GAUSS arimaSS Example

Introduction

The following is an example of implementing the arimaSS procedure for state space estimation of ARIMA models. It considers an ARIMA(1,1,1) model of the U.S wholesale price index (WPI) between 1960q1 and 1990q4 and follows the model of Enders (2004).

Load data

This example loads the data using the GAUSS function loadd.

new;
library tsmt;

// Create file name with full path
fname = getGAUSSHome() $+ "pkgs/tsmt/examples/wpi1.dat";

// Load variable 'wpi' from dataset
y = loadd(fname, "wpi");

Estimate The Model

The GAUSS function arimaSS uses Kalman Filtering and State Space modeling to estimate the ARIMA(1,1,1) model.

// ARIMA model settings
p = 1;
d = 1;
q = 1;
trend = 0;
const = 1;

// Perform estimation and print report
call arimaSS(y, p, d, q, trend, const);

Output

The output reads:

Number of Observations:                 123.0000
Degrees of Freedom:                          119
Mean of Y:                               62.7742
Standard Deviation of Y:                 30.2436
Sum of Squares of Y:                 112504.7755

                           COEFFICIENTS

Coefficient Estimates

     Variables      Coefficient             se          tstat             pval
  phi : y[t-1]         0.868***         0.0639           13.6         4.66e-42
theta : e[t-1]        -0.406***          0.123           -3.3         0.000983
        Sigma2         0.524***         0.0462           11.3         7.69e-30
      Constant            0.8**          0.296           2.71           0.0068

*p-val<0.1 **p-val<0.05 ***p-val<0.001
Dep. Variable(s) : Y1 No. of Observations : 123 Degrees of Freedom : 119 Mean of Y : 0.6951 Std. Dev. of Y : 0.9800 Y Sum of Squares : 117.1570 SSE : 68.4063 MSE : 17.1016 sqrt(MSE) : 4.1354 Model Selection (Information) Criteria ...................................... Likelihood Function : -135.4639 Akaike AIC : 262.9278 Schwarz BIC : 290.1765 Likelihood Ratio : 270.9278

Have a Specific Question?

Get a real answer from a real person

Need Support?

Get help from our friendly experts.

REQUEST A FREE QUOTE

Thank you for your interest in the GAUSS family of products.

© Aptech Systems, Inc. All rights reserved.

Privacy Policy | Sitemap