GAUSS sarimaSS example

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
------------------------------------------------------------------------------------------

       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
------------------------------------------------------------------------------------------
*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

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