical values of supF(i+1|i) at the 10.000000 % level are (for i=1 to 5.0000000 ) are:
9.8100000 11.400000 12.290000 12.900000 13.470000
The critical values of supF(i+1|i) at the 5.0000000 % level are (for i=1 to 5.0000000 ) are:
11.470000 12.950000 14.030000 14.850000 15.290000
The critical values of supF(i+1|i) at the 2.5000000 % level are (for i=1 to 5.0000000 ) are:
12.960000 14.920000 15.810000 16.510000 16.840000
The critical values of supF(i+1|i) at the 1.0000000 % level are (for i=1 to 5.0000000 ) are:
15.370000 16.840000 17.720000 18.670000 19.170000
********************************************************
Output from the application of Information criteria
--------------------------------------------------------------
Values of BIC and lwz with 0.00000000 breaks: -3.5954739 -3.5793445
Values of BIC and lwz with 1.0000000 breaks: -5.1620318 -5.0412712
Values of BIC and lwz with 2.0000000 breaks: -5.5596250 -5.3336080
Values of BIC and lwz with 3.0000000 breaks: -5.6230690 -5.2911379
Values of BIC and lwz with 4.0000000 breaks: -5.6565882 -5.2180502
Values of BIC and lwz with 5.0000000 breaks: -5.6654313 -5.1195557
The number of breaks chosen by BIC is : 5.0000000
The number of breaks chosen by LWZ is : 2.0000000
********************************************************
Output from the sequential procedure at significance level 10.000000 %
--------------------------------------------------------------
The first break found is at: 60.000000
The next break found is at: 22.000000
The next break found is at: 98.000000
The next break found is at: 42.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 5.0000000 %
--------------------------------------------------------------
The first break found is at: 60.000000
The next break found is at: 22.000000
The next break found is at: 98.000000
The next break found is at: 42.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 2.5000000 %
--------------------------------------------------------------
The first break found is at: 60.000000
The next break found is at: 22.000000
The next break found is at: 98.000000
The next break found is at: 42.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 1.0000000 %
--------------------------------------------------------------
The first break found is at: 60.000000
The next break found is at: 22.000000
The next break found is at: 98.000000
The next break found is at: 42.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the repartition procedure for the 10.000000 % significance level
----------------------------------------
The updated break dates are :
22.000000
42.000000
60.000000
98.000000
********************************************************
Output from the repartition procedure for the 5.0000000 % significance level
----------------------------------------
The updated break dates are :
22.000000
42.000000
60.000000
98.000000
********************************************************
Output from the repartition procedure for the 2.5000000 % significance level
----------------------------------------
The updated break dates are :
22.000000
42.000000
60.000000
98.000000
********************************************************
Output from the repartition procedure for the 1.0000000 % significance level
----------------------------------------
The updated break dates are :
22.000000
42.000000
60.000000
98.000000
********************************************************
Output from the estimation of the model selected by BIC
--------------------------------------------------------------
Valid cases: 125 Dependent variable: Y
Missing cases: 0 Deletion method: None
Total SS: 9715.009 Degrees of freedom: 113
R-squared: 1.000 Rbar-squared: 1.000
Residual SS: 0.243 Std error of est: 0.046
F(12,113): 377150.178 Probability of F: 0.000
Durbin-Watson: 1.131

Standard Prob Standardized Cor with
Variable Estimate Error t-value >|t| Estimate Dep Var
-------------------------------------------------------------------------------
X01 8.252417 0.020449 403.564095 0.000 0.392709 0.399910
X02 0.013158 0.001557 8.451430 0.000 0.008224 0.352078
X03 7.854342 0.067196 116.886860 0.000 0.338084 0.360293
X04 0.016380 0.002105 7.781915 0.000 0.022508 0.356098
X05 8.459208 0.097609 86.663943 0.000 0.374098 0.378970
X06 0.002204 0.001941 1.135570 0.259 0.004902 0.376775
X07 6.831745 0.144595 47.247351 0.000 0.294067 0.372287
X08 0.026528 0.002105 12.603488 0.000 0.078444 0.371671
X09 7.142570 0.147276 48.497914 0.000 0.332080 0.418201
X10 0.021049 0.001670 12.607068 0.000 0.086324 0.417621
X11 7.674172 0.128522 59.711008 0.000 0.404568 0.502973
X12 0.016666 0.001145 14.558786 0.000 0.098642 0.502236
--------------------------------------------------------------
Corrected standard errors for the coefficients
--------------------------------------------------------------
The corrected standard error for coefficient 1.0000000 is: 0.018528507
The corrected standard error for coefficient 2.0000000 is: 0.0014107364
The corrected standard error for coefficient 3.0000000 is: 0.078828928
The corrected standard error for coefficient 4.0000000 is: 0.0024692383
The corrected standard error for coefficient 5.0000000 is: 0.11371312
The corrected standard error for coefficient 6.0000000 is: 0.0022607385
The corrected standard error for coefficient 7.0000000 is: 0.19939422
The corrected standard error for coefficient 8.0000000 is: 0.0029025513
The corrected standard error for coefficient 9.0000000 is: 0.073625873
The corrected standard error for coefficient 10.000000 is: 0.00083468394
The corrected standard error for coefficient 11.000000 is: 0.054767424
The corrected standard error for coefficient 12.000000 is: 0.00048781667
--------------------------------------------------------------
Confidence intervals for the break dates
--------------------------------------------------------------
The 95% C.I. for the 1.0000000 th break is: 20.000000 23.000000
The 90% C.I. for the 1.0000000 th break is: 20.000000 23.000000
The 95% C.I. for the 2.0000000 th break is: 37.000000 42.000000
The 90% C.I. for the 2.0000000 th break is: 37.000000 41.000000
The 95% C.I. for the 3.0000000 th break is: 55.000000 60.000000
The 90% C.I. for the 3.0000000 th break is: 56.000000 60.000000
The 95% C.I. for the 4.0000000 th break is: 75.000000 160.00000
The 90% C.I. for the 4.0000000 th break is: 75.000000 160.00000
The 95% C.I. for the 5.0000000 th break is: 95.000000 99.000000
The 90% C.I. for the 5.0000000 th break is: 96.000000 99.000000
********************************************************
K_BIC 2.0000000
The options chosen are:
h = 18.000000
eps1 = 0.15000000
hetdat = 1.0000000
hetvar = 1.0000000
hetomega = 1.0000000
hetq = 1.0000000
robust = 0.00000000 (prewhit = 0.00000000 )
The maximum number of breaks is: 5.0000000
********************************************************
Output from the global optimization
********************************************************
The model with 1.0000000 breaks has SSR : 2.4211955
The dates of the breaks are: 75.000000
The model with 2.0000000 breaks has SSR : 1.2462590
The dates of the breaks are:
75.000000
93.000000
The model with 3.0000000 breaks has SSR : 0.70571898
The dates of the breaks are:
44.000000
75.000000
93.000000
The model with 4.0000000 breaks has SSR : 0.69990374
The dates of the breaks are:
20.000000
44.000000
75.000000
93.000000
The model with 5.0000000 breaks has SSR : 0.74336824
The dates of the breaks are:
18.000000
36.000000
54.000000
75.000000
93.000000
********************************************************
Output from the testing procedures
********************************************************
a) supF tests against a fixed number of breaks
--------------------------------------------------------------
The supF test for 0 versus 1.0000000 breaks (scaled by q) is: 375.26209
The supF test for 0 versus 2.0000000 breaks (scaled by q) is: 484.75241
The supF test for 0 versus 3.0000000 breaks (scaled by q) is: 416.18971
The supF test for 0 versus 4.0000000 breaks (scaled by q) is: 316.27218
The supF test for 0 versus 5.0000000 breaks (scaled by q) is: 253.60450
-------------------------
The critical values at the 10.000000 % level are (for k=1 to 5.0000000 ):
9.8100000 8.6300000 7.5400000 6.5100000 5.2700000
The critical values at the 5.0000000 % level are (for k=1 to 5.0000000 ):
11.470000 9.7500000 8.3600000 7.1900000 5.8500000
The critical values at the 2.5000000 % level are (for k=1 to 5.0000000 ):
12.960000 10.750000 9.1500000 7.8100000 6.3800000
The critical values at the 1.0000000 % level are (for k=1 to 5.0000000 ):
15.370000 12.150000 10.270000 8.6500000 7.0000000
--------------------------------------------------------------
b) Dmax tests against an unknown number of breaks
--------------------------------------------------------------
The UDmax test is: 484.75241
(the critical value at the 10.000000 % level is: 10.160000 )
(the critical value at the 5.0000000 % level is: 11.700000 )
(the critical value at the 2.5000000 % level is: 13.180000 )
(the critical value at the 1.0000000 % level is: 15.410000 )
********************************************************
---------------------
The WDmax test at the 10.000000 % level is: 551.03374
(The critical value is: 11.150000 )
---------------------
The WDmax test at the 5.0000000 % level is: 571.01626
(The critical value is: 12.810000 )
---------------------
The WDmax test at the 2.5000000 % level is: 589.48838
(The critical value is: 14.580000 )
---------------------
The WDmax test at the 1.0000000 % level is: 622.86620
(The critical value is: 17.010000 )
********************************************************
supF(l+1|l) tests using global otimizers under the null
--------------------------------------------------------------
The supF( 2.0000000 | 1.0000000 ) test is : 212.97786
It corresponds to a new break at: 44.000000
The supF( 3.0000000 | 2.0000000 ) test is : 212.97786
It corresponds to a new break at: 44.000000
The supF( 4.0000000 | 3.0000000 ) test is : 16.568290
It corresponds to a new break at: 20.000000
Given the location of the breaks from the global optimization
with 4.0000000 breaks there was no more place to insert
an additional breaks that satisfy the minimal length requirement.
The supF( 5.0000000 | 4.0000000 ) test is : 0.00000000
It corresponds to a new break at: 0.00000000
********************************************************
The critical values of supF(i+1|i) at the 10.000000 % level are (for i=1 to 5.0000000 ) are:
9.8100000 11.400000 12.290000 12.900000 13.470000
The critical values of supF(i+1|i) at the 5.0000000 % level are (for i=1 to 5.0000000 ) are:
11.470000 12.950000 14.030000 14.850000 15.290000
The critical values of supF(i+1|i) at the 2.5000000 % level are (for i=1 to 5.0000000 ) are:
12.960000 14.920000 15.810000 16.510000 16.840000
The critical values of supF(i+1|i) at the 1.0000000 % level are (for i=1 to 5.0000000 ) are:
15.370000 16.840000 17.720000 18.670000 19.170000
********************************************************
Output from the application of Information criteria
--------------------------------------------------------------
Values of BIC and lwz with 0.00000000 breaks: -2.4301776 -2.4140482
Values of BIC and lwz with 1.0000000 breaks: -3.8281728 -3.7074122
Values of BIC and lwz with 2.0000000 breaks: -4.3764084 -4.1503914
Values of BIC and lwz with 3.0000000 breaks: -4.8292133 -4.4972822
Values of BIC and lwz with 4.0000000 breaks: -4.7216081 -4.2830701
Values of BIC and lwz with 5.0000000 breaks: -4.5454798 -3.9996042
The number of breaks chosen by BIC is : 3.0000000
The number of breaks chosen by LWZ is : 3.0000000
********************************************************
Output from the sequential procedure at significance level 10.000000 %
--------------------------------------------------------------
The first break found is at: 75.000000
The next break found is at: 44.000000
The next break found is at: 93.000000
The next break found is at: 20.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 5.0000000 %
--------------------------------------------------------------
The first break found is at: 75.000000
The next break found is at: 44.000000
The next break found is at: 93.000000
The next break found is at: 20.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 2.5000000 %
--------------------------------------------------------------
The first break found is at: 75.000000
The next break found is at: 44.000000
The next break found is at: 93.000000
The next break found is at: 20.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 1.0000000 %
--------------------------------------------------------------
The first break found is at: 75.000000
The next break found is at: 44.000000
The next break found is at: 93.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 3.0000000
********************************************************
Output from the repartition procedure for the 10.000000 % significance level
----------------------------------------
The updated break dates are :
20.000000
44.000000
75.000000
93.000000
********************************************************
Output from the repartition procedure for the 5.0000000 % significance level
----------------------------------------
The updated break dates are :
20.000000
44.000000
75.000000
93.000000
********************************************************
Output from the repartition procedure for the 2.5000000 % significance level
----------------------------------------
The updated break dates are :
20.000000
44.000000
75.000000
93.000000
********************************************************
Output from the repartition procedure for the 1.0000000 % significance level
----------------------------------------
The updated break dates are :
44.000000
75.000000
93.000000
********************************************************
Output from the estimation of the model selected by BIC
--------------------------------------------------------------
Valid cases: 125 Dependent variable: Y
Missing cases: 0 Deletion method: None
Total SS: 8819.546 Degrees of freedom: 117
R-squared: 1.000 Rbar-squared: 1.000
Residual SS: 0.706 Std error of est: 0.078
F(8,117): 182757.654 Probability of F: 0.000
Durbin-Watson: 0.429

Standard Prob Standardized Cor with
Variable Estimate Error t-value >|t| Estimate Dep Var
-------------------------------------------------------------------------------
X1 7.508771 0.023822 315.207428 0.000 0.530362 0.553889
X2 0.014804 0.000922 16.055878 0.000 0.027015 0.488895
X3 7.171995 0.094607 75.808677 0.000 0.425204 0.478323
X4 0.014933 0.001560 9.575050 0.000 0.053706 0.474263
X5 1.703140 0.298710 5.701650 0.000 0.076942 0.376512
X6 0.078474 0.003528 22.240900 0.000 0.300134 0.376931
X7 6.343478 0.163400 38.821658 0.000 0.382102 0.567232
X8 0.028068 0.001487 18.876017 0.000 0.185787 0.566538
--------------------------------------------------------------
Corrected standard errors for the coefficients
--------------------------------------------------------------
The corrected standard error for coefficient 1.0000000 is: 0.0064077694
The corrected standard error for coefficient 2.0000000 is: 0.00024801688
The corrected standard error for coefficient 3.0000000 is: 0.13327645
The corrected standard error for coefficient 4.0000000 is: 0.0021969972
The corrected standard error for coefficient 5.0000000 is: 0.41970721
The corrected standard error for coefficient 6.0000000 is: 0.0049576136
The corrected standard error for coefficient 7.0000000 is: 0.11825097
The corrected standard error for coefficient 8.0000000 is: 0.0010760988
the procedure to get critical values for the break dates has
reached the upper bound on the number of iterations. This may
be due to incorrect specifications of the upper or lower bound
in the procedure cvg. The resulting confidence interval for this
break date is incorrect.
--------------------------------------------------------------
Confidence intervals for the break dates
--------------------------------------------------------------
The 95% C.I. for the 1.0000000 th break is: 42.000000 45.000000
The 90% C.I. for the 1.0000000 th break is: 42.000000 44.000000
The 95% C.I. for the 2.0000000 th break is: 74.000000 76.000000
The 90% C.I. for the 2.0000000 th break is: 73.000000 76.000000
The 95% C.I. for the 3.0000000 th break is: 91.000000 99.000000
The 90% C.I. for the 3.0000000 th break is: 91.000000 99.000000
********************************************************
K_BIC 3.0000000
The options chosen are:
h = 18.000000
eps1 = 0.15000000
hetdat = 1.0000000
hetvar = 1.0000000
hetomega = 1.0000000
hetq = 1.0000000
robust = 0.00000000 (prewhit = 0.00000000 )
The maximum number of breaks is: 5.0000000
********************************************************
Output from the global optimization
********************************************************
The model with 1.0000000 breaks has SSR : 0.53363558
The dates of the breaks are: 71.000000
The model with 2.0000000 breaks has SSR : 0.37893724
The dates of the breaks are:
71.000000
102.00000
The model with 3.0000000 breaks has SSR : 0.31026029
The dates of the breaks are:
44.000000
71.000000
102.00000
The model with 4.0000000 breaks has SSR : 0.21932138
The dates of the breaks are:
34.000000
52.000000
72.000000
102.00000
The model with 5.0000000 breaks has SSR : 0.20784146
The dates of the breaks are:
34.000000
52.000000
71.000000
89.000000
107.00000
********************************************************
Output from the testing procedures
********************************************************
a) supF tests against a fixed number of breaks
--------------------------------------------------------------
The supF test for 0 versus 1.0000000 breaks (scaled by q) is: 1040.4535
The supF test for 0 versus 2.0000000 breaks (scaled by q) is: 1467.4134
The supF test for 0 versus 3.0000000 breaks (scaled by q) is: 1558.9623
The supF test for 0 versus 4.0000000 breaks (scaled by q) is: 1323.4419
The supF test for 0 versus 5.0000000 breaks (scaled by q) is: 1084.4169
-------------------------
The critical values at the 10.000000 % level are (for k=1 to 5.0000000 ):
9.8100000 8.6300000 7.5400000 6.5100000 5.2700000
The critical values at the 5.0000000 % level are (for k=1 to 5.0000000 ):
11.470000 9.7500000 8.3600000 7.1900000 5.8500000
The critical values at the 2.5000000 % level are (for k=1 to 5.0000000 ):
12.960000 10.750000 9.1500000 7.8100000 6.3800000
The critical values at the 1.0000000 % level are (for k=1 to 5.0000000 ):
15.370000 12.150000 10.270000 8.6500000 7.0000000
--------------------------------------------------------------
b) Dmax tests against an unknown number of breaks
--------------------------------------------------------------
The UDmax test is: 1558.9623
(the critical value at the 10.000000 % level is: 10.160000 )
(the critical value at the 5.0000000 % level is: 11.700000 )
(the critical value at the 2.5000000 % level is: 13.180000 )
(the critical value at the 1.0000000 % level is: 15.410000 )
********************************************************
---------------------
The WDmax test at the 10.000000 % level is: 2028.3050
(The critical value is: 11.150000 )
---------------------
The WDmax test at the 5.0000000 % level is: 2138.9112
(The critical value is: 12.810000 )
---------------------
The WDmax test at the 2.5000000 % level is: 2208.1039
(The critical value is: 14.580000 )
---------------------
The WDmax test at the 1.0000000 % level is: 2381.0698
(The critical value is: 17.010000 )
********************************************************
supF(l+1|l) tests using global otimizers under the null
--------------------------------------------------------------
The supF( 2.0000000 | 1.0000000 ) test is : 329.70606
It corresponds to a new break at: 102.00000
The supF( 3.0000000 | 2.0000000 ) test is : 21.050279
It corresponds to a new break at: 44.000000
The supF( 4.0000000 | 3.0000000 ) test is : 9.3491507
It corresponds to a new break at: 19.000000
Given the location of the breaks from the global optimization
with 4.0000000 breaks there was no more place to insert
an additional breaks that satisfy the minimal length requirement.
The supF( 5.0000000 | 4.0000000 ) test is : 0.00000000
It corresponds to a new break at: 0.00000000
********************************************************
The critical values of supF(i+1|i) at the 10.000000 % level are (for i=1 to 5.0000000 ) are:
9.8100000 11.400000 12.290000 12.900000 13.470000
The critical values of supF(i+1|i) at the 5.0000000 % level are (for i=1 to 5.0000000 ) are:
11.470000 12.950000 14.030000 14.850000 15.290000
The critical values of supF(i+1|i) at the 2.5000000 % level are (for i=1 to 5.0000000 ) are:
12.960000 14.920000 15.810000 16.510000 16.840000
The critical values of supF(i+1|i) at the 1.0000000 % level are (for i=1 to 5.0000000 ) are:
15.370000 16.840000 17.720000 18.670000 19.170000
********************************************************
Output from the application of Information criteria
--------------------------------------------------------------
Values of BIC and lwz with 0.00000000 breaks: -3.2506618 -3.2345324
Values of BIC and lwz with 1.0000000 breaks: -5.3404763 -5.2197157
Values of BIC and lwz with 2.0000000 breaks: -5.5669394 -5.3409223
Values of BIC and lwz with 3.0000000 breaks: -5.6510188 -5.3190877
Values of BIC and lwz with 4.0000000 breaks: -5.8820128 -5.4434748
Values of BIC and lwz with 5.0000000 breaks: -5.8198958 -5.2740202
The number of breaks chosen by BIC is : 4.0000000
The number of breaks chosen by LWZ is : 4.0000000
********************************************************
Output from the sequential procedure at significance level 10.000000 %
--------------------------------------------------------------
The first break found is at: 71.000000
The next break found is at: 102.00000
The next break found is at: 44.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 3.0000000
********************************************************
Output from the sequential procedure at significance level 5.0000000 %
--------------------------------------------------------------
The first break found is at: 71.000000
The next break found is at: 102.00000
The next break found is at: 44.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 3.0000000
********************************************************
Output from the sequential procedure at significance level 2.5000000 %
--------------------------------------------------------------
The first break found is at: 71.000000
The next break found is at: 102.00000
The next break found is at: 44.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 3.0000000
********************************************************
Output from the sequential procedure at significance level 1.0000000 %
--------------------------------------------------------------
The first break found is at: 71.000000
The next break found is at: 102.00000
The next break found is at: 44.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 3.0000000
********************************************************
Output from the repartition procedure for the 10.000000 % significance level
----------------------------------------
The updated break dates are :
44.000000
71.000000
102.00000
********************************************************
Output from the repartition procedure for the 5.0000000 % significance level
----------------------------------------
The updated break dates are :
44.000000
71.000000
102.00000
********************************************************
Output from the repartition procedure for the 2.5000000 % significance level
----------------------------------------
The updated break dates are :
44.000000
71.000000
102.00000
********************************************************
Output from the repartition procedure for the 1.0000000 % significance level
----------------------------------------
The updated break dates are :
44.000000
71.000000
102.00000
********************************************************
Output from the estimation of the model selected by BIC
--------------------------------------------------------------
Valid cases: 125 Dependent variable: Y
Missing cases: 0 Deletion method: None
Total SS: 9264.503 Degrees of freedom: 115
R-squared: 1.000 Rbar-squared: 1.000
Residual SS: 0.219 Std error of est: 0.044
F(10,115): 485767.802 Probability of F: 0.000
Durbin-Watson: 1.085

Standard Prob Standardized Cor with
Variable Estimate Error t-value >|t| Estimate Dep Var
-------------------------------------------------------------------------------
X01 7.878472 0.015316 514.407512 0.000 0.477277 0.488108
X02 0.010217 0.000763 13.383080 0.000 0.012417 0.428735
X03 8.474288 0.086916 97.499455 0.000 0.373532 0.363071
X04 -0.005456 0.001984 -2.750101 0.007 -0.010536 0.360368
X05 8.390559 0.106292 78.938632 0.000 0.389848 0.392580
X06 0.000941 0.001693 0.555594 0.580 0.002744 0.390943
X07 5.826108 0.080996 71.930703 0.000 0.331534 0.498091
X08 0.033451 0.000921 36.313039 0.000 0.167370 0.497293
X09 7.451628 0.156762 47.534736 0.000 0.371282 0.476808
X10 0.018578 0.001373 13.533167 0.000 0.105704 0.476359
--------------------------------------------------------------
Corrected standard errors for the coefficients
--------------------------------------------------------------
The corrected standard error for coefficient 1.0000000 is: 0.0041128239
The corrected standard error for coefficient 2.0000000 is: 0.00020500156
The corrected standard error for coefficient 3.0000000 is: 0.17046312
The corrected standard error for coefficient 4.0000000 is: 0.0038911153
The corrected standard error for coefficient 5.0000000 is: 0.11306238
The corrected standard error for coefficient 6.0000000 is: 0.0018013478
The corrected standard error for coefficient 7.0000000 is: 0.059593573
The corrected standard error for coefficient 8.0000000 is: 0.00067776152
The corrected standard error for coefficient 9.0000000 is: 0.068900370
The corrected standard error for coefficient 10.000000 is: 0.00060336868
the procedure to get critical values for the break dates has
reached the upper bound on the number of iterations. This may
be due to incorrect specifications of the upper or lower bound
in the procedure cvg. The resulting confidence interval for this
break date is incorrect.
--------------------------------------------------------------
Confidence intervals for the break dates
--------------------------------------------------------------
The 95% C.I. for the 1.0000000 th break is: 33.000000 34.000000
The 90% C.I. for the 1.0000000 th break is: 33.000000 34.000000
The 95% C.I. for the 2.0000000 th break is: 50.000000 71.000000
The 90% C.I. for the 2.0000000 th break is: 50.000000 71.000000
The 95% C.I. for the 3.0000000 th break is: 70.000000 73.000000
The 90% C.I. for the 3.0000000 th break is: 70.000000 73.000000
The 95% C.I. for the 4.0000000 th break is: 100.00000 103.00000
The 90% C.I. for the 4.0000000 th break is: 100.00000 103.00000
********************************************************
K_BIC 2.0000000
The options chosen are:
h = 18.000000
eps1 = 0.15000000
hetdat = 1.0000000
hetvar = 1.0000000
hetomega = 1.0000000
hetq = 1.0000000
robust = 0.00000000 (prewhit = 0.00000000 )
The maximum number of breaks is: 5.0000000
********************************************************
Output from the global optimization
********************************************************
The model with 1.0000000 breaks has SSR : 1.1704814
The dates of the breaks are: 50.000000
The model with 2.0000000 breaks has SSR : 0.77327840
The dates of the breaks are:
35.000000
70.000000
The model with 3.0000000 breaks has SSR : 0.64727247
The dates of the breaks are:
30.000000
49.000000
70.000000
The model with 4.0000000 breaks has SSR : 0.55969522
The dates of the breaks are:
30.000000
49.000000
70.000000
103.00000
The model with 5.0000000 breaks has SSR : 0.52299861
The dates of the breaks are:
25.000000
43.000000
61.000000
79.000000
103.00000
********************************************************
Output from the testing procedures
********************************************************
a) supF tests against a fixed number of breaks
--------------------------------------------------------------
The supF test for 0 versus 1.0000000 breaks (scaled by q) is: 113.49376
The supF test for 0 versus 2.0000000 breaks (scaled by q) is: 85.344180
The supF test for 0 versus 3.0000000 breaks (scaled by q) is: 79.723717
The supF test for 0 versus 4.0000000 breaks (scaled by q) is: 75.202418
The supF test for 0 versus 5.0000000 breaks (scaled by q) is: 83.472404
-------------------------
The critical values at the 10.000000 % level are (for k=1 to 5.0000000 ):
9.8100000 8.6300000 7.5400000 6.5100000 5.2700000
The critical values at the 5.0000000 % level are (for k=1 to 5.0000000 ):
11.470000 9.7500000 8.3600000 7.1900000 5.8500000
The critical values at the 2.5000000 % level are (for k=1 to 5.0000000 ):
12.960000 10.750000 9.1500000 7.8100000 6.3800000
The critical values at the 1.0000000 % level are (for k=1 to 5.0000000 ):
15.370000 12.150000 10.270000 8.6500000 7.0000000
--------------------------------------------------------------
b) Dmax tests against an unknown number of breaks
--------------------------------------------------------------
The UDmax test is: 113.49376
(the critical value at the 10.000000 % level is: 10.160000 )
(the critical value at the 5.0000000 % level is: 11.700000 )
(the critical value at the 2.5000000 % level is: 13.180000 )
(the critical value at the 1.0000000 % level is: 15.410000 )
********************************************************
---------------------
The WDmax test at the 10.000000 % level is: 155.38222
(The critical value is: 11.150000 )
---------------------
The WDmax test at the 5.0000000 % level is: 163.66299
(The critical value is: 12.810000 )
---------------------
The WDmax test at the 2.5000000 % level is: 169.56150
(The critical value is: 14.580000 )
---------------------
The WDmax test at the 1.0000000 % level is: 183.28155
(The critical value is: 17.010000 )
********************************************************
supF(l+1|l) tests using global otimizers under the null
--------------------------------------------------------------
The supF( 2.0000000 | 1.0000000 ) test is : 42.130669
It corresponds to a new break at: 31.000000
The supF( 3.0000000 | 2.0000000 ) test is : 36.725708
It corresponds to a new break at: 103.00000
The supF( 4.0000000 | 3.0000000 ) test is : 36.725708
It corresponds to a new break at: 103.00000
Given the location of the breaks from the global optimization
with 4.0000000 breaks there was no more place to insert
an additional breaks that satisfy the minimal length requirement.
The supF( 5.0000000 | 4.0000000 ) test is : 0.00000000
It corresponds to a new break at: 0.00000000
********************************************************
The critical values of supF(i+1|i) at the 10.000000 % level are (for i=1 to 5.0000000 ) are:
9.8100000 11.400000 12.290000 12.900000 13.470000
The critical values of supF(i+1|i) at the 5.0000000 % level are (for i=1 to 5.0000000 ) are:
11.470000 12.950000 14.030000 14.850000 15.290000
The critical values of supF(i+1|i) at the 2.5000000 % level are (for i=1 to 5.0000000 ) are:
12.960000 14.920000 15.810000 16.510000 16.840000
The critical values of supF(i+1|i) at the 1.0000000 % level are (for i=1 to 5.0000000 ) are:
15.370000 16.840000 17.720000 18.670000 19.170000
********************************************************
Output from the application of Information criteria
--------------------------------------------------------------
Values of BIC and lwz with 0.00000000 breaks: -3.9567759 -3.9406465
Values of BIC and lwz with 1.0000000 breaks: -4.5550191 -4.4342584
Values of BIC and lwz with 2.0000000 breaks: -4.8536708 -4.6276538
Values of BIC and lwz with 3.0000000 breaks: -4.9156631 -4.5837319
Values of BIC and lwz with 4.0000000 breaks: -4.9451585 -4.5066205
Values of BIC and lwz with 5.0000000 breaks: -4.8970926 -4.3512169
The number of breaks chosen by BIC is : 4.0000000
The number of breaks chosen by LWZ is : 2.0000000
********************************************************
Output from the sequential procedure at significance level 10.000000 %
--------------------------------------------------------------
The first break found is at: 50.000000
The next break found is at: 31.000000
The next break found is at: 70.000000
The next break found is at: 103.00000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 5.0000000 %
--------------------------------------------------------------
The first break found is at: 50.000000
The next break found is at: 31.000000
The next break found is at: 70.000000
The next break found is at: 103.00000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 2.5000000 %
--------------------------------------------------------------
The first break found is at: 50.000000
The next break found is at: 31.000000
The next break found is at: 70.000000
The next break found is at: 103.00000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 1.0000000 %
--------------------------------------------------------------
The first break found is at: 50.000000
The next break found is at: 31.000000
The next break found is at: 70.000000
The next break found is at: 103.00000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the repartition procedure for the 10.000000 % significance level
----------------------------------------
The updated break dates are :
31.000000
49.000000
70.000000
103.00000
********************************************************
Output from the repartition procedure for the 5.0000000 % significance level
----------------------------------------
The updated break dates are :
31.000000
49.000000
70.000000
103.00000
********************************************************
Output from the repartition procedure for the 2.5000000 % significance level
----------------------------------------
The updated break dates are :
31.000000
49.000000
70.000000
103.00000
********************************************************
Output from the repartition procedure for the 1.0000000 % significance level
----------------------------------------
The updated break dates are :
31.000000
49.000000
70.000000
103.00000
********************************************************
Output from the estimation of the model selected by BIC
--------------------------------------------------------------
Valid cases: 125 Dependent variable: Y
Missing cases: 0 Deletion method: None
Total SS: 9219.440 Degrees of freedom: 115
R-squared: 1.000 Rbar-squared: 1.000
Residual SS: 0.560 Std error of est: 0.070
F(10,115): 189419.384 Probability of F: 0.000
Durbin-Watson: 0.749

Standard Prob Standardized Cor with
Variable Estimate Error t-value >|t| Estimate Dep Var
-------------------------------------------------------------------------------
X01 7.335747 0.026124 280.800052 0.000 0.418459 0.432598
X02 0.015992 0.001472 10.867164 0.000 0.016195 0.381549
X03 7.243503 0.117973 61.399580 0.000 0.328831 0.372371
X04 0.023977 0.002922 8.205593 0.000 0.043946 0.369737
X05 8.004250 0.151612 52.794339 0.000 0.382013 0.395303
X06 0.004641 0.002514 1.846098 0.067 0.013358 0.393440
X07 7.006036 0.111622 62.765553 0.000 0.419157 0.539763
X08 0.023171 0.001275 18.167659 0.000 0.121326 0.537995
X09 7.881185 0.268846 29.314857 0.000 0.384991 0.475636
X10 0.016206 0.002344 6.912673 0.000 0.090784 0.475185
--------------------------------------------------------------
Corrected standard errors for the coefficients
--------------------------------------------------------------
The corrected standard error for coefficient 1.0000000 is: 0.019736363
The corrected standard error for coefficient 2.0000000 is: 0.0011117240
The corrected standard error for coefficient 3.0000000 is: 0.078214284
The corrected standard error for coefficient 4.0000000 is: 0.0019372795
The corrected standard error for coefficient 5.0000000 is: 0.25854228
The corrected standard error for coefficient 6.0000000 is: 0.0042872600
The corrected standard error for coefficient 7.0000000 is: 0.084382087
The corrected standard error for coefficient 8.0000000 is: 0.00096415160
The corrected standard error for coefficient 9.0000000 is: 0.17758739
The corrected standard error for coefficient 10.000000 is: 0.0015486062
--------------------------------------------------------------
Confidence intervals for the break dates
--------------------------------------------------------------
The 95% C.I. for the 1.0000000 th break is: -20.000000 36.000000
The 90% C.I. for the 1.0000000 th break is: -20.000000 34.000000
The 95% C.I. for the 2.0000000 th break is: 29.000000 51.000000
The 90% C.I. for the 2.0000000 th break is: 29.000000 50.000000
The 95% C.I. for the 3.0000000 th break is: 13.000000 126.00000
The 90% C.I. for the 3.0000000 th break is: 13.000000 126.00000
The 95% C.I. for the 4.0000000 th break is: 99.000000 104.00000
The 90% C.I. for the 4.0000000 th break is: 100.00000 104.00000
********************************************************
K_BIC 4.0000000
The options chosen are:
h = 18.000000
eps1 = 0.15000000
hetdat = 1.0000000
hetvar = 1.0000000
hetomega = 1.0000000
hetq = 1.0000000
robust = 0.00000000 (prewhit = 0.00000000 )
The maximum number of breaks is: 5.0000000
********************************************************
Output from the global optimization
********************************************************
The model with 1.0000000 breaks has SSR : 0.36518109
The dates of the breaks are: 70.000000
The model with 2.0000000 breaks has SSR : 0.18912283
The dates of the breaks are:
70.000000
104.00000
The model with 3.0000000 breaks has SSR : 0.14214378
The dates of the breaks are:
47.000000
70.000000
104.00000
The model with 4.0000000 breaks has SSR : 0.10125656
The dates of the breaks are:
20.000000
45.000000
70.000000
104.00000
The model with 5.0000000 breaks has SSR : 0.10835791
The dates of the breaks are:
20.000000
45.000000
70.000000
89.000000
107.00000
********************************************************
Output from the testing procedures
********************************************************
a) supF tests against a fixed number of breaks
--------------------------------------------------------------
The supF test for 0 versus 1.0000000 breaks (scaled by q) is: 336.93363
The supF test for 0 versus 2.0000000 breaks (scaled by q) is: 553.41306
The supF test for 0 versus 3.0000000 breaks (scaled by q) is: 408.49751
The supF test for 0 versus 4.0000000 breaks (scaled by q) is: 414.98685
The supF test for 0 versus 5.0000000 breaks (scaled by q) is: 271.50660
-------------------------
The critical values at the 10.000000 % level are (for k=1 to 5.0000000 ):
9.8100000 8.6300000 7.5400000 6.5100000 5.2700000
The critical values at the 5.0000000 % level are (for k=1 to 5.0000000 ):
11.470000 9.7500000 8.3600000 7.1900000 5.8500000
The critical values at the 2.5000000 % level are (for k=1 to 5.0000000 ):
12.960000 10.750000 9.1500000 7.8100000 6.3800000
The critical values at the 1.0000000 % level are (for k=1 to 5.0000000 ):
15.370000 12.150000 10.270000 8.6500000 7.0000000
--------------------------------------------------------------
b) Dmax tests against an unknown number of breaks
--------------------------------------------------------------
The UDmax test is: 553.41306
(the critical value at the 10.000000 % level is: 10.160000 )
(the critical value at the 5.0000000 % level is: 11.700000 )
(the critical value at the 2.5000000 % level is: 13.180000 )
(the critical value at the 1.0000000 % level is: 15.410000 )
********************************************************
---------------------
The WDmax test at the 10.000000 % level is: 629.08252
(The critical value is: 11.150000 )
---------------------
The WDmax test at the 5.0000000 % level is: 662.01658
(The critical value is: 12.810000 )
---------------------
The WDmax test at the 2.5000000 % level is: 688.63375
(The critical value is: 14.580000 )
---------------------
The WDmax test at the 1.0000000 % level is: 737.38126
(The critical value is: 17.010000 )
********************************************************
supF(l+1|l) tests using global otimizers under the null
--------------------------------------------------------------
The supF( 2.0000000 | 1.0000000 ) test is : 201.92493
It corresponds to a new break at: 104.00000
The supF( 3.0000000 | 2.0000000 ) test is : 31.530636
It corresponds to a new break at: 47.000000
The supF( 4.0000000 | 3.0000000 ) test is : 129.66441
It corresponds to a new break at: 20.000000
Given the location of the breaks from the global optimization
with 4.0000000 breaks there was no more place to insert
an additional breaks that satisfy the minimal length requirement.
The supF( 5.0000000 | 4.0000000 ) test is : 0.00000000
It corresponds to a new break at: 0.00000000
********************************************************
The critical values of supF(i+1|i) at the 10.000000 % level are (for i=1 to 5.0000000 ) are:
9.8100000 11.400000 12.290000 12.900000 13.470000
The critical values of supF(i+1|i) at the 5.0000000 % level are (for i=1 to 5.0000000 ) are:
11.470000 12.950000 14.030000 14.850000 15.290000
The critical values of supF(i+1|i) at the 2.5000000 % level are (for i=1 to 5.0000000 ) are:
12.960000 14.920000 15.810000 16.510000 16.840000
The critical values of supF(i+1|i) at the 1.0000000 % level are (for i=1 to 5.0000000 ) are:
15.370000 16.840000 17.720000 18.670000 19.170000
********************************************************
Output from the application of Information criteria
--------------------------------------------------------------
Values of BIC and lwz with 0.00000000 breaks: -4.3623991 -4.3462697
Values of BIC and lwz with 1.0000000 breaks: -5.7197961 -5.5990355
Values of BIC and lwz with 2.0000000 breaks: -6.2619133 -6.0358962
Values of BIC and lwz with 3.0000000 breaks: -6.4315914 -6.0996602
Values of BIC and lwz with 4.0000000 breaks: -6.6548934 -6.2163554
Values of BIC and lwz with 5.0000000 breaks: -6.4712316 -5.9253560
The number of breaks chosen by BIC is : 4.0000000
The number of breaks chosen by LWZ is : 4.0000000
********************************************************
Output from the sequential procedure at significance level 10.000000 %
--------------------------------------------------------------
The first break found is at: 70.000000
The next break found is at: 104.00000
The next break found is at: 47.000000
The next break found is at: 20.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 5.0000000 %
--------------------------------------------------------------
The first break found is at: 70.000000
The next break found is at: 104.00000
The next break found is at: 47.000000
The next break found is at: 20.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 2.5000000 %
--------------------------------------------------------------
The first break found is at: 70.000000
The next break found is at: 104.00000
The next break found is at: 47.000000
The next break found is at: 20.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 1.0000000 %
--------------------------------------------------------------
The first break found is at: 70.000000
The next break found is at: 104.00000
The next break found is at: 47.000000
The next break found is at: 20.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the repartition procedure for the 10.000000 % significance level
----------------------------------------
The updated break dates are :
20.000000
45.000000
70.000000
104.00000
********************************************************
Output from the repartition procedure for the 5.0000000 % significance level
----------------------------------------
The updated break dates are :
20.000000
45.000000
70.000000
104.00000
********************************************************
Output from the repartition procedure for the 2.5000000 % significance level
----------------------------------------
The updated break dates are :
20.000000
45.000000
70.000000
104.00000
********************************************************
Output from the repartition procedure for the 1.0000000 % significance level
----------------------------------------
The updated break dates are :
20.000000
45.000000
70.000000
104.00000
********************************************************
Output from the estimation of the model selected by BIC
--------------------------------------------------------------
Valid cases: 125 Dependent variable: Y
Missing cases: 0 Deletion method: None
Total SS: 9245.673 Degrees of freedom: 115
R-squared: 1.000 Rbar-squared: 1.000
Residual SS: 0.101 Std error of est: 0.030
F(10,115): 1050046.356 Probability of F: 0.000
Durbin-Watson: 1.413

Standard Prob Standardized Cor with
Variable Estimate Error t-value >|t| Estimate Dep Var
-------------------------------------------------------------------------------
X01 7.547951 0.013784 547.584703 0.000 0.351055 0.355814
X02 0.009745 0.001151 8.468763 0.000 0.005429 0.313137
X03 7.359885 0.027799 264.750772 0.000 0.382712 0.417096
X04 0.020038 0.000823 24.347705 0.000 0.035196 0.409085
X05 7.157587 0.048101 148.804730 0.000 0.372192 0.437314
X06 0.021592 0.000823 26.236619 0.000 0.065623 0.434972
X07 6.045173 0.045671 132.362515 0.000 0.366589 0.543024
X08 0.033251 0.000519 64.103777 0.000 0.177541 0.541846
X09 7.477966 0.123145 60.724944 0.000 0.356389 0.461245
X10 0.019132 0.001069 17.891272 0.000 0.105002 0.460898
--------------------------------------------------------------
Corrected standard errors for the coefficients
--------------------------------------------------------------
The corrected standard error for coefficient 1.0000000 is: 0.0071896391
The corrected standard error for coefficient 2.0000000 is: 0.00060017948
The corrected standard error for coefficient 3.0000000 is: 0.0097591627
The corrected standard error for coefficient 4.0000000 is: 0.00028891477
The corrected standard error for coefficient 5.0000000 is: 0.064719671
The corrected standard error for coefficient 6.0000000 is: 0.0011073308
The corrected standard error for coefficient 7.0000000 is: 0.056387605
The corrected standard error for coefficient 8.0000000 is: 0.00064041686
The corrected standard error for coefficient 9.0000000 is: 0.082348483
The corrected standard error for coefficient 10.000000 is: 0.00071508315
--------------------------------------------------------------
Confidence intervals for the break dates
--------------------------------------------------------------
The 95% C.I. for the 1.0000000 th break is: 18.000000 21.000000
The 90% C.I. for the 1.0000000 th break is: 18.000000 21.000000
The 95% C.I. for the 2.0000000 th break is: 43.000000 46.000000
The 90% C.I. for the 2.0000000 th break is: 43.000000 46.000000
The 95% C.I. for the 3.0000000 th break is: 68.000000 71.000000
The 90% C.I. for the 3.0000000 th break is: 68.000000 71.000000
The 95% C.I. for the 4.0000000 th break is: 102.00000 107.00000
The 90% C.I. for the 4.0000000 th break is: 102.00000 107.00000
********************************************************
K_BIC 5.0000000
The options chosen are:
h = 18.000000
eps1 = 0.15000000
hetdat = 1.0000000
hetvar = 1.0000000
hetomega = 1.0000000
hetq = 1.0000000
robust = 0.00000000 (prewhit = 0.00000000 )
The maximum number of breaks is: 5.0000000
********************************************************
Output from the global optimization
********************************************************
The model with 1.0000000 breaks has SSR : 0.68939411
The dates of the breaks are: 47.000000
The model with 2.0000000 breaks has SSR : 0.51064299
The dates of the breaks are:
47.000000
100.00000
The model with 3.0000000 breaks has SSR : 0.36330598
The dates of the breaks are:
47.000000
70.000000
102.00000
The model with 4.0000000 breaks has SSR : 0.29248732
The dates of the breaks are:
25.000000
47.000000
70.000000
102.00000
The model with 5.0000000 breaks has SSR : 0.27818963
The dates of the breaks are:
25.000000
47.000000
70.000000
88.000000
106.00000
********************************************************
Output from the testing procedures
********************************************************
a) supF tests against a fixed number of breaks
--------------------------------------------------------------
The supF test for 0 versus 1.0000000 breaks (scaled by q) is: 678.76144
The supF test for 0 versus 2.0000000 breaks (scaled by q) is: 461.25021
The supF test for 0 versus 3.0000000 breaks (scaled by q) is: 454.91678
The supF test for 0 versus 4.0000000 breaks (scaled by q) is: 421.92046
The supF test for 0 versus 5.0000000 breaks (scaled by q) is: 416.05735
-------------------------
The critical values at the 10.000000 % level are (for k=1 to 5.0000000 ):
9.8100000 8.6300000 7.5400000 6.5100000 5.2700000
The critical values at the 5.0000000 % level are (for k=1 to 5.0000000 ):
11.470000 9.7500000 8.3600000 7.1900000 5.8500000
The critical values at the 2.5000000 % level are (for k=1 to 5.0000000 ):
12.960000 10.750000 9.1500000 7.8100000 6.3800000
The critical values at the 1.0000000 % level are (for k=1 to 5.0000000 ):
15.370000 12.150000 10.270000 8.6500000 7.0000000
--------------------------------------------------------------
b) Dmax tests against an unknown number of breaks
--------------------------------------------------------------
The UDmax test is: 678.76144
(the critical value at the 10.000000 % level is: 10.160000 )
(the critical value at the 5.0000000 % level is: 11.700000 )
(the critical value at the 2.5000000 % level is: 13.180000 )
(the critical value at the 1.0000000 % level is: 15.410000 )
********************************************************
---------------------
The WDmax test at the 10.000000 % level is: 774.48246
(The critical value is: 11.150000 )
---------------------
The WDmax test at the 5.0000000 % level is: 815.75688
(The critical value is: 12.810000 )
---------------------
The WDmax test at the 2.5000000 % level is: 845.15724
(The critical value is: 14.580000 )
---------------------
The WDmax test at the 1.0000000 % level is: 913.54306
(The critical value is: 17.010000 )
********************************************************
supF(l+1|l) tests using global otimizers under the null
--------------------------------------------------------------
The supF( 2.0000000 | 1.0000000 ) test is : 52.859345
It corresponds to a new break at: 25.000000
The supF( 3.0000000 | 2.0000000 ) test is : 61.331431
It corresponds to a new break at: 70.000000
The supF( 4.0000000 | 3.0000000 ) test is : 52.859345
It corresponds to a new break at: 25.000000
Given the location of the breaks from the global optimization
with 4.0000000 breaks there was no more place to insert
an additional breaks that satisfy the minimal length requirement.
The supF( 5.0000000 | 4.0000000 ) test is : 0.00000000
It corresponds to a new break at: 0.00000000
********************************************************
The critical values of supF(i+1|i) at the 10.000000 % level are (for i=1 to 5.0000000 ) are:
9.8100000 11.400000 12.290000 12.900000 13.470000
The critical values of supF(i+1|i) at the 5.0000000 % level are (for i=1 to 5.0000000 ) are:
11.470000 12.950000 14.030000 14.850000 15.290000
The critical values of supF(i+1|i) at the 2.5000000 % level are (for i=1 to 5.0000000 ) are:
12.960000 14.920000 15.810000 16.510000 16.840000
The critical values of supF(i+1|i) at the 1.0000000 % level are (for i=1 to 5.0000000 ) are:
15.370000 16.840000 17.720000 18.670000 19.170000
********************************************************
Output from the application of Information criteria
--------------------------------------------------------------
Values of BIC and lwz with 0.00000000 breaks: -3.3313585 -3.3152291
Values of BIC and lwz with 1.0000000 breaks: -5.0843764 -4.9636158
Values of BIC and lwz with 2.0000000 breaks: -5.2686393 -5.0426222
Values of BIC and lwz with 3.0000000 breaks: -5.4931850 -5.1612539
Values of BIC and lwz with 4.0000000 breaks: -5.5941296 -5.1555916
Values of BIC and lwz with 5.0000000 breaks: -5.5283684 -4.9824928
The number of breaks chosen by BIC is : 4.0000000
The number of breaks chosen by LWZ is : 3.0000000
********************************************************
Output from the sequential procedure at significance level 10.000000 %
--------------------------------------------------------------
The first break found is at: 47.000000
The next break found is at: 25.000000
The next break found is at: 100.00000
The next break found is at: 70.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 5.0000000 %
--------------------------------------------------------------
The first break found is at: 47.000000
The next break found is at: 25.000000
The next break found is at: 100.00000
The next break found is at: 70.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 2.5000000 %
--------------------------------------------------------------
The first break found is at: 47.000000
The next break found is at: 25.000000
The next break found is at: 100.00000
The next break found is at: 70.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 1.0000000 %
--------------------------------------------------------------
The first break found is at: 47.000000
The next break found is at: 25.000000
The next break found is at: 100.00000
The next break found is at: 70.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the repartition procedure for the 10.000000 % significance level
----------------------------------------
The updated break dates are :
25.000000
47.000000
70.000000
102.00000
********************************************************
Output from the repartition procedure for the 5.0000000 % significance level
----------------------------------------
The updated break dates are :
25.000000
47.000000
70.000000
102.00000
********************************************************
Output from the repartition procedure for the 2.5000000 % significance level
----------------------------------------
The updated break dates are :
25.000000
47.000000
70.000000
102.00000
********************************************************
Output from the repartition procedure for the 1.0000000 % significance level
----------------------------------------
The updated break dates are :
25.000000
47.000000
70.000000
102.00000
********************************************************
Output from the estimation of the model selected by BIC
--------------------------------------------------------------
Valid cases: 125 Dependent variable: Y
Missing cases: 0 Deletion method: None
Total SS: 8281.676 Degrees of freedom: 115
R-squared: 1.000 Rbar-squared: 1.000
Residual SS: 0.292 Std error of est: 0.050
F(10,115): 325606.966 Probability of F: 0.000
Durbin-Watson: 0.785

Standard Prob Standardized Cor with
Variable Estimate Error t-value >|t| Estimate Dep Var
-------------------------------------------------------------------------------
X01 6.993631 0.020794 336.336217 0.000 0.384250 0.389471
X02 0.007310 0.001399 5.226250 0.000 0.005971 0.341987
X03 6.969109 0.062787 110.996873 0.000 0.359194 0.383968
X04 0.013169 0.001695 7.770346 0.000 0.025145 0.379034
X05 5.603146 0.094123 59.530299 0.000 0.295282 0.409437
X06 0.036715 0.001585 23.159312 0.000 0.114875 0.408308
X07 5.431183 0.083996 64.660012 0.000 0.337606 0.531533
X08 0.036067 0.000966 37.352764 0.000 0.195028 0.530727
X09 7.167445 0.181031 39.592346 0.000 0.377719 0.500009
X10 0.020355 0.001585 12.839996 0.000 0.122496 0.499578
--------------------------------------------------------------
Corrected standard errors for the coefficients
--------------------------------------------------------------
The corrected standard error for coefficient 1.0000000 is: 0.014442698
The corrected standard error for coefficient 2.0000000 is: 0.00097152103
The corrected standard error for coefficient 3.0000000 is: 0.043398896
The corrected standard error for coefficient 4.0000000 is: 0.0011714466
The corrected standard error for coefficient 5.0000000 is: 0.13233360
The corrected standard error for coefficient 6.0000000 is: 0.0022288999
The corrected standard error for coefficient 7.0000000 is: 0.061050770
The corrected standard error for coefficient 8.0000000 is: 0.00070180253
The corrected standard error for coefficient 9.0000000 is: 0.20695093
The corrected standard error for coefficient 10.000000 is: 0.0018122938
the procedure to get critical values for the break dates has
reached the upper bound on the number of iterations. This may
be due to incorrect specifications of the upper or lower bound
in the procedure cvg. The resulting confidence interval for this
break date is incorrect.
the procedure to get critical values for the break dates has
reached the upper bound on the number of iterations. This may
be due to incorrect specifications of the upper or lower bound
in the procedure cvg. The resulting confidence interval for this
break date is incorrect.
--------------------------------------------------------------
Confidence intervals for the break dates
--------------------------------------------------------------
The 95% C.I. for the 1.0000000 th break is: -4.0000000 29.000000
The 90% C.I. for the 1.0000000 th break is: -4.0000000 28.000000
The 95% C.I. for the 2.0000000 th break is: 46.000000 48.000000
The 90% C.I. for the 2.0000000 th break is: 46.000000 48.000000
The 95% C.I. for the 3.0000000 th break is: 68.000000 82.000000
The 90% C.I. for the 3.0000000 th break is: 68.000000 82.000000
The 95% C.I. for the 4.0000000 th break is: 101.00000 103.00000
The 90% C.I. for the 4.0000000 th break is: 101.00000 103.00000
********************************************************
K_BIC 1.0000000
The options chosen are:
h = 18.000000
eps1 = 0.15000000
hetdat = 1.0000000
hetvar = 1.0000000
hetomega = 1.0000000
hetq = 1.0000000
robust = 0.00000000 (prewhit = 0.00000000 )
The maximum number of breaks is: 5.0000000
********************************************************
Output from the global optimization
********************************************************
The model with 1.0000000 breaks has SSR : 1.6266042
The dates of the breaks are: 71.000000
The model with 2.0000000 breaks has SSR : 0.80609932
The dates of the breaks are:
71.000000
100.00000
The model with 3.0000000 breaks has SSR : 0.67908091
The dates of the breaks are:
58.000000
76.000000
104.00000
The model with 4.0000000 breaks has SSR : 0.60256209
The dates of the breaks are:
53.000000
71.000000
89.000000
107.00000
The model with 5.0000000 breaks has SSR : 0.55489020
The dates of the breaks are:
34.000000
52.000000
71.000000
89.000000
107.00000
********************************************************
Output from the testing procedures
********************************************************
a) supF tests against a fixed number of breaks
--------------------------------------------------------------
The supF test for 0 versus 1.0000000 breaks (scaled by q) is: 307.76471
The supF test for 0 versus 2.0000000 breaks (scaled by q) is: 397.74650
The supF test for 0 versus 3.0000000 breaks (scaled by q) is: 783.19122
The supF test for 0 versus 4.0000000 breaks (scaled by q) is: 350.38207
The supF test for 0 versus 5.0000000 breaks (scaled by q) is: 319.85838
-------------------------
The critical values at the 10.000000 % level are (for k=1 to 5.0000000 ):
9.8100000 8.6300000 7.5400000 6.5100000 5.2700000
The critical values at the 5.0000000 % level are (for k=1 to 5.0000000 ):
11.470000 9.7500000 8.3600000 7.1900000 5.8500000
The critical values at the 2.5000000 % level are (for k=1 to 5.0000000 ):
12.960000 10.750000 9.1500000 7.8100000 6.3800000
The critical values at the 1.0000000 % level are (for k=1 to 5.0000000 ):
15.370000 12.150000 10.270000 8.6500000 7.0000000
--------------------------------------------------------------
b) Dmax tests against an unknown number of breaks
--------------------------------------------------------------
The UDmax test is: 783.19122
(the critical value at the 10.000000 % level is: 10.160000 )
(the critical value at the 5.0000000 % level is: 11.700000 )
(the critical value at the 2.5000000 % level is: 13.180000 )
(the critical value at the 1.0000000 % level is: 15.410000 )
********************************************************
---------------------
The WDmax test at the 10.000000 % level is: 1018.9796
(The critical value is: 11.150000 )
---------------------
The WDmax test at the 5.0000000 % level is: 1074.5458
(The critical value is: 12.810000 )
---------------------
The WDmax test at the 2.5000000 % level is: 1109.3069
(The critical value is: 14.580000 )
---------------------
The WDmax test at the 1.0000000 % level is: 1172.1177
(The critical value is: 17.010000 )
********************************************************
supF(l+1|l) tests using global otimizers under the null
--------------------------------------------------------------
The supF( 2.0000000 | 1.0000000 ) test is : 362.44980
It corresponds to a new break at: 100.00000
The supF( 3.0000000 | 2.0000000 ) test is : 30.033204
It corresponds to a new break at: 53.000000
The supF( 4.0000000 | 3.0000000 ) test is : 0.92585165
It corresponds to a new break at: 40.000000
The supF( 5.0000000 | 4.0000000 ) test is : 6.8291549
It corresponds to a new break at: 35.000000
********************************************************
The critical values of supF(i+1|i) at the 10.000000 % level are (for i=1 to 5.0000000 ) are:
9.8100000 11.400000 12.290000 12.900000 13.470000
The critical values of supF(i+1|i) at the 5.0000000 % level are (for i=1 to 5.0000000 ) are:
11.470000 12.950000 14.030000 14.850000 15.290000
The critical values of supF(i+1|i) at the 2.5000000 % level are (for i=1 to 5.0000000 ) are:
12.960000 14.920000 15.810000 16.510000 16.840000
The critical values of supF(i+1|i) at the 1.0000000 % level are (for i=1 to 5.0000000 ) are:
15.370000 16.840000 17.720000 18.670000 19.170000
********************************************************
Output from the application of Information criteria
--------------------------------------------------------------
Values of BIC and lwz with 0.00000000 breaks: -2.9368833 -2.9207539
Values of BIC and lwz with 1.0000000 breaks: -4.2259397 -4.1051791
Values of BIC and lwz with 2.0000000 breaks: -4.8121030 -4.5860860
Values of BIC and lwz with 3.0000000 breaks: -4.8676901 -4.5357590
Values of BIC and lwz with 4.0000000 breaks: -4.8713602 -4.4328222
Values of BIC and lwz with 5.0000000 breaks: -4.8379011 -4.2920255
The number of breaks chosen by BIC is : 4.0000000
The number of breaks chosen by LWZ is : 2.0000000
********************************************************
Output from the sequential procedure at significance level 10.000000 %
--------------------------------------------------------------
The first break found is at: 71.000000
The next break found is at: 100.00000
The next break found is at: 53.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 3.0000000
********************************************************
Output from the sequential procedure at significance level 5.0000000 %
--------------------------------------------------------------
The first break found is at: 71.000000
The next break found is at: 100.00000
The next break found is at: 53.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 3.0000000
********************************************************
Output from the sequential procedure at significance level 2.5000000 %
--------------------------------------------------------------
The first break found is at: 71.000000
The next break found is at: 100.00000
The next break found is at: 53.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 3.0000000
********************************************************
Output from the sequential procedure at significance level 1.0000000 %
--------------------------------------------------------------
The first break found is at: 71.000000
The next break found is at: 100.00000
The next break found is at: 53.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 3.0000000
********************************************************
Output from the repartition procedure for the 10.000000 % significance level
----------------------------------------
The updated break dates are :
53.000000
71.000000
100.00000
********************************************************
Output from the repartition procedure for the 5.0000000 % significance level
----------------------------------------
The updated break dates are :
53.000000
71.000000
100.00000
********************************************************
Output from the repartition procedure for the 2.5000000 % significance level
----------------------------------------
The updated break dates are :
53.000000
71.000000
100.00000
********************************************************
Output from the repartition procedure for the 1.0000000 % significance level
----------------------------------------
The updated break dates are :
53.000000
71.000000
100.00000
********************************************************
Output from the estimation of the model selected by BIC
--------------------------------------------------------------
Valid cases: 125 Dependent variable: Y
Missing cases: 0 Deletion method: None
Total SS: 9021.402 Degrees of freedom: 115
R-squared: 1.000 Rbar-squared: 1.000
Residual SS: 0.603 Std error of est: 0.072
F(10,115): 172163.485 Probability of F: 0.000
Durbin-Watson: 1.068

Standard Prob Standardized Cor with
Variable Estimate Error t-value >|t| Estimate Dep Var
-------------------------------------------------------------------------------
X01 7.558619 0.020171 374.734065 0.000 0.579353 0.601612
X02 0.010756 0.000650 16.547673 0.000 0.025583 0.529657
X03 8.117492 0.206242 39.359139 0.000 0.362594 0.372932
X04 0.003703 0.003289 1.126023 0.263 0.010373 0.371725
X05 3.475995 0.265278 13.103220 0.000 0.155267 0.375823
X06 0.061337 0.003289 18.651713 0.000 0.221014 0.375959
X07 5.309468 0.324372 16.368472 0.000 0.237165 0.412188
X08 0.039780 0.003289 12.096380 0.000 0.175266 0.412102
X09 7.933289 0.383496 20.686740 0.000 0.354366 0.432801
X10 0.015072 0.003289 4.583283 0.000 0.078512 0.432528
--------------------------------------------------------------
Corrected standard errors for the coefficients
--------------------------------------------------------------
The corrected standard error for coefficient 1.0000000 is: 0.019225483
The corrected standard error for coefficient 2.0000000 is: 0.00061953252
The corrected standard error for coefficient 3.0000000 is: 0.15800568
The corrected standard error for coefficient 4.0000000 is: 0.0025194255
The corrected standard error for coefficient 5.0000000 is: 0.45943915
The corrected standard error for coefficient 6.0000000 is: 0.0056955023
The corrected standard error for coefficient 7.0000000 is: 0.094770321
The corrected standard error for coefficient 8.0000000 is: 0.00096080340
The corrected standard error for coefficient 9.0000000 is: 0.078669975
The corrected standard error for coefficient 10.000000 is: 0.00067461014
the procedure to get critical values for the break dates has
reached the upper bound on the number of iterations. This may
be due to incorrect specifications of the upper or lower bound
in the procedure cvg. The resulting confidence interval for this
break date is incorrect.
--------------------------------------------------------------
Confidence intervals for the break dates
--------------------------------------------------------------
The 95% C.I. for the 1.0000000 th break is: 49.000000 54.000000
The 90% C.I. for the 1.0000000 th break is: 50.000000 54.000000
The 95% C.I. for the 2.0000000 th break is: 70.000000 72.000000
The 90% C.I. for the 2.0000000 th break is: 70.000000 72.000000
The 95% C.I. for the 3.0000000 th break is: 87.000000 161.00000
The 90% C.I. for the 3.0000000 th break is: 159.00000 161.00000
The 95% C.I. for the 4.0000000 th break is: 105.00000 108.00000
The 90% C.I. for the 4.0000000 th break is: 105.00000 108.00000
********************************************************
K_BIC 1.0000000
The options chosen are:
h = 18.000000
eps1 = 0.15000000
hetdat = 1.0000000
hetvar = 1.0000000
hetomega = 1.0000000
hetq = 1.0000000
robust = 0.00000000 (prewhit = 0.00000000 )
The maximum number of breaks is: 5.0000000
********************************************************
Output from the global optimization
********************************************************
The model with 1.0000000 breaks has SSR : 2.1151756
The dates of the breaks are: 85.000000
The model with 2.0000000 breaks has SSR : 1.0418624
The dates of the breaks are:
76.000000
94.000000
The model with 3.0000000 breaks has SSR : 0.62673758
The dates of the breaks are:
45.000000
76.000000
94.000000
The model with 4.0000000 breaks has SSR : 0.60627802
The dates of the breaks are:
18.000000
44.000000
76.000000
94.000000
The model with 5.0000000 breaks has SSR : 0.61959918
The dates of the breaks are:
18.000000
36.000000
54.000000
76.000000
94.000000
********************************************************
Output from the testing procedures
********************************************************
a) supF tests against a fixed number of breaks
--------------------------------------------------------------
The supF test for 0 versus 1.0000000 breaks (scaled by q) is: 286.68860
The supF test for 0 versus 2.0000000 breaks (scaled by q) is: 397.98874
The supF test for 0 versus 3.0000000 breaks (scaled by q) is: 327.15550
The supF test for 0 versus 4.0000000 breaks (scaled by q) is: 252.13880
The supF test for 0 versus 5.0000000 breaks (scaled by q) is: 211.48500
-------------------------
The critical values at the 10.000000 % level are (for k=1 to 5.0000000 ):
9.8100000 8.6300000 7.5400000 6.5100000 5.2700000
The critical values at the 5.0000000 % level are (for k=1 to 5.0000000 ):
11.470000 9.7500000 8.3600000 7.1900000 5.8500000
The critical values at the 2.5000000 % level are (for k=1 to 5.0000000 ):
12.960000 10.750000 9.1500000 7.8100000 6.3800000
The critical values at the 1.0000000 % level are (for k=1 to 5.0000000 ):
15.370000 12.150000 10.270000 8.6500000 7.0000000
--------------------------------------------------------------
b) Dmax tests against an unknown number of breaks
--------------------------------------------------------------
The UDmax test is: 397.98874
(the critical value at the 10.000000 % level is: 10.160000 )
(the critical value at the 5.0000000 % level is: 11.700000 )
(the critical value at the 2.5000000 % level is: 13.180000 )
(the critical value at the 1.0000000 % level is: 15.410000 )
********************************************************
---------------------
The WDmax test at the 10.000000 % level is: 452.40667
(The critical value is: 11.150000 )
---------------------
The WDmax test at the 5.0000000 % level is: 468.19804
(The critical value is: 12.810000 )
---------------------
The WDmax test at the 2.5000000 % level is: 479.80783
(The critical value is: 14.580000 )
---------------------
The WDmax test at the 1.0000000 % level is: 503.46395
(The critical value is: 17.010000 )
********************************************************
supF(l+1|l) tests using global otimizers under the null
--------------------------------------------------------------
The supF( 2.0000000 | 1.0000000 ) test is : 188.62418
It corresponds to a new break at: 103.00000
The supF( 3.0000000 | 2.0000000 ) test is : 51.774503
It corresponds to a new break at: 45.000000
The supF( 4.0000000 | 3.0000000 ) test is : 14.125989
It corresponds to a new break at: 23.000000
Given the location of the breaks from the global optimization
with 4.0000000 breaks there was no more place to insert
an additional breaks that satisfy the minimal length requirement.
The supF( 5.0000000 | 4.0000000 ) test is : 0.00000000
It corresponds to a new break at: 0.00000000
********************************************************
The critical values of supF(i+1|i) at the 10.000000 % level are (for i=1 to 5.0000000 ) are:
9.8100000 11.400000 12.290000 12.900000 13.470000
The critical values of supF(i+1|i) at the 5.0000000 % level are (for i=1 to 5.0000000 ) are:
11.470000 12.950000 14.030000 14.850000 15.290000
The critical values of supF(i+1|i) at the 2.5000000 % level are (for i=1 to 5.0000000 ) are:
12.960000 14.920000 15.810000 16.510000 16.840000
The critical values of supF(i+1|i) at the 1.0000000 % level are (for i=1 to 5.0000000 ) are:
15.370000 16.840000 17.720000 18.670000 19.170000
********************************************************
Output from the application of Information criteria
--------------------------------------------------------------
Values of BIC and lwz with 0.00000000 breaks: -2.9274726 -2.9113432
Values of BIC and lwz with 1.0000000 breaks: -3.9632964 -3.8425358
Values of BIC and lwz with 2.0000000 breaks: -4.5555448 -4.3295278
Values of BIC and lwz with 3.0000000 breaks: -4.9479025 -4.6159714
Values of BIC and lwz with 4.0000000 breaks: -4.8652122 -4.4266742
Values of BIC and lwz with 5.0000000 breaks: -4.7275986 -4.1817230
The number of breaks chosen by BIC is : 3.0000000
The number of breaks chosen by LWZ is : 3.0000000
********************************************************
Output from the sequential procedure at significance level 10.000000 %
--------------------------------------------------------------
The first break found is at: 85.000000
The next break found is at: 103.00000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 2.0000000
********************************************************
Output from the sequential procedure at significance level 5.0000000 %
--------------------------------------------------------------
The first break found is at: 85.000000
The next break found is at: 103.00000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 2.0000000
********************************************************
Output from the sequential procedure at significance level 2.5000000 %
--------------------------------------------------------------
The first break found is at: 85.000000
The next break found is at: 103.00000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 2.0000000
********************************************************
Output from the sequential procedure at significance level 1.0000000 %
--------------------------------------------------------------
The first break found is at: 85.000000
The next break found is at: 103.00000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 2.0000000
********************************************************
Output from the repartition procedure for the 10.000000 % significance level
----------------------------------------
The updated break dates are :
76.000000
103.00000
********************************************************
Output from the repartition procedure for the 5.0000000 % significance level
----------------------------------------
The updated break dates are :
76.000000
103.00000
********************************************************
Output from the repartition procedure for the 2.5000000 % significance level
----------------------------------------
The updated break dates are :
76.000000
103.00000
********************************************************
Output from the repartition procedure for the 1.0000000 % significance level
----------------------------------------
The updated break dates are :
76.000000
103.00000
********************************************************
Output from the estimation of the model selected by BIC
--------------------------------------------------------------
Valid cases: 125 Dependent variable: Y
Missing cases: 0 Deletion method: None
Total SS: 9119.662 Degrees of freedom: 117
R-squared: 1.000 Rbar-squared: 1.000
Residual SS: 0.627 Std error of est: 0.073
F(8,117): 212793.837 Probability of F: 0.000
Durbin-Watson: 0.816

Standard Prob Standardized Cor with
Variable Estimate Error t-value >|t| Estimate Dep Var
-------------------------------------------------------------------------------
X1 7.533042 0.022190 339.482473 0.000 0.529160 0.553705
X2 0.015192 0.000840 18.083620 0.000 0.028187 0.488965
X3 6.869257 0.090609 75.811791 0.000 0.400499 0.483784
X4 0.023418 0.001470 15.933923 0.000 0.084176 0.480438
X5 2.146380 0.284818 7.535973 0.000 0.095357 0.383350
X6 0.075817 0.003325 22.801608 0.000 0.288522 0.383705
X7 7.045386 0.162199 43.436725 0.000 0.410768 0.558164
X8 0.022983 0.001470 15.637940 0.000 0.147883 0.557300
--------------------------------------------------------------
Corrected standard errors for the coefficients
--------------------------------------------------------------
The corrected standard error for coefficient 1.0000000 is: 0.011989649
The corrected standard error for coefficient 2.0000000 is: 0.00045392329
The corrected standard error for coefficient 3.0000000 is: 0.13876122
The corrected standard error for coefficient 4.0000000 is: 0.0022507081
The corrected standard error for coefficient 5.0000000 is: 0.33725918
The corrected standard error for coefficient 6.0000000 is: 0.0039373098
The corrected standard error for coefficient 7.0000000 is: 0.070885224
The corrected standard error for coefficient 8.0000000 is: 0.00064229135
the procedure to get critical values for the break dates has
reached the upper bound on the number of iterations. This may
be due to incorrect specifications of the upper or lower bound
in the procedure cvg. The resulting confidence interval for this
break date is incorrect.
--------------------------------------------------------------
Confidence intervals for the break dates
--------------------------------------------------------------
The 95% C.I. for the 1.0000000 th break is: 44.000000 46.000000
The 90% C.I. for the 1.0000000 th break is: 44.000000 46.000000
The 95% C.I. for the 2.0000000 th break is: 74.000000 77.000000
The 90% C.I. for the 2.0000000 th break is: 74.000000 77.000000
The 95% C.I. for the 3.0000000 th break is: 92.000000 98.000000
The 90% C.I. for the 3.0000000 th break is: 92.000000 98.000000
********************************************************
K_BIC 1.0000000
The options chosen are:
h = 18.000000
eps1 = 0.15000000
hetdat = 1.0000000
hetvar = 1.0000000
hetomega = 1.0000000
hetq = 1.0000000
robust = 0.00000000 (prewhit = 0.00000000 )
The maximum number of breaks is: 5.0000000
********************************************************
Output from the global optimization
********************************************************
The model with 1.0000000 breaks has SSR : 1.5255273
The dates of the breaks are: 73.000000
The model with 2.0000000 breaks has SSR : 0.78390737
The dates of the breaks are:
74.000000
98.000000
The model with 3.0000000 breaks has SSR : 0.41759122
The dates of the breaks are:
37.000000
74.000000
98.000000
The model with 4.0000000 breaks has SSR : 0.24056281
The dates of the breaks are:
27.000000
49.000000
74.000000
98.000000
The model with 5.0000000 breaks has SSR : 0.37629384
The dates of the breaks are:
19.000000
37.000000
56.000000
74.000000
98.000000
********************************************************
Output from the testing procedures
********************************************************
a) supF tests against a fixed number of breaks
--------------------------------------------------------------
The supF test for 0 versus 1.0000000 breaks (scaled by q) is: 399.42613
The supF test for 0 versus 2.0000000 breaks (scaled by q) is: 730.58471
The supF test for 0 versus 3.0000000 breaks (scaled by q) is: 697.92295
The supF test for 0 versus 4.0000000 breaks (scaled by q) is: 860.30545
The supF test for 0 versus 5.0000000 breaks (scaled by q) is: 645.01141
-------------------------
The critical values at the 10.000000 % level are (for k=1 to 5.0000000 ):
9.8100000 8.6300000 7.5400000 6.5100000 5.2700000
The critical values at the 5.0000000 % level are (for k=1 to 5.0000000 ):
11.470000 9.7500000 8.3600000 7.1900000 5.8500000
The critical values at the 2.5000000 % level are (for k=1 to 5.0000000 ):
12.960000 10.750000 9.1500000 7.8100000 6.3800000
The critical values at the 1.0000000 % level are (for k=1 to 5.0000000 ):
15.370000 12.150000 10.270000 8.6500000 7.0000000
--------------------------------------------------------------
b) Dmax tests against an unknown number of breaks
--------------------------------------------------------------
The UDmax test is: 860.30545
(the critical value at the 10.000000 % level is: 10.160000 )
(the critical value at the 5.0000000 % level is: 11.700000 )
(the critical value at the 2.5000000 % level is: 13.180000 )
(the critical value at the 1.0000000 % level is: 15.410000 )
********************************************************
---------------------
The WDmax test at the 10.000000 % level is: 1296.4050
(The critical value is: 11.150000 )
---------------------
The WDmax test at the 5.0000000 % level is: 1372.4205
(The critical value is: 12.810000 )
---------------------
The WDmax test at the 2.5000000 % level is: 1427.6003
(The critical value is: 14.580000 )
---------------------
The WDmax test at the 1.0000000 % level is: 1528.6584
(The critical value is: 17.010000 )
********************************************************
supF(l+1|l) tests using global otimizers under the null
--------------------------------------------------------------
The supF( 2.0000000 | 1.0000000 ) test is : 330.56478
It corresponds to a new break at: 99.000000
The supF( 3.0000000 | 2.0000000 ) test is : 119.99605
It corresponds to a new break at: 37.000000
The supF( 4.0000000 | 3.0000000 ) test is : 17.526261
It corresponds to a new break at: 19.000000
Given the location of the breaks from the global optimization
with 4.0000000 breaks there was no more place to insert
an additional breaks that satisfy the minimal length requirement.
The supF( 5.0000000 | 4.0000000 ) test is : 0.00000000
It corresponds to a new break at: 0.00000000
********************************************************
The critical values of supF(i+1|i) at the 10.000000 % level are (for i=1 to 5.0000000 ) are:
9.8100000 11.400000 12.290000 12.900000 13.470000
The critical values of supF(i+1|i) at the 5.0000000 % level are (for i=1 to 5.0000000 ) are:
11.470000 12.950000 14.030000 14.850000 15.290000
The critical values of supF(i+1|i) at the 2.5000000 % level are (for i=1 to 5.0000000 ) are:
12.960000 14.920000 15.810000 16.510000 16.840000
The critical values of supF(i+1|i) at the 1.0000000 % level are (for i=1 to 5.0000000 ) are:
15.370000 16.840000 17.720000 18.670000 19.170000
********************************************************
Output from the application of Information criteria
--------------------------------------------------------------
Values of BIC and lwz with 0.00000000 breaks: -2.8394698 -2.8233405
Values of BIC and lwz with 1.0000000 breaks: -4.2900941 -4.1693335
Values of BIC and lwz with 2.0000000 breaks: -4.8400191 -4.6140021
Values of BIC and lwz with 3.0000000 breaks: -5.3539274 -5.0219963
Values of BIC and lwz with 4.0000000 breaks: -5.7895697 -5.3510317
Values of BIC and lwz with 5.0000000 breaks: -5.2263010 -4.6804254
The number of breaks chosen by BIC is : 4.0000000
The number of breaks chosen by LWZ is : 4.0000000
********************************************************
Output from the sequential procedure at significance level 10.000000 %
--------------------------------------------------------------
The first break found is at: 73.000000
The next break found is at: 99.000000
The next break found is at: 37.000000
The next break found is at: 19.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 5.0000000 %
--------------------------------------------------------------
The first break found is at: 73.000000
The next break found is at: 99.000000
The next break found is at: 37.000000
The next break found is at: 19.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 2.5000000 %
--------------------------------------------------------------
The first break found is at: 73.000000
The next break found is at: 99.000000
The next break found is at: 37.000000
The next break found is at: 19.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 1.0000000 %
--------------------------------------------------------------
The first break found is at: 73.000000
The next break found is at: 99.000000
The next break found is at: 37.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 3.0000000
********************************************************
Output from the repartition procedure for the 10.000000 % significance level
----------------------------------------
The updated break dates are :
19.000000
50.000000
74.000000
99.000000
********************************************************
Output from the repartition procedure for the 5.0000000 % significance level
----------------------------------------
The updated break dates are :
19.000000
50.000000
74.000000
99.000000
********************************************************
Output from the repartition procedure for the 2.5000000 % significance level
----------------------------------------
The updated break dates are :
19.000000
50.000000
74.000000
99.000000
********************************************************
Output from the repartition procedure for the 1.0000000 % significance level
----------------------------------------
The updated break dates are :
37.000000
74.000000
99.000000
********************************************************
Output from the estimation of the model selected by BIC
--------------------------------------------------------------
Valid cases: 125 Dependent variable: Y
Missing cases: 0 Deletion method: None
Total SS: 8458.351 Degrees of freedom: 115
R-squared: 1.000 Rbar-squared: 1.000
Residual SS: 0.241 Std error of est: 0.046
F(10,115): 404336.291 Probability of F: 0.000
Durbin-Watson: 1.261

Standard Prob Standardized Cor with
Variable Estimate Error t-value >|t| Estimate Dep Var
-------------------------------------------------------------------------------
X01 7.282657 0.018105 402.250655 0.000 0.411461 0.414310
X02 0.003602 0.001130 3.187078 0.002 0.003260 0.362821
X03 6.385473 0.059972 106.473956 0.000 0.325658 0.392018
X04 0.033797 0.001537 21.989190 0.000 0.067255 0.388580
X05 7.324231 0.079178 92.503659 0.000 0.398189 0.434026
X06 0.010632 0.001269 8.381398 0.000 0.036078 0.431601
X07 3.428071 0.117036 29.290792 0.000 0.182605 0.448235
X08 0.057650 0.001349 42.744613 0.000 0.266479 0.448502
X09 6.720299 0.126874 52.968114 0.000 0.379689 0.533518
X10 0.024310 0.001130 21.511723 0.000 0.154201 0.532975
--------------------------------------------------------------
Corrected standard errors for the coefficients
--------------------------------------------------------------
The corrected standard error for coefficient 1.0000000 is: 0.010413262
The corrected standard error for coefficient 2.0000000 is: 0.00064998310
The corrected standard error for coefficient 3.0000000 is: 0.055877716
The corrected standard error for coefficient 4.0000000 is: 0.0014320560
The corrected standard error for coefficient 5.0000000 is: 0.080507650
The corrected standard error for coefficient 6.0000000 is: 0.0012898157
The corrected standard error for coefficient 7.0000000 is: 0.17184116
The corrected standard error for coefficient 8.0000000 is: 0.0019802723
The corrected standard error for coefficient 9.0000000 is: 0.074790558
The corrected standard error for coefficient 10.000000 is: 0.00066616390
--------------------------------------------------------------
Confidence intervals for the break dates
--------------------------------------------------------------
The 95% C.I. for the 1.0000000 th break is: 25.000000 28.000000
The 90% C.I. for the 1.0000000 th break is: 25.000000 28.000000
The 95% C.I. for the 2.0000000 th break is: 40.000000 50.000000
The 90% C.I. for the 2.0000000 th break is: 40.000000 50.000000
The 95% C.I. for the 3.0000000 th break is: 72.000000 75.000000
The 90% C.I. for the 3.0000000 th break is: 72.000000 75.000000
The 95% C.I. for the 4.0000000 th break is: 96.000000 101.00000
The 90% C.I. for the 4.0000000 th break is: 96.000000 101.00000
********************************************************
K_BIC 1.0000000
The options chosen are:
h = 18.000000
eps1 = 0.15000000
hetdat = 1.0000000
hetvar = 1.0000000
hetomega = 1.0000000
hetq = 1.0000000
robust = 0.00000000 (prewhit = 0.00000000 )
The maximum number of breaks is: 5.0000000
********************************************************
Output from the global optimization
********************************************************
The model with 1.0000000 breaks has SSR : 1.5917660
The dates of the breaks are: 71.000000
The model with 2.0000000 breaks has SSR : 0.94689906
The dates of the breaks are:
56.000000
77.000000
The model with 3.0000000 breaks has SSR : 0.67960518
The dates of the breaks are:
56.000000
76.000000
105.00000
The model with 4.0000000 breaks has SSR : 0.62673848
The dates of the breaks are:
40.000000
58.000000
76.000000
105.00000
The model with 5.0000000 breaks has SSR : 0.57410691
The dates of the breaks are:
18.000000
40.000000
58.000000
76.000000
105.00000
********************************************************
Output from the testing procedures
********************************************************
a) supF tests against a fixed number of breaks
--------------------------------------------------------------
The supF test for 0 versus 1.0000000 breaks (scaled by q) is: 249.60024
The supF test for 0 versus 2.0000000 breaks (scaled by q) is: 245.51987
The supF test for 0 versus 3.0000000 breaks (scaled by q) is: 537.42107
The supF test for 0 versus 4.0000000 breaks (scaled by q) is: 418.58584
The supF test for 0 versus 5.0000000 breaks (scaled by q) is: 378.41733
-------------------------
The critical values at the 10.000000 % level are (for k=1 to 5.0000000 ):
9.8100000 8.6300000 7.5400000 6.5100000 5.2700000
The critical values at the 5.0000000 % level are (for k=1 to 5.0000000 ):
11.470000 9.7500000 8.3600000 7.1900000 5.8500000
The critical values at the 2.5000000 % level are (for k=1 to 5.0000000 ):
12.960000 10.750000 9.1500000 7.8100000 6.3800000
The critical values at the 1.0000000 % level are (for k=1 to 5.0000000 ):
15.370000 12.150000 10.270000 8.6500000 7.0000000
--------------------------------------------------------------
b) Dmax tests against an unknown number of breaks
--------------------------------------------------------------
The UDmax test is: 537.42107
(the critical value at the 10.000000 % level is: 10.160000 )
(the critical value at the 5.0000000 % level is: 11.700000 )
(the critical value at the 2.5000000 % level is: 13.180000 )
(the critical value at the 1.0000000 % level is: 15.410000 )
********************************************************
---------------------
The WDmax test at the 10.000000 % level is: 704.41632
(The critical value is: 11.150000 )
---------------------
The WDmax test at the 5.0000000 % level is: 741.95672
(The critical value is: 12.810000 )
---------------------
The WDmax test at the 2.5000000 % level is: 768.69727
(The critical value is: 14.580000 )
---------------------
The WDmax test at the 1.0000000 % level is: 830.89634
(The critical value is: 17.010000 )
********************************************************
supF(l+1|l) tests using global otimizers under the null
--------------------------------------------------------------
The supF( 2.0000000 | 1.0000000 ) test is : 203.94140
It corresponds to a new break at: 101.00000
The supF( 3.0000000 | 2.0000000 ) test is : 365.14407
It corresponds to a new break at: 103.00000
The supF( 4.0000000 | 3.0000000 ) test is : 40.694648
It corresponds to a new break at: 18.000000
The supF( 5.0000000 | 4.0000000 ) test is : 42.172096
It corresponds to a new break at: 18.000000
********************************************************
The critical values of supF(i+1|i) at the 10.000000 % level are (for i=1 to 5.0000000 ) are:
9.8100000 11.400000 12.290000 12.900000 13.470000
The critical values of supF(i+1|i) at the 5.0000000 % level are (for i=1 to 5.0000000 ) are:
11.470000 12.950000 14.030000 14.850000 15.290000
The critical values of supF(i+1|i) at the 2.5000000 % level are (for i=1 to 5.0000000 ) are:
12.960000 14.920000 15.810000 16.510000 16.840000
The critical values of supF(i+1|i) at the 1.0000000 % level are (for i=1 to 5.0000000 ) are:
15.370000 16.840000 17.720000 18.670000 19.170000
********************************************************
Output from the application of Information criteria
--------------------------------------------------------------
Values of BIC and lwz with 0.00000000 breaks: -3.1215722 -3.1054428
Values of BIC and lwz with 1.0000000 breaks: -4.2475901 -4.1268295
Values of BIC and lwz with 2.0000000 breaks: -4.6511175 -4.4251004
Values of BIC and lwz with 3.0000000 breaks: -4.8669184 -4.5349873
Values of BIC and lwz with 4.0000000 breaks: -4.8320215 -4.3934835
Values of BIC and lwz with 5.0000000 breaks: -4.8038557 -4.2579801
The number of breaks chosen by BIC is : 3.0000000
The number of breaks chosen by LWZ is : 3.0000000
********************************************************
Output from the sequential procedure at significance level 10.000000 %
--------------------------------------------------------------
The first break found is at: 71.000000
The next break found is at: 101.00000
The next break found is at: 53.000000
The next break found is at: 18.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 5.0000000 %
--------------------------------------------------------------
The first break found is at: 71.000000
The next break found is at: 101.00000
The next break found is at: 53.000000
The next break found is at: 18.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 2.5000000 %
--------------------------------------------------------------
The first break found is at: 71.000000
The next break found is at: 101.00000
The next break found is at: 53.000000
The next break found is at: 18.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 1.0000000 %
--------------------------------------------------------------
The first break found is at: 71.000000
The next break found is at: 101.00000
The next break found is at: 53.000000
The next break found is at: 18.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the repartition procedure for the 10.000000 % significance level
----------------------------------------
The updated break dates are :
18.000000
52.000000
76.000000
101.00000
********************************************************
Output from the repartition procedure for the 5.0000000 % significance level
----------------------------------------
The updated break dates are :
18.000000
52.000000
76.000000
101.00000
********************************************************
Output from the repartition procedure for the 2.5000000 % significance level
----------------------------------------
The updated break dates are :
18.000000
52.000000
76.000000
101.00000
********************************************************
Output from the repartition procedure for the 1.0000000 % significance level
----------------------------------------
The updated break dates are :
18.000000
52.000000
76.000000
101.00000
********************************************************
Output from the estimation of the model selected by BIC
--------------------------------------------------------------
Valid cases: 125 Dependent variable: Y
Missing cases: 0 Deletion method: None
Total SS: 9337.171 Degrees of freedom: 117
R-squared: 1.000 Rbar-squared: 1.000
Residual SS: 0.680 Std error of est: 0.076
F(8,117): 200919.870 Probability of F: 0.000
Durbin-Watson: 0.747

Standard Prob Standardized Cor with
Variable Estimate Error t-value >|t| Estimate Dep Var
-------------------------------------------------------------------------------
X1 7.914017 0.020645 383.338740 0.000 0.612891 0.630749
X2 0.008091 0.000630 12.840662 0.000 0.020530 0.553653
X3 10.282522 0.197275 52.122690 0.000 0.475890 0.390694
X4 -0.027682 0.002955 -9.366289 0.000 -0.085516 0.388595
X5 5.768770 0.154581 37.318707 0.000 0.321495 0.501069
X6 0.035409 0.001692 20.932573 0.000 0.180331 0.500476
X7 8.047870 0.341780 23.546906 0.000 0.372467 0.444891
X8 0.013548 0.002955 4.584227 0.000 0.072514 0.444518
--------------------------------------------------------------
Corrected standard errors for the coefficients
--------------------------------------------------------------
The corrected standard error for coefficient 1.0000000 is: 0.016873445
The corrected standard error for coefficient 2.0000000 is: 0.00051499468
The corrected standard error for coefficient 3.0000000 is: 0.37325364
The corrected standard error for coefficient 4.0000000 is: 0.0055918540
The corrected standard error for coefficient 5.0000000 is: 0.070150311
The corrected standard error for coefficient 6.0000000 is: 0.00076764489
The corrected standard error for coefficient 7.0000000 is: 0.10869576
The corrected standard error for coefficient 8.0000000 is: 0.00093991823
the procedure to get critical values for the break dates has
reached the upper bound on the number of iterations. This may
be due to incorrect specifications of the upper or lower bound
in the procedure cvg. The resulting confidence interval for this
break date is incorrect.
--------------------------------------------------------------
Confidence intervals for the break dates
--------------------------------------------------------------
The 95% C.I. for the 1.0000000 th break is: 55.000000 57.000000
The 90% C.I. for the 1.0000000 th break is: 55.000000 57.000000
The 95% C.I. for the 2.0000000 th break is: 74.000000 85.000000
The 90% C.I. for the 2.0000000 th break is: 74.000000 85.000000
The 95% C.I. for the 3.0000000 th break is: 103.00000 106.00000
The 90% C.I. for the 3.0000000 th break is: 103.00000 106.00000
********************************************************
K_BIC 1.0000000
The options chosen are:
h = 18.000000
eps1 = 0.15000000
hetdat = 1.0000000
hetvar = 1.0000000
hetomega = 1.0000000
hetq = 1.0000000
robust = 0.00000000 (prewhit = 0.00000000 )
The maximum number of breaks is: 5.0000000
********************************************************
Output from the global optimization
********************************************************
The model with 1.0000000 breaks has SSR : 0.69296468
The dates of the breaks are: 67.000000
The model with 2.0000000 breaks has SSR : 0.41139905
The dates of the breaks are:
33.000000
66.000000
The model with 3.0000000 breaks has SSR : 0.29229239
The dates of the breaks are:
33.000000
66.000000
107.00000
The model with 4.0000000 breaks has SSR : 0.23092882
The dates of the breaks are:
24.000000
42.000000
66.000000
107.00000
The model with 5.0000000 breaks has SSR : 0.22598701
The dates of the breaks are:
24.000000
42.000000
66.000000
84.000000
107.00000
********************************************************
Output from the testing procedures
********************************************************
a) supF tests against a fixed number of breaks
--------------------------------------------------------------
The supF test for 0 versus 1.0000000 breaks (scaled by q) is: 163.89996
The supF test for 0 versus 2.0000000 breaks (scaled by q) is: 193.09881
The supF test for 0 versus 3.0000000 breaks (scaled by q) is: 186.70741
The supF test for 0 versus 4.0000000 breaks (scaled by q) is: 173.58205
The supF test for 0 versus 5.0000000 breaks (scaled by q) is: 140.58614
-------------------------
The critical values at the 10.000000 % level are (for k=1 to 5.0000000 ):
9.8100000 8.6300000 7.5400000 6.5100000 5.2700000
The critical values at the 5.0000000 % level are (for k=1 to 5.0000000 ):
11.470000 9.7500000 8.3600000 7.1900000 5.8500000
The critical values at the 2.5000000 % level are (for k=1 to 5.0000000 ):
12.960000 10.750000 9.1500000 7.8100000 6.3800000
The critical values at the 1.0000000 % level are (for k=1 to 5.0000000 ):
15.370000 12.150000 10.270000 8.6500000 7.0000000
--------------------------------------------------------------
b) Dmax tests against an unknown number of breaks
--------------------------------------------------------------
The UDmax test is: 193.09881
(the critical value at the 10.000000 % level is: 10.160000 )
(the critical value at the 5.0000000 % level is: 11.700000 )
(the critical value at the 2.5000000 % level is: 13.180000 )
(the critical value at the 1.0000000 % level is: 15.410000 )
********************************************************
---------------------
The WDmax test at the 10.000000 % level is: 261.69830
(The critical value is: 11.150000 )
---------------------
The WDmax test at the 5.0000000 % level is: 276.91044
(The critical value is: 12.810000 )
---------------------
The WDmax test at the 2.5000000 % level is: 288.04396
(The critical value is: 14.580000 )
---------------------
The WDmax test at the 1.0000000 % level is: 308.68699
(The critical value is: 17.010000 )
********************************************************
supF(l+1|l) tests using global otimizers under the null
--------------------------------------------------------------
The supF( 2.0000000 | 1.0000000 ) test is : 101.22539
It corresponds to a new break at: 107.00000
The supF( 3.0000000 | 2.0000000 ) test is : 107.80845
It corresponds to a new break at: 107.00000
The supF( 4.0000000 | 3.0000000 ) test is : 4.5660391
It corresponds to a new break at: 84.000000
The supF( 5.0000000 | 4.0000000 ) test is : 4.5660391
It corresponds to a new break at: 84.000000
********************************************************
The critical values of supF(i+1|i) at the 10.000000 % level are (for i=1 to 5.0000000 ) are:
9.8100000 11.400000 12.290000 12.900000 13.470000
The critical values of supF(i+1|i) at the 5.0000000 % level are (for i=1 to 5.0000000 ) are:
11.470000 12.950000 14.030000 14.850000 15.290000
The critical values of supF(i+1|i) at the 2.5000000 % level are (for i=1 to 5.0000000 ) are:
12.960000 14.920000 15.810000 16.510000 16.840000
The critical values of supF(i+1|i) at the 1.0000000 % level are (for i=1 to 5.0000000 ) are:
15.370000 16.840000 17.720000 18.670000 19.170000
********************************************************
Output from the application of Information criteria
--------------------------------------------------------------
Values of BIC and lwz with 0.00000000 breaks: -4.2631320 -4.2470027
Values of BIC and lwz with 1.0000000 breaks: -5.0792105 -4.9584498
Values of BIC and lwz with 2.0000000 breaks: -5.4847463 -5.2587292
Values of BIC and lwz with 3.0000000 breaks: -5.7106758 -5.3787447
Values of BIC and lwz with 4.0000000 breaks: -5.8304414 -5.3919034
Values of BIC and lwz with 5.0000000 breaks: -5.7361938 -5.1903182
The number of breaks chosen by BIC is : 4.0000000
The number of breaks chosen by LWZ is : 4.0000000
********************************************************
Output from the sequential procedure at significance level 10.000000 %
--------------------------------------------------------------
The first break found is at: 67.000000
The next break found is at: 107.00000
The next break found is at: 33.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 3.0000000
********************************************************
Output from the sequential procedure at significance level 5.0000000 %
--------------------------------------------------------------
The first break found is at: 67.000000
The next break found is at: 107.00000
The next break found is at: 33.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 3.0000000
********************************************************
Output from the sequential procedure at significance level 2.5000000 %
--------------------------------------------------------------
The first break found is at: 67.000000
The next break found is at: 107.00000
The next break found is at: 33.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 3.0000000
********************************************************
Output from the sequential procedure at significance level 1.0000000 %
--------------------------------------------------------------
The first break found is at: 67.000000
The next break found is at: 107.00000
The next break found is at: 33.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 3.0000000
********************************************************
Output from the repartition procedure for the 10.000000 % significance level
----------------------------------------
The updated break dates are :
33.000000
66.000000
107.00000
********************************************************
Output from the repartition procedure for the 5.0000000 % significance level
----------------------------------------
The updated break dates are :
33.000000
66.000000
107.00000
********************************************************
Output from the repartition procedure for the 2.5000000 % significance level
----------------------------------------
The updated break dates are :
33.000000
66.000000
107.00000
********************************************************
Output from the repartition procedure for the 1.0000000 % significance level
----------------------------------------
The updated break dates are :
33.000000
66.000000
107.00000
********************************************************
Output from the estimation of the model selected by BIC
--------------------------------------------------------------
Valid cases: 125 Dependent variable: Y
Missing cases: 0 Deletion method: None
Total SS: 9653.283 Degrees of freedom: 115
R-squared: 1.000 Rbar-squared: 1.000
Residual SS: 0.231 Std error of est: 0.045
F(10,115): 480711.337 Probability of F: 0.000
Durbin-Watson: 1.284

Standard Prob Standardized Cor with
Variable Estimate Error t-value >|t| Estimate Dep Var
-------------------------------------------------------------------------------
X01 8.178232 0.018881 433.137505 0.000 0.407782 0.409405
X02 0.002605 0.001321 1.971441 0.051 0.001856 0.358591
X03 7.624352 0.069014 110.476060 0.000 0.329232 0.363214
X04 0.023491 0.002036 11.538863 0.000 0.034387 0.359740
X05 8.785508 0.072596 121.019129 0.000 0.438061 0.424972
X06 -0.004817 0.001321 -3.645113 0.000 -0.013194 0.421376
X07 7.367271 0.051932 141.864402 0.000 0.480132 0.592209
X08 0.019767 0.000591 33.420142 0.000 0.113109 0.588861
X09 8.305159 0.237410 34.982315 0.000 0.358630 0.410922
X10 0.010395 0.002036 5.105849 0.000 0.052344 0.410619
--------------------------------------------------------------
Corrected standard errors for the coefficients
--------------------------------------------------------------
The corrected standard error for coefficient 1.0000000 is: 0.025617073
The corrected standard error for coefficient 2.0000000 is: 0.0017928216
The corrected standard error for coefficient 3.0000000 is: 0.058527241
The corrected standard error for coefficient 4.0000000 is: 0.0017264998
The corrected standard error for coefficient 5.0000000 is: 0.077476774
The corrected standard error for coefficient 6.0000000 is: 0.0014102624
The corrected standard error for coefficient 7.0000000 is: 0.039470248
The corrected standard error for coefficient 8.0000000 is: 0.00044954258
The corrected standard error for coefficient 9.0000000 is: 0.14653225
The corrected standard error for coefficient 10.000000 is: 0.0012565422
--------------------------------------------------------------
Confidence intervals for the break dates
--------------------------------------------------------------
The 95% C.I. for the 1.0000000 th break is: 22.000000 25.000000
The 90% C.I. for the 1.0000000 th break is: 22.000000 25.000000
The 95% C.I. for the 2.0000000 th break is: 40.000000 43.000000
The 90% C.I. for the 2.0000000 th break is: 40.000000 43.000000
The 95% C.I. for the 3.0000000 th break is: 58.000000 67.000000
The 90% C.I. for the 3.0000000 th break is: 58.000000 67.000000
The 95% C.I. for the 4.0000000 th break is: 105.00000 108.00000
The 90% C.I. for the 4.0000000 th break is: 105.00000 108.00000
********************************************************
K_BIC 2.0000000
The options chosen are:
h = 18.000000
eps1 = 0.15000000
hetdat = 1.0000000
hetvar = 1.0000000
hetomega = 1.0000000
hetq = 1.0000000
robust = 0.00000000 (prewhit = 0.00000000 )
The maximum number of breaks is: 5.0000000
********************************************************
Output from the global optimization
********************************************************
The model with 1.0000000 breaks has SSR : 0.53973689
The dates of the breaks are: 56.000000
The model with 2.0000000 breaks has SSR : 0.24988297
The dates of the breaks are:
34.000000
72.000000
The model with 3.0000000 breaks has SSR : 0.19620018
The dates of the breaks are:
34.000000
72.000000
107.00000
The model with 4.0000000 breaks has SSR : 0.15743473
The dates of the breaks are:
29.000000
47.000000
70.000000
107.00000
The model with 5.0000000 breaks has SSR : 0.14967253
The dates of the breaks are:
29.000000
47.000000
70.000000
88.000000
107.00000
********************************************************
Output from the testing procedures
********************************************************
a) supF tests against a fixed number of breaks
--------------------------------------------------------------
The supF test for 0 versus 1.0000000 breaks (scaled by q) is: 840.43935
The supF test for 0 versus 2.0000000 breaks (scaled by q) is: 949.27350
The supF test for 0 versus 3.0000000 breaks (scaled by q) is: 857.62623
The supF test for 0 versus 4.0000000 breaks (scaled by q) is: 745.01163
The supF test for 0 versus 5.0000000 breaks (scaled by q) is: 654.23803
-------------------------
The critical values at the 10.000000 % level are (for k=1 to 5.0000000 ):
9.8100000 8.6300000 7.5400000 6.5100000 5.2700000
The critical values at the 5.0000000 % level are (for k=1 to 5.0000000 ):
11.470000 9.7500000 8.3600000 7.1900000 5.8500000
The critical values at the 2.5000000 % level are (for k=1 to 5.0000000 ):
12.960000 10.750000 9.1500000 7.8100000 6.3800000
The critical values at the 1.0000000 % level are (for k=1 to 5.0000000 ):
15.370000 12.150000 10.270000 8.6500000 7.0000000
--------------------------------------------------------------
b) Dmax tests against an unknown number of breaks
--------------------------------------------------------------
The UDmax test is: 949.27350
(the critical value at the 10.000000 % level is: 10.160000 )
(the critical value at the 5.0000000 % level is: 11.700000 )
(the critical value at the 2.5000000 % level is: 13.180000 )
(the critical value at the 1.0000000 % level is: 15.410000 )
********************************************************
---------------------
The WDmax test at the 10.000000 % level is: 1217.8511
(The critical value is: 11.150000 )
---------------------
The WDmax test at the 5.0000000 % level is: 1282.7539
(The critical value is: 12.810000 )
---------------------
The WDmax test at the 2.5000000 % level is: 1328.9851
(The critical value is: 14.580000 )
---------------------
The WDmax test at the 1.0000000 % level is: 1436.5198
(The critical value is: 17.010000 )
********************************************************
supF(l+1|l) tests using global otimizers under the null
--------------------------------------------------------------
The supF( 2.0000000 | 1.0000000 ) test is : 58.012928
It corresponds to a new break at: 38.000000
The supF( 3.0000000 | 2.0000000 ) test is : 54.833909
It corresponds to a new break at: 107.00000
The supF( 4.0000000 | 3.0000000 ) test is : 8.4825276
It corresponds to a new break at: 54.000000
The supF( 5.0000000 | 4.0000000 ) test is : 6.9142932
It corresponds to a new break at: 88.000000
********************************************************
The critical values of supF(i+1|i) at the 10.000000 % level are (for i=1 to 5.0000000 ) are:
9.8100000 11.400000 12.290000 12.900000 13.470000
The critical values of supF(i+1|i) at the 5.0000000 % level are (for i=1 to 5.0000000 ) are:
11.470000 12.950000 14.030000 14.850000 15.290000
The critical values of supF(i+1|i) at the 2.5000000 % level are (for i=1 to 5.0000000 ) are:
12.960000 14.920000 15.810000 16.510000 16.840000
The critical values of supF(i+1|i) at the 1.0000000 % level are (for i=1 to 5.0000000 ) are:
15.370000 16.840000 17.720000 18.670000 19.170000
********************************************************
Output from the application of Information criteria
--------------------------------------------------------------
Values of BIC and lwz with 0.00000000 breaks: -3.5523072 -3.5361778
Values of BIC and lwz with 1.0000000 breaks: -5.3291077 -5.2083471
Values of BIC and lwz with 2.0000000 breaks: -5.9833173 -5.7573002
Values of BIC and lwz with 3.0000000 breaks: -6.1092949 -5.7773638
Values of BIC and lwz with 4.0000000 breaks: -6.2135399 -5.7750019
Values of BIC and lwz with 5.0000000 breaks: -6.1482216 -5.6023460
The number of breaks chosen by BIC is : 4.0000000
The number of breaks chosen by LWZ is : 3.0000000
********************************************************
Output from the sequential procedure at significance level 10.000000 %
--------------------------------------------------------------
The first break found is at: 56.000000
The next break found is at: 38.000000
The next break found is at: 77.000000
The next break found is at: 106.00000
The next break found is at: 19.000000
The sequential procedure has reached the upper limit
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 5.0000000
********************************************************
Output from the sequential procedure at significance level 5.0000000 %
--------------------------------------------------------------
The first break found is at: 56.000000
The next break found is at: 38.000000
The next break found is at: 77.000000
The next break found is at: 106.00000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 2.5000000 %
--------------------------------------------------------------
The first break found is at: 56.000000
The next break found is at: 38.000000
The next break found is at: 77.000000
The next break found is at: 106.00000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 1.0000000 %
--------------------------------------------------------------
The first break found is at: 56.000000
The next break found is at: 38.000000
The next break found is at: 77.000000
The next break found is at: 106.00000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the repartition procedure for the 10.000000 % significance level
----------------------------------------
The updated break dates are :
19.000000
38.000000
59.000000
77.000000
106.00000
********************************************************
Output from the repartition procedure for the 5.0000000 % significance level
----------------------------------------
The updated break dates are :
38.000000
59.000000
77.000000
106.00000
********************************************************
Output from the repartition procedure for the 2.5000000 % significance level
----------------------------------------
The updated break dates are :
38.000000
59.000000
77.000000
106.00000
********************************************************
Output from the repartition procedure for the 1.0000000 % significance level
----------------------------------------
The updated break dates are :
38.000000
59.000000
77.000000
106.00000
********************************************************
Output from the estimation of the model selected by BIC
--------------------------------------------------------------
Valid cases: 125 Dependent variable: Y
Missing cases: 0 Deletion method: None
Total SS: 8565.908 Degrees of freedom: 115
R-squared: 1.000 Rbar-squared: 1.000
Residual SS: 0.157 Std error of est: 0.037
F(10,115): 625695.034 Probability of F: 0.000
Durbin-Watson: 0.861

Standard Prob Standardized Cor with
Variable Estimate Error t-value >|t| Estimate Dep Var
-------------------------------------------------------------------------------
X01 7.190830 0.014105 509.817440 0.000 0.418400 0.425971
X02 0.008675 0.000821 10.563745 0.000 0.008670 0.374072
X03 6.814588 0.065301 104.355785 0.000 0.312384 0.348052
X04 0.020210 0.001681 12.022926 0.000 0.035990 0.345576
X05 6.298939 0.069054 91.217205 0.000 0.326396 0.414046
X06 0.028670 0.001163 24.649599 0.000 0.088202 0.412554
X07 5.756007 0.051067 112.714624 0.000 0.378299 0.574321
X08 0.033512 0.000570 58.823586 0.000 0.197427 0.573033
X09 6.951149 0.196025 35.460590 0.000 0.318644 0.442030
X10 0.023104 0.001681 13.744740 0.000 0.123508 0.441837
--------------------------------------------------------------
Corrected standard errors for the coefficients
--------------------------------------------------------------
The corrected standard error for coefficient 1.0000000 is: 0.010879256
The corrected standard error for coefficient 2.0000000 is: 0.00063341476
The corrected standard error for coefficient 3.0000000 is: 0.050351192
The corrected standard error for coefficient 4.0000000 is: 0.0012961079
The corrected standard error for coefficient 5.0000000 is: 0.066206200
The corrected standard error for coefficient 6.0000000 is: 0.0011151136
The corrected standard error for coefficient 7.0000000 is: 0.062174464
The corrected standard error for coefficient 8.0000000 is: 0.00069361601
The corrected standard error for coefficient 9.0000000 is: 0.15364020
The corrected standard error for coefficient 10.000000 is: 0.0013174942
--------------------------------------------------------------
Confidence intervals for the break dates
--------------------------------------------------------------
The 95% C.I. for the 1.0000000 th break is: 26.000000 30.000000
The 90% C.I. for the 1.0000000 th break is: 27.000000 30.000000
The 95% C.I. for the 2.0000000 th break is: 41.000000 48.000000
The 90% C.I. for the 2.0000000 th break is: 43.000000 48.000000
The 95% C.I. for the 3.0000000 th break is: 67.000000 71.000000
The 90% C.I. for the 3.0000000 th break is: 67.000000 71.000000
The 95% C.I. for the 4.0000000 th break is: 103.00000 108.00000
The 90% C.I. for the 4.0000000 th break is: 104.00000 108.00000
********************************************************
K_BIC 4.0000000
The options chosen are:
h = 18.000000
eps1 = 0.15000000
hetdat = 1.0000000
hetvar = 1.0000000
hetomega = 1.0000000
hetq = 1.0000000
robust = 0.00000000 (prewhit = 0.00000000 )
The maximum number of breaks is: 5.0000000
********************************************************
Output from the global optimization
********************************************************
The model with 1.0000000 breaks has SSR : 0.47468683
The dates of the breaks are: 47.000000
The model with 2.0000000 breaks has SSR : 0.16080429
The dates of the breaks are:
47.000000
100.00000
The model with 3.0000000 breaks has SSR : 0.11988732
The dates of the breaks are:
25.000000
47.000000
100.00000
The model with 4.0000000 breaks has SSR : 0.10960448
The dates of the breaks are:
25.000000
47.000000
85.000000
103.00000
The model with 5.0000000 breaks has SSR : 0.10892228
The dates of the breaks are:
25.000000
47.000000
66.000000
85.000000
103.00000
********************************************************
Output from the testing procedures
********************************************************
a) supF tests against a fixed number of breaks
--------------------------------------------------------------
The supF test for 0 versus 1.0000000 breaks (scaled by q) is: 574.32779
The supF test for 0 versus 2.0000000 breaks (scaled by q) is: 1029.9942
The supF test for 0 versus 3.0000000 breaks (scaled by q) is: 785.47695
The supF test for 0 versus 4.0000000 breaks (scaled by q) is: 632.19947
The supF test for 0 versus 5.0000000 breaks (scaled by q) is: 480.61866
-------------------------
The critical values at the 10.000000 % level are (for k=1 to 5.0000000 ):
9.8100000 8.6300000 7.5400000 6.5100000 5.2700000
The critical values at the 5.0000000 % level are (for k=1 to 5.0000000 ):
11.470000 9.7500000 8.3600000 7.1900000 5.8500000
The critical values at the 2.5000000 % level are (for k=1 to 5.0000000 ):
12.960000 10.750000 9.1500000 7.8100000 6.3800000
The critical values at the 1.0000000 % level are (for k=1 to 5.0000000 ):
15.370000 12.150000 10.270000 8.6500000 7.0000000
--------------------------------------------------------------
b) Dmax tests against an unknown number of breaks
--------------------------------------------------------------
The UDmax test is: 1029.9942
(the critical value at the 10.000000 % level is: 10.160000 )
(the critical value at the 5.0000000 % level is: 11.700000 )
(the critical value at the 2.5000000 % level is: 13.180000 )
(the critical value at the 1.0000000 % level is: 15.410000 )
********************************************************
---------------------
The WDmax test at the 10.000000 % level is: 1170.8277
(The critical value is: 11.150000 )
---------------------
The WDmax test at the 5.0000000 % level is: 1211.6958
(The critical value is: 12.810000 )
---------------------
The WDmax test at the 2.5000000 % level is: 1241.7419
(The critical value is: 14.580000 )
---------------------
The WDmax test at the 1.0000000 % level is: 1302.9639
(The critical value is: 17.010000 )
********************************************************
supF(l+1|l) tests using global otimizers under the null
--------------------------------------------------------------
The supF( 2.0000000 | 1.0000000 ) test is : 289.76020
It corresponds to a new break at: 100.00000
The supF( 3.0000000 | 2.0000000 ) test is : 36.788486
It corresponds to a new break at: 25.000000
The supF( 4.0000000 | 3.0000000 ) test is : 18.131018
It corresponds to a new break at: 82.000000
The supF( 5.0000000 | 4.0000000 ) test is : 0.54897974
It corresponds to a new break at: 66.000000
********************************************************
The critical values of supF(i+1|i) at the 10.000000 % level are (for i=1 to 5.0000000 ) are:
9.8100000 11.400000 12.290000 12.900000 13.470000
The critical values of supF(i+1|i) at the 5.0000000 % level are (for i=1 to 5.0000000 ) are:
11.470000 12.950000 14.030000 14.850000 15.290000
The critical values of supF(i+1|i) at the 2.5000000 % level are (for i=1 to 5.0000000 ) are:
12.960000 14.920000 15.810000 16.510000 16.840000
The critical values of supF(i+1|i) at the 1.0000000 % level are (for i=1 to 5.0000000 ) are:
15.370000 16.840000 17.720000 18.670000 19.170000
********************************************************
Output from the application of Information criteria
--------------------------------------------------------------
Values of BIC and lwz with 0.00000000 breaks: -3.8433997 -3.8272703
Values of BIC and lwz with 1.0000000 breaks: -5.4575342 -5.3367736
Values of BIC and lwz with 2.0000000 breaks: -6.4241219 -6.1981049
Values of BIC and lwz with 3.0000000 breaks: -6.6018781 -6.2699470
Values of BIC and lwz with 4.0000000 breaks: -6.5756726 -6.1371346
Values of BIC and lwz with 5.0000000 breaks: -6.4660368 -5.9201612
The number of breaks chosen by BIC is : 3.0000000
The number of breaks chosen by LWZ is : 3.0000000
********************************************************
Output from the sequential procedure at significance level 10.000000 %
--------------------------------------------------------------
The first break found is at: 47.000000
The next break found is at: 100.00000
The next break found is at: 25.000000
The next break found is at: 82.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 5.0000000 %
--------------------------------------------------------------
The first break found is at: 47.000000
The next break found is at: 100.00000
The next break found is at: 25.000000
The next break found is at: 82.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 2.5000000 %
--------------------------------------------------------------
The first break found is at: 47.000000
The next break found is at: 100.00000
The next break found is at: 25.000000
The next break found is at: 82.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 1.0000000 %
--------------------------------------------------------------
The first break found is at: 47.000000
The next break found is at: 100.00000
The next break found is at: 25.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 3.0000000
********************************************************
Output from the repartition procedure for the 10.000000 % significance level
----------------------------------------
The updated break dates are :
25.000000
47.000000
82.000000
104.00000
********************************************************
Output from the repartition procedure for the 5.0000000 % significance level
----------------------------------------
The updated break dates are :
25.000000
47.000000
82.000000
104.00000
********************************************************
Output from the repartition procedure for the 2.5000000 % significance level
----------------------------------------
The updated break dates are :
25.000000
47.000000
82.000000
104.00000
********************************************************
Output from the repartition procedure for the 1.0000000 % significance level
----------------------------------------
The updated break dates are :
25.000000
47.000000
100.00000
********************************************************
Output from the estimation of the model selected by BIC
--------------------------------------------------------------
Valid cases: 125 Dependent variable: Y
Missing cases: 0 Deletion method: None
Total SS: 9055.625 Degrees of freedom: 117
R-squared: 1.000 Rbar-squared: 1.000
Residual SS: 0.120 Std error of est: 0.032
F(8,117): 1104677.041 Probability of F: 0.000
Durbin-Watson: 0.830

Standard Prob Standardized Cor with
Variable Estimate Error t-value >|t| Estimate Dep Var
-------------------------------------------------------------------------------
X1 7.447421 0.013198 564.271001 0.000 0.391306 0.397261
X2 0.008717 0.000888 9.818931 0.000 0.006809 0.348996
X3 7.391357 0.039853 185.467820 0.000 0.364314 0.389873
X4 0.014207 0.001076 13.206623 0.000 0.025942 0.384874
X5 6.418860 0.021720 295.523494 0.000 0.491062 0.657826
X6 0.029457 0.000287 102.481060 0.000 0.170290 0.651185
X7 8.095617 0.100527 80.531717 0.000 0.425364 0.506151
X8 0.013607 0.000888 15.326101 0.000 0.080952 0.505452
--------------------------------------------------------------
Corrected standard errors for the coefficients
--------------------------------------------------------------
The corrected standard error for coefficient 1.0000000 is: 0.013379346
The corrected standard error for coefficient 2.0000000 is: 0.00089999222
The corrected standard error for coefficient 3.0000000 is: 0.031402469
The corrected standard error for coefficient 4.0000000 is: 0.00084763254
The corrected standard error for coefficient 5.0000000 is: 0.021611935
The corrected standard error for coefficient 6.0000000 is: 0.00028600630
The corrected standard error for coefficient 7.0000000 is: 0.10088300
The corrected standard error for coefficient 8.0000000 is: 0.00089095764
--------------------------------------------------------------
Confidence intervals for the break dates
--------------------------------------------------------------
The 95% C.I. for the 1.0000000 th break is: -35.000000 32.000000
The 90% C.I. for the 1.0000000 th break is: -35.000000 30.000000
The 95% C.I. for the 2.0000000 th break is: 45.000000 48.000000
The 90% C.I. for the 2.0000000 th break is: 45.000000 48.000000
The 95% C.I. for the 3.0000000 th break is: 98.000000 101.00000
The 90% C.I. for the 3.0000000 th break is: 98.000000 101.00000
********************************************************
K_BIC 4.0000000
The options chosen are:
h = 18.000000
eps1 = 0.15000000
hetdat = 1.0000000
hetvar = 1.0000000
hetomega = 1.0000000
hetq = 1.0000000
robust = 0.00000000 (prewhit = 0.00000000 )
The maximum number of breaks is: 5.0000000
********************************************************
Output from the global optimization
********************************************************
The model with 1.0000000 breaks has SSR : 0.25831098
The dates of the breaks are: 50.000000
The model with 2.0000000 breaks has SSR : 0.16570097
The dates of the breaks are:
50.000000
76.000000
The model with 3.0000000 breaks has SSR : 0.15326927
The dates of the breaks are:
50.000000
76.000000
105.00000
The model with 4.0000000 breaks has SSR : 0.14773265
The dates of the breaks are:
18.000000
50.000000
76.000000
105.00000
The model with 5.0000000 breaks has SSR : 0.15864602
The dates of the breaks are:
18.000000
50.000000
70.000000
88.000000
106.00000
********************************************************
Output from the testing procedures
********************************************************
a) supF tests against a fixed number of breaks
--------------------------------------------------------------
The supF test for 0 versus 1.0000000 breaks (scaled by q) is: 594.51710
The supF test for 0 versus 2.0000000 breaks (scaled by q) is: 584.04262
The supF test for 0 versus 3.0000000 breaks (scaled by q) is: 628.79136
The supF test for 0 versus 4.0000000 breaks (scaled by q) is: 510.01728
The supF test for 0 versus 5.0000000 breaks (scaled by q) is: 274.04521
-------------------------
The critical values at the 10.000000 % level are (for k=1 to 5.0000000 ):
9.8100000 8.6300000 7.5400000 6.5100000 5.2700000
The critical values at the 5.0000000 % level are (for k=1 to 5.0000000 ):
11.470000 9.7500000 8.3600000 7.1900000 5.8500000
The critical values at the 2.5000000 % level are (for k=1 to 5.0000000 ):
12.960000 10.750000 9.1500000 7.8100000 6.3800000
The critical values at the 1.0000000 % level are (for k=1 to 5.0000000 ):
15.370000 12.150000 10.270000 8.6500000 7.0000000
--------------------------------------------------------------
b) Dmax tests against an unknown number of breaks
--------------------------------------------------------------
The UDmax test is: 628.79136
(the critical value at the 10.000000 % level is: 10.160000 )
(the critical value at the 5.0000000 % level is: 11.700000 )
(the critical value at the 2.5000000 % level is: 13.180000 )
(the critical value at the 1.0000000 % level is: 15.410000 )
********************************************************
---------------------
The WDmax test at the 10.000000 % level is: 818.09592
(The critical value is: 11.150000 )
---------------------
The WDmax test at the 5.0000000 % level is: 862.70776
(The critical value is: 12.810000 )
---------------------
The WDmax test at the 2.5000000 % level is: 890.61596
(The critical value is: 14.580000 )
---------------------
The WDmax test at the 1.0000000 % level is: 941.04413
(The critical value is: 17.010000 )
********************************************************
supF(l+1|l) tests using global otimizers under the null
--------------------------------------------------------------
The supF( 2.0000000 | 1.0000000 ) test is : 67.985445
It corresponds to a new break at: 76.000000
The supF( 3.0000000 | 2.0000000 ) test is : 29.366585
It corresponds to a new break at: 105.00000
The supF( 4.0000000 | 3.0000000 ) test is : 17.814380
It corresponds to a new break at: 18.000000
Given the location of the breaks from the global optimization
with 4.0000000 breaks there was no more place to insert
an additional breaks that satisfy the minimal length requirement.
The supF( 5.0000000 | 4.0000000 ) test is : 0.00000000
It corresponds to a new break at: 0.00000000
********************************************************
The critical values of supF(i+1|i) at the 10.000000 % level are (for i=1 to 5.0000000 ) are:
9.8100000 11.400000 12.290000 12.900000 13.470000
The critical values of supF(i+1|i) at the 5.0000000 % level are (for i=1 to 5.0000000 ) are:
11.470000 12.950000 14.030000 14.850000 15.290000
The critical values of supF(i+1|i) at the 2.5000000 % level are (for i=1 to 5.0000000 ) are:
12.960000 14.920000 15.810000 16.510000 16.840000
The critical values of supF(i+1|i) at the 1.0000000 % level are (for i=1 to 5.0000000 ) are:
15.370000 16.840000 17.720000 18.670000 19.170000
********************************************************
Output from the application of Information criteria
--------------------------------------------------------------
Values of BIC and lwz with 0.00000000 breaks: -4.2543427 -4.2382133
Values of BIC and lwz with 1.0000000 breaks: -6.0660253 -5.9452647
Values of BIC and lwz with 2.0000000 breaks: -6.3941252 -6.1681081
Values of BIC and lwz with 3.0000000 breaks: -6.3562341 -6.0243030
Values of BIC and lwz with 4.0000000 breaks: -6.2771467 -5.8386087
Values of BIC and lwz with 5.0000000 breaks: -6.0899959 -5.5441203
The number of breaks chosen by BIC is : 2.0000000
The number of breaks chosen by LWZ is : 2.0000000
********************************************************
Output from the sequential procedure at significance level 10.000000 %
--------------------------------------------------------------
The first break found is at: 50.000000
The next break found is at: 76.000000
The next break found is at: 105.00000
The next break found is at: 18.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 5.0000000 %
--------------------------------------------------------------
The first break found is at: 50.000000
The next break found is at: 76.000000
The next break found is at: 105.00000
The next break found is at: 18.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 2.5000000 %
--------------------------------------------------------------
The first break found is at: 50.000000
The next break found is at: 76.000000
The next break found is at: 105.00000
The next break found is at: 18.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 1.0000000 %
--------------------------------------------------------------
The first break found is at: 50.000000
The next break found is at: 76.000000
The next break found is at: 105.00000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 3.0000000
********************************************************
Output from the repartition procedure for the 10.000000 % significance level
----------------------------------------
The updated break dates are :
18.000000
50.000000
76.000000
105.00000
********************************************************
Output from the repartition procedure for the 5.0000000 % significance level
----------------------------------------
The updated break dates are :
18.000000
50.000000
76.000000
105.00000
********************************************************
Output from the repartition procedure for the 2.5000000 % significance level
----------------------------------------
The updated break dates are :
18.000000
50.000000
76.000000
105.00000
********************************************************
Output from the repartition procedure for the 1.0000000 % significance level
----------------------------------------
The updated break dates are :
50.000000
76.000000
105.00000
********************************************************
Output from the estimation of the model selected by BIC
--------------------------------------------------------------
Valid cases: 125 Dependent variable: Y
Missing cases: 0 Deletion method: None
Total SS: 9609.729 Degrees of freedom: 119
R-squared: 1.000 Rbar-squared: 1.000
Residual SS: 0.166 Std error of est: 0.037
F(6,119): 1150202.466 Probability of F: 0.000
Durbin-Watson: 0.854

Standard Prob Standardized Cor with
Variable Estimate Error t-value >|t| Estimate Dep Var
-------------------------------------------------------------------------------
X1 8.082784 0.010715 754.361067 0.000 0.583029 0.601603
X2 0.010098 0.000366 27.612978 0.000 0.021341 0.528753
X3 7.312407 0.062391 117.202594 0.000 0.380357 0.447797
X4 0.020418 0.000976 20.925220 0.000 0.067909 0.445640
X5 7.156022 0.038443 186.147876 0.000 0.510992 0.660999
X6 0.020799 0.000377 55.178728 0.000 0.151470 0.657526
--------------------------------------------------------------
Corrected standard errors for the coefficients
--------------------------------------------------------------
The corrected standard error for coefficient 1.0000000 is: 0.0091339376
The corrected standard error for coefficient 2.0000000 is: 0.00031173667
The corrected standard error for coefficient 3.0000000 is: 0.089428866
The corrected standard error for coefficient 4.0000000 is: 0.0013986071
The corrected standard error for coefficient 5.0000000 is: 0.029700402
The corrected standard error for coefficient 6.0000000 is: 0.00029122240
the procedure to get critical values for the break dates has
reached the upper bound on the number of iterations. This may
be due to incorrect specifications of the upper or lower bound
in the procedure cvg. The resulting confidence interval for this
break date is incorrect.
--------------------------------------------------------------
Confidence intervals for the break dates
--------------------------------------------------------------
The 95% C.I. for the 1.0000000 th break is: 49.000000 51.000000
The 90% C.I. for the 1.0000000 th break is: 49.000000 51.000000
The 95% C.I. for the 2.0000000 th break is: 74.000000 93.000000
The 90% C.I. for the 2.0000000 th break is: 74.000000 93.000000
********************************************************
K_BIC 1.0000000
The options chosen are:
h = 18.000000
eps1 = 0.15000000
hetdat = 1.0000000
hetvar = 1.0000000
hetomega = 1.0000000
hetq = 1.0000000
robust = 0.00000000 (prewhit = 0.00000000 )
The maximum number of breaks is: 5.0000000
********************************************************
Output from the global optimization
********************************************************
The model with 1.0000000 breaks has SSR : 0.92640744
The dates of the breaks are: 71.000000
The model with 2.0000000 breaks has SSR : 0.62271078
The dates of the breaks are:
61.000000
79.000000
The model with 3.0000000 breaks has SSR : 0.58428643
The dates of the breaks are:
53.000000
71.000000
94.000000
The model with 4.0000000 breaks has SSR : 0.54819477
The dates of the breaks are:
31.000000
53.000000
71.000000
94.000000
The model with 5.0000000 breaks has SSR : 0.54355262
The dates of the breaks are:
31.000000
53.000000
71.000000
89.000000
107.00000
********************************************************
Output from the testing procedures
********************************************************
a) supF tests against a fixed number of breaks
--------------------------------------------------------------
The supF test for 0 versus 1.0000000 breaks (scaled by q) is: 65.568130
The supF test for 0 versus 2.0000000 breaks (scaled by q) is: 36.339247
The supF test for 0 versus 3.0000000 breaks (scaled by q) is: 31.241482
The supF test for 0 versus 4.0000000 breaks (scaled by q) is: 29.289099
The supF test for 0 versus 5.0000000 breaks (scaled by q) is: 31.315396
-------------------------
The critical values at the 10.000000 % level are (for k=1 to 5.0000000 ):
9.8100000 8.6300000 7.5400000 6.5100000 5.2700000
The critical values at the 5.0000000 % level are (for k=1 to 5.0000000 ):
11.470000 9.7500000 8.3600000 7.1900000 5.8500000
The critical values at the 2.5000000 % level are (for k=1 to 5.0000000 ):
12.960000 10.750000 9.1500000 7.8100000 6.3800000
The critical values at the 1.0000000 % level are (for k=1 to 5.0000000 ):
15.370000 12.150000 10.270000 8.6500000 7.0000000
--------------------------------------------------------------
b) Dmax tests against an unknown number of breaks
--------------------------------------------------------------
The UDmax test is: 65.568130
(the critical value at the 10.000000 % level is: 10.160000 )
(the critical value at the 5.0000000 % level is: 11.700000 )
(the critical value at the 2.5000000 % level is: 13.180000 )
(the critical value at the 1.0000000 % level is: 15.410000 )
********************************************************
---------------------
The WDmax test at the 10.000000 % level is: 65.568130
(The critical value is: 11.150000 )
---------------------
The WDmax test at the 5.0000000 % level is: 65.568130
(The critical value is: 12.810000 )
---------------------
The WDmax test at the 2.5000000 % level is: 65.568130
(The critical value is: 14.580000 )
---------------------
The WDmax test at the 1.0000000 % level is: 68.759663
(The critical value is: 17.010000 )
********************************************************
supF(l+1|l) tests using global otimizers under the null
--------------------------------------------------------------
The supF( 2.0000000 | 1.0000000 ) test is : 28.383975
It corresponds to a new break at: 53.000000
The supF( 3.0000000 | 2.0000000 ) test is : 32.329972
It corresponds to a new break at: 97.000000
The supF( 4.0000000 | 3.0000000 ) test is : 19.582047
It corresponds to a new break at: 31.000000
Given the location of the breaks from the global optimization
with 4.0000000 breaks there was no more place to insert
an additional breaks that satisfy the minimal length requirement.
The supF( 5.0000000 | 4.0000000 ) test is : 0.00000000
It corresponds to a new break at: 0.00000000
********************************************************
The critical values of supF(i+1|i) at the 10.000000 % level are (for i=1 to 5.0000000 ) are:
9.8100000 11.400000 12.290000 12.900000 13.470000
The critical values of supF(i+1|i) at the 5.0000000 % level are (for i=1 to 5.0000000 ) are:
11.470000 12.950000 14.030000 14.850000 15.290000
The critical values of supF(i+1|i) at the 2.5000000 % level are (for i=1 to 5.0000000 ) are:
12.960000 14.920000 15.810000 16.510000 16.840000
The critical values of supF(i+1|i) at the 1.0000000 % level are (for i=1 to 5.0000000 ) are:
15.370000 16.840000 17.720000 18.670000 19.170000
********************************************************
Output from the application of Information criteria
--------------------------------------------------------------
Values of BIC and lwz with 0.00000000 breaks: -4.4383447 -4.4222154
Values of BIC and lwz with 1.0000000 breaks: -4.7888753 -4.6681147
Values of BIC and lwz with 2.0000000 breaks: -5.0702278 -4.8442107
Values of BIC and lwz with 3.0000000 breaks: -5.0180391 -4.6861080
Values of BIC and lwz with 4.0000000 breaks: -4.9659203 -4.5273822
Values of BIC and lwz with 5.0000000 breaks: -4.8585448 -4.3126692
The number of breaks chosen by BIC is : 2.0000000
The number of breaks chosen by LWZ is : 2.0000000
********************************************************
Output from the sequential procedure at significance level 10.000000 %
--------------------------------------------------------------
The first break found is at: 71.000000
The next break found is at: 53.000000
The next break found is at: 31.000000
The next break found is at: 94.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 4.0000000
********************************************************
Output from the sequential procedure at significance level 5.0000000 %
--------------------------------------------------------------
The first break found is at: 71.000000
The next break found is at: 53.000000
The next break found is at: 31.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 3.0000000
********************************************************
Output from the sequential procedure at significance level 2.5000000 %
--------------------------------------------------------------
The first break found is at: 71.000000
The next break found is at: 53.000000
The next break found is at: 31.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 3.0000000
********************************************************
Output from the sequential procedure at significance level 1.0000000 %
--------------------------------------------------------------
The first break found is at: 71.000000
The next break found is at: 53.000000
The next break found is at: 31.000000
----------------------------------------------------
The sequential procedure estimated the number of breaks at: 3.0000000
********************************************************
Output from the repartition procedure for the 10.000000 % significance level
----------------------------------------
The updated break dates are :
31.000000
53.000000
71.000000
94.000000
********************************************************
Output from the repartition procedure for the 5.0000000 % significance level
----------------------------------------
The updated break dates are :
31.000000
53.000000
71.000000
********************************************************
Output from the repartition procedure for the 2.5000000 % significance level
----------------------------------------
The updated break dates are :
31.000000
53.000000
71.000000
********************************************************
Output from the repartition procedure for the 1.0000000 % significance level
----------------------------------------
The updated break dates are :
31.000000
53.000000
71.000000
********************************************************
Output from the estimation of the model selected by BIC
--------------------------------------------------------------
Valid cases: 125 Dependent variable: Y
Missing cases: 0 Deletion method: None
Total SS: 9918.800 Degrees of freedom: 119
R-squared: 1.000 Rbar-squared: 1.000
Residual SS: 0.623 Std error of est: 0.072
F(6,119): 315893.861 Probability of F: 0.000
Durbin-Watson: 0.765

Standard Prob Standardized Cor with
Variable Estimate Error t-value >|t| Estimate Dep Var
-------------------------------------------------------------------------------
X1 7.800595 0.018754 415.940293 0.000 0.611735 0.652507
X2 0.016771 0.000526 31.881820 0.000 0.046889 0.578816
X3 5.333243 0.232319 22.956551 0.000 0.227195 0.379416
X4 0.050685 0.003286 15.422565 0.000 0.152633 0.379215
X5 7.538087 0.083035 90.781733 0.000 0.513346 0.655146
X6 0.020314 0.000803 25.285782 0.000 0.142984 0.652078
--------------------------------------------------------------
Corrected standard errors for the coefficients
--------------------------------------------------------------
The corrected standard error for coefficient 1.0000000 is: 0.013356950
The corrected standard error for coefficient 2.0000000 is: 0.00037465759
The corrected standard error for coefficient 3.0000000 is: 0.47365312
The corrected standard error for coefficient 4.0000000 is: 0.0067003653
The corrected standard error for coefficient 5.0000000 is: 0.044542497
The corrected standard error for coefficient 6.0000000 is: 0.00043096114
the procedure to get critical values for the break dates has
reached the upper bound on the number of iterations. This may
be due to incorrect specifications of the upper or lower bound
in the procedure cvg. The resulting confidence interval for this
break date is incorrect.
--------------------------------------------------------------
Confidence intervals for the break dates
--------------------------------------------------------------
The 95% C.I. for the 1.0000000 th break is: 60.000000 62.000000
The 90% C.I. for the 1.0000000 th break is: 60.000000 62.000000
The 95% C.I. for the 2.0000000 th break is: 2.0000000 155.00000
The 90% C.I. for the 2.0000000 th break is: 2.0000000 155.00000
********************************************************
K_BIC 3.0000000
************************************
Results for the PANKPSS test
************************************
Stationarity test with structural breaks (homogeneous): 0.69337678 with p-val: 0.24403656
Stationarity test with structural breaks (heterogeneous): 3.2101459 with p-val: 0.00066333796
Nombre de breaks permesos com a maxim 5.0000000
Matriu de tests individuals
0.024033701 2.0000000 5.0000000 2.0000000
0.026577112 3.0000000 3.0000000 3.0000000
0.020815550 4.0000000 4.0000000 4.0000000
0.053431243 2.0000000 4.0000000 2.0000000
0.037536172 4.0000000 4.0000000 4.0000000
0.017808975 3.0000000 4.0000000 3.0000000
0.015197415 2.0000000 4.0000000 2.0000000
0.012648744 3.0000000 3.0000000 3.0000000
0.018172372 4.0000000 4.0000000 4.0000000
0.014890219 3.0000000 3.0000000 3.0000000
0.031912327 4.0000000 4.0000000 4.0000000
0.027926285 3.0000000 4.0000000 3.0000000
0.045915719 3.0000000 3.0000000 3.0000000
0.020162133 2.0000000 2.0000000 2.0000000
0.032277998 2.0000000 2.0000000 2.0000000
Nombre d'observacions 125.00000
Punts de trencament estimats
60.000000 22.000000 22.000000 22.000000 22.000000
0.00000000 59.000000 42.000000 42.000000 40.000000
0.00000000 0.00000000 60.000000 60.000000 59.000000
0.00000000 0.00000000 0.00000000 98.000000 77.000000
0.00000000 0.00000000 0.00000000 0.00000000 98.000000
75.000000 75.000000 44.000000 20.000000 18.000000
0.00000000 93.000000 75.000000 44.000000 36.000000
0.00000000 0.00000000 93.000000 75.000000 54.000000
0.00000000 0.00000000 0.00000000 93.000000 75.000000
0.00000000 0.00000000 0.00000000 0.00000000 93.000000
71.000000 71.000000 44.000000 34.000000 34.000000
0.00000000 102.00000 71.000000 52.000000 52.000000
0.00000000 0.00000000 102.00000 72.000000 71.000000
0.00000000 0.00000000 0.00000000 102.00000 89.000000
0.00000000 0.00000000 0.00000000 0.00000000 107.00000
50.000000 35.000000 30.000000 30.000000 25.000000
0.00000000 70.000000 49.000000 49.000000 43.000000
0.00000000 0.00000000 70.000000 70.000000 61.000000
0.00000000 0.00000000 0.00000000 103.00000 79.000000
0.00000000 0.00000000 0.00000000 0.00000000 103.00000
70.000000 70.000000 47.000000 20.000000 20.000000
0.00000000 104.00000 70.000000 45.000000 45.000000
0.00000000 0.00000000 104.00000 70.000000 70.000000
0.00000000 0.00000000 0.00000000 104.00000 89.000000
0.00000000 0.00000000 0.00000000 0.00000000 107.00000
47.000000 47.000000 47.000000 25.000000 25.000000
0.00000000 100.00000 70.000000 47.000000 47.000000
0.00000000 0.00000000 102.00000 70.000000 70.000000
0.00000000 0.00000000 0.00000000 102.00000 88.000000
0.00000000 0.00000000 0.00000000 0.00000000 106.00000
71.000000 71.000000 58.000000 53.000000 34.000000
0.00000000 100.00000 76.000000 71.000000 52.000000
0.00000000 0.00000000 104.00000 89.000000 71.000000
0.00000000 0.00000000 0.00000000 107.00000 89.000000
0.00000000 0.00000000 0.00000000 0.00000000 107.00000
85.000000 76.000000 45.000000 18.000000 18.000000
0.00000000 94.000000 76.000000 44.000000 36.000000
0.00000000 0.00000000 94.000000 76.000000 54.000000
0.00000000 0.00000000 0.00000000 94.000000 76.000000
0.00000000 0.00000000 0.00000000 0.00000000 94.000000
73.000000 74.000000 37.000000 27.000000 19.000000
0.00000000 98.000000 74.000000 49.000000 37.000000
0.00000000 0.00000000 98.000000 74.000000 56.000000
0.00000000 0.00000000 0.00000000 98.000000 74.000000
0.00000000 0.00000000 0.00000000 0.00000000 98.000000
71.000000 56.000000 56.000000 40.000000 18.000000
0.00000000 77.000000 76.000000 58.000000 40.000000
0.00000000 0.00000000 105.00000 76.000000 58.000000
0.00000000 0.00000000 0.00000000 105.00000 76.000000
0.00000000 0.00000000 0.00000000 0.00000000 105.00000
67.000000 33.000000 33.000000 24.000000 24.000000
0.00000000 66.000000 66.000000 42.000000 42.000000
0.00000000 0.00000000 107.00000 66.000000 66.000000
0.00000000 0.00000000 0.00000000 107.00000 84.000000
0.00000000 0.00000000 0.00000000 0.00000000 107.00000
56.000000 34.000000 34.000000 29.000000 29.000000
0.00000000 72.000000 72.000000 47.000000 47.000000
0.00000000 0.00000000 107.00000 70.000000 70.000000
0.00000000 0.00000000 0.00000000 107.00000 88.000000
0.00000000 0.00000000 0.00000000 0.00000000 107.00000
47.000000 47.000000 25.000000 25.000000 25.000000
0.00000000 100.00000 47.000000 47.000000 47.000000
0.00000000 0.00000000 100.00000 85.000000 66.000000
0.00000000 0.00000000 0.00000000 103.00000 85.000000
0.00000000 0.00000000 0.00000000 0.00000000 103.00000
50.000000 50.000000 50.000000 18.000000 18.000000
0.00000000 76.000000 76.000000 50.000000 50.000000
0.00000000 0.00000000 105.00000 76.000000 70.000000
0.00000000 0.00000000 0.00000000 105.00000 88.000000
0.00000000 0.00000000 0.00000000 0.00000000 106.00000
71.000000 61.000000 53.000000 31.000000 31.000000
0.00000000 79.000000 71.000000 53.000000 53.000000
0.00000000 0.00000000 94.000000 71.000000 71.000000
0.00000000 0.00000000 0.00000000 94.000000 89.000000
0.00000000 0.00000000 0.00000000 0.00000000 107.00000
Homogeneous

0.010000000 0.69337678
0.025000000 0.69337678
0.050000000 0.69337678
0.10000000 0.69337678
0.90000000 0.69337678
0.95000000 0.69337678
0.97500000 0.69337678
0.99000000 0.69337678
Heterogeneous

0.010000000 3.2101459
0.025000000 3.2101459
0.050000000 3.2101459
0.10000000 3.2101459
0.90000000 3.2101459
0.95000000 3.2101459
0.97500000 3.2101459
0.99000000 3.2101459

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013179

0

013179 · Answer 3

P.S. the values should match what is in Table 3 of the aforementioned Carrion-i-Silvestre (2005) paper. Thanks again!

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013179

0

013179 · Answer 4

Hi,

Under closer inspection the "do while i <= n;" fix doesn't actually work and when I implement it I still get an error message regarding the below row:

yb[.,i]=m_deter[.,i]+m_resb[.,i];

Please take another look and let me know if you can spot the problem. I've messed around with various iterations of the i and n part of the 'do while' and 'do until' statements and when I get the code to run it still isn't correct as the bootstrap values at each level of significance are exactly the same.

Thanks again,

James

The part of the code in question is below:

@++++++++++++@
@ Bootstrap @
@++++++++++++@
n=cols(data);
t=rows(data);
m_res=zeros(t,n); @ Matriu per deixar els residus @
i=1;
do until i>n; @ Residuals @
m_res[.,i]=data[.,i]-m_deter[.,i];
i=i+1;
endo;
re=2000; @ Nombre de rèpliques del Bootstrap @
m_kpss_hom=zeros(re,1);
m_kpss_het=zeros(re,1);
m_had_test=zeros(n,3);
j=1;
do while j<=re;
tt=rows(m_res);
m_resb=zeros(t+30,n);
i=1;
do while i<=n;
yb[.,i]=m_deter[.,i]+m_resb[.,i];
i=i+1;
endo;
i=1;
do until i>n;
temp1=m_tb[(i*m)-m+1:(i*m),.]; @ Matrix of Breaks @
dd_tb=temp1[.,m_lee_est[i,2]];
if nbr > 0;
dd_tb=selif(dd_tb,dd_tb .gt 0);
{kpsstest,num,den}=pankpss(yb[.,i],dd_tb,model,kernel);
elseif nbr == 0;
{kpsstest,num,den}=pankpss(yb[.,i],0,model0,kernel);
endif;
numkpss[i]=num;
denkpss[i]=den;
m_lee_est[i,.]=kpsstest~nbr~mbic~mlwz;
i=i+1;
endo;
test_hom=meanc(numkpss)./meanc(denkpss); @ Assuming homogeneous long-run variance @
test_het=meanc(m_lee_est[.,1]); @ Assuming heterogeneous long-run variance @
m_kpss_hom[j,.]=sqrt(n)*(test_hom-test_mean)./sqrt(test_var);
m_kpss_het[j,.]=sqrt(n)*(test_het-test_mean)./sqrt(test_var);
j=j+1;
endo;
e=0.01|0.025|0.05|0.1|0.9|0.95|0.975|0.99;
print "Homogeneous";
q=quantile(m_kpss_hom,e);
e~q;
print "Heterogeneous";
q=quantile(m_kpss_het,e);
e~q;
/****************************************/
/****************************************/
#include c:\gauss16\brcode2.src;
#include granada.src;

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013179

0

aptech · Answer 5

It looks to me as if the reference to m_resb is a mistake. In the original code:

do while j<=re;
    tt=rows(m_res);
    m_resb=zeros(t+30,n);
    i=1;
    do while i<=n;
        yb[.,i]=m_deter[.,i]+m_resb[.,i];
        i=i+1;
    endo;

One of the problems is that m_resb is defined to be 't + 30' rows by 'n' columns, while m_deter is 't' rows by 'n' columns. So trying to add these columns with different lengths won't work. Since m_resb is defined to be all zeros, adding this to yb would not do anything. Additionally, since these are the only two references in the file to m_resb, I think m_resb should be replaces with m_res. If you replace the code above with the code below, the code runs.

//preinitialize 'yb' to zeros of final size
yb = zeros(rows(m_deter), cols(m_deter));
do while j<=re;
    tt=rows(m_res);

    i=1;
    do while i<=n;
        yb[.,i]=m_deter[.,i]+m_res[.,i];
        i=i+1;
    endo;

link

aptech

1,773

aptech · Answer 6

In the code, we see that both n and k are assigned to be the number of columns in the variable data. In the loop in which you have the question:

i=1;
    do while in;
        yb[.,i]=m_deter[.,i]+m_resb[.,i];
        i=i+1;
    endo;

the code is using columns from m_deter and m_resb. These variables are assigned with the following lines:

m_resb=zeros(t+30,n);
m_deter=zeros(bigt,k);

Since both variables have the same number of columns and the loop counter starts at 1 and ends in reference to n, I think it is safe to assume that the do while statement should be:

do while i <= n;

which would make the loop use all columns of m_deter and all columns of m_resb.

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aptech

1,773

013179 · Answer 7