# 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).

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

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.