The VARMAX Procedure
- Overview
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Getting Started
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Syntax
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Details
Missing Values VARMAX Model Dynamic Simultaneous Equations Modeling Impulse Response Function Forecasting Tentative Order Selection VAR and VARX Modeling Bayesian VAR and VARX Modeling VARMA and VARMAX Modeling Model Diagnostic Checks Cointegration Vector Error Correction Modeling I(2) Model Multivariate GARCH Modeling Output Data Sets OUT= Data Set OUTEST= Data Set OUTHT= Data Set OUTSTAT= Data Set Printed Output ODS Table Names ODS Graphics Computational Issues
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Examples
- References
| Model Diagnostic Checks |
Multivariate Model Diagnostic Checks
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Information Criterion After fitting some candidate models to the data, various model selection criteria (normalized by
) can be used to choose the appropriate model. The following list includes the Akaike information criterion (AIC), the corrected Akaike information criterion (AICC), the final prediction error criterion (FPE), the Hannan-Quinn criterion (HQC), and the Schwarz Bayesian criterion (SBC, also referred to as BIC): 
where
denotes the number of parameters estimated, 
is the number of dependent variables, is the number of observations used to estimate the model, and 
is the maximum likelihood estimate of 
. When comparing models, choose the model with the smallest criterion values. An example of the output was displayed in Figure 35.4.
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Portmanteau
statistic The Portmanteau statistic is used to test whether correlation remains on the model residuals. The null hypothesis is that the residuals are uncorrelated. Let 
be the residual cross-covariance matrices, 
be the residual cross-correlation matrices as 
and
where
and 
are the diagonal elements of 
. The multivariate portmanteau test defined in Hosking (1980) is 
The statistic
has approximately the chi-square distribution with 
degrees of freedom. An example of the output is displayed in Figure 35.7.
Univariate Model Diagnostic Checks
There are various ways to perform diagnostic checks for a univariate model. For details, see the section Testing for Nonlinear Dependence: Heteroscedasticity Tests in Chapter 8, The AUTOREG Procedure. An example of the output is displayed in Figure 35.8 and Figure 35.9.
Durbin-Watson (DW) statistics: The DW test statistics test for the first order autocorrelation in the residuals.
Jarque-Bera normality test: This test is helpful in determining whether the model residuals represent a white noise process. This tests the null hypothesis that the residuals have normality.
tests for autoregressive conditional heteroscedastic (ARCH) disturbances: test statistics test for the heteroscedastic disturbances in the residuals. This tests the null hypothesis that the residuals have equal covariances - tests for AR disturbance: These test statistics are computed from the residuals of the univariate AR(1), AR(1,2), AR(1,2,3) and AR(1,2,3,4) models to test the null hypothesis that the residuals are uncorrelated.