Introduction
The following is an example of implementing the sarimaSS procedure for state space estimation of SARIMA models. This example reproduces the Box and Jenkins (1976) Series G dataset to estimate the SARIMA(0,1,1)(0,1,1) "airline model".
Step 1: Load data
This example loads the data using the GAUSS function loadd.
new;
library tsmt;
// Create file name with full path
dataset = getGAUSSHome() $+ "pkgs/tsmt/examples/airline.dat";
// Load and transform data
y = loadd(dataset, "ln(airline)");Step 2: Estimate the model
The GAUSS function sarimaSS uses Kalman Filtering and State Space modelling to estimate the SARIMA(0,1,1)(0,1,1) model.
p = 0;
d = 1;
q = 1;
P_s = 0;
D_s = 1;
Q_s = 1;
s = 12;
trend = 0;
const = 0;
// Estimate model
call sarimaSS(y, p, d, q, P_s, D_s, Q_s, s, trend, const);Step 3: Output
The output reads
SARIMA(0,1,1)(0,1,1) Results
Number of Observations: 131.0000
Degrees of Freedom: 127
Mean of Y: 5.5422
Standard Deviation of Y : 0.4415
Sum of Squares of Y: 27.8684
COEFFICIENTS
Coefficient Estimates
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Variables Coefficient se tstat pval
theta : e[t-1] -0.407 1 -0.407 0.684
theta : e[t-1] -0.551 1 -0.551 0.582
Sigma2 0.0014 1 0.0014 0.999
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*p-val<0.1 **p-val<0.05 ***p-val<0.001
Dep. Variable(s) : Y1 No. of Observations : 131
Degrees of Freedom : 127
Mean of Y : 0.0003
Std. Dev. of Y : 0.0458
Y Sum of Squares : 0.2733
SSE : 0.1835
MSE : 0.0459
sqrt(MSE) : 0.2142
Model Selection (Information) Criteria
......................................
Likelihood Function : 244.5181
Akaike AIC : -497.0362
Schwarz BIC : -469.5354
Likelihood Ratio : -489.0362