GAUSS varmaFit example

Introduction

This example estimates a VARMA(3,0,0) model following Example 4.1 found on page 86 of Reinsel, G.C. Elements of Multivariate Time Series Analysis. The dataset "mink.csv" contains the data.

Step 1: Load data

This example loads the data using the GAUSS function loadd. The function loadd utilizes the GAUSS formula string syntax and allows users to load and transform specific variables directly from the dataset.

new;
library tsmt;

// Load data
// Create file name with full path
fname = getGAUSSHome() $+ "pkgs/tsmt/examples/mink.csv";

// Load two variables from dataset
y = loadd(fname, "LogMink + LogMusk");

// Difference the data
y = vmdiffmt(y, 1);

Step 2: Estimate The Model

Because this model is strictly a VAR model, the only additional input after the data matrix is the AR order.

// Estimate the parameters of the VAR(3) model
// and print diagnostic information
call varmaFit(y, 3);

Step 3: Output

The coefficient estimates from varmaFit read

Phi

Plane [1,.,.]

 -0.065819    0.56348
  -0.55990    0.25347

Plane [2,.,.]

   0.16426   -0.27348
  -0.31914   -0.30793

Plane [3,.,.]

  -0.21124    0.34758
  -0.45904    0.32457

In addition to estimating coefficients, varmaFit provides a number of diagnostic tests. The tests include unit root and cointegration tests:

Augmented Dickey-Fuller UNIT ROOT Test for    Y1
                                                          Critical Values
                               ADF Stat        1%       5%       10%      90%      95%     99%
   No Intercept                -5.2278     -2.5328  -1.9498  -1.6266   0.9152   1.3168   2.1179
   Intercept                   -5.1774     -3.5663  -2.9370  -2.6152  -0.4393  -0.0499   0.6942
   Intercept and Time Trend    -5.2981     -4.0892  -3.4615  -3.1709  -1.2584  -0.9195  -0.2986

Augmented Dickey-Fuller UNIT ROOT Test for    Y2
                                                          Critical Values
                               ADF Stat        1%       5%       10%      90%      95%     99%
   No Intercept                -4.7720     -2.5328  -1.9498  -1.6266   0.9152   1.3168   2.1179
   Intercept                   -4.7352     -3.5663  -2.9370  -2.6152  -0.4393  -0.0499   0.6942
   Intercept and Time Trend    -4.6155     -4.0892  -3.4615  -3.1709  -1.2584  -0.9195  -0.2986

Phillips-Perron UNIT ROOT Test for    Y1
                                  PPt      1%      5%
   No Intercept                -7.2621  -2.5328  -1.9498
   Intercept                   -6.9186  -3.5663  -2.9370
   Intercept and Time Trend    -6.9497  -4.0892  -3.4615

Phillips-Perron UNIT ROOT Test for    Y2
                                  PPt      1%      5%
   No Intercept                -6.3499  -2.5328  -1.9498
   Intercept                   -5.9127  -3.5663  -2.9370
   Intercept and Time Trend    -5.8505  -4.0892  -3.4615

Augmented Dickey-Fuller COINTEGRATION Test for    Y1    Y2

                                                          Critical Values
                               ADF Stat        1%       5%       10%      90%      95%     99%
   No Intercept                -5.0448     -3.4003  -2.8198  -2.4901  -0.2841   0.1628   0.9912
   Intercept                   -5.0375     -4.0246  -3.4040  -3.0890  -0.9988  -0.6383   0.0929
   Intercept and Time Trend    -5.1691     -4.5041  -3.9157  -3.6062  -1.6464  -1.3413  -0.6750

Johansen's  Trace  and  Maximum  Eigenvalue  Statistics. r = # of CI Equations
                                                                      Critical Values
                               r    Trace    Max. Eig          1%       5%       10%      90%
   No Intercept                0   65.5906   46.3981
                               1   19.1925   19.1925         1.0524   1.7046   2.1927   9.3918

   Intercept                   0   65.6102   46.4140
                               1   19.1962   19.1962         2.2515   3.3599   4.0975  12.8635

   Intercept and Time Trend    0   66.2392   46.3986
                               1   19.8406   19.8406         4.0389   5.3796   6.1879  16.1762