# 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".

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";

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

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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