Object Reference : Object View and Procedure Reference : System
Multivariate residual normality test.
You must specify a factorization method using the “factor=” option.
Factorization by the inverse of the Cholesky factor of the residual covariance matrix.
Factorization by the inverse square root of the residual correlation matrix (Doornik and Hansen, 1994).
Factorization by the inverse square root of the residual covariance matrix (Urzua, 1997).
Save the test statistics in a named matrix object. See below for a description of the statistics contained in the stored matrix.
Force the dialog to appear from within a program.
Print the test results.
The “name=” option stores the following matrix. Let the VAR have endogenous variables. Then the stored matrix will have dimension . The first rows contain statistics for each orthogonal component, where the first column contains the third moments, the second column contains the statistics for the third moments, the third column contains the fourth moments, and the fourth column holds the statistics for the fourth moments. The sum of the second and fourth columns are the Jarque-Bera statistics reported in the last output table.
The last row contains statistics for the joint test. The second and fourth column of the row is simply the sum of all the rows above in the corresponding column and are the statistics for the joint skewness and kurtosis tests, respectively. These joint skewness and kurtosis statistics add up to the joint Jarque-Bera statistic reported in the output table, except for the “factor=cov” option. When this option is set, the joint Jarque-Bera statistic includes all cross moments (in addition to the pure third and fourth moments). The overall Jarque-Bera statistic for this statistic is stored in the first column of the row (which will be a missing value for all other options).
carries out the residual multivariate normality test using the inverse square root of the residual correlation matrix as the factorization matrix and stores the results in a matrix named JB.
See “Vector Autoregression (VAR) Models” for a discussion of the test in the context of VAR diagnostics.