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