VARFROMDLM Procedure

@VARFromDLM generates a VAR representation for a selection of variables from a stationary DLM. The underlying state space model takes the form

\({{\bf{X}}_t} = {\bf{A}}{{\bf{X}}_{t - 1}} + {\bf{F}}{{\bf{w}}_t}\)

and the observables take the form

\({{\bf{Y}}_t} = {\bf{C'}}{{\bf{X}}_t}\)

The procedure generates the implied VAR coefficients and covariance matrix of residuals for \({\bf{Y}}\) given this structure.

@VARFromDLM( options )

Options

A=A matrix

F=F matrix [identity]

SW=Covariance matrix of W

C=loading matrix [identity]

LAGS=number of lags in the generated VAR [1]

CVOUT=(output) Implied VAR covariance matrix

PHI=(output) RECT[RECT] of implied VAR coefficients

This is a LAGS x LAGS array of m x m matrices. PHI(k,l) is an m x m matrix of lag coefficients at lag l for a k lag VAR. Thus, the final VAR will have coefficients in PHI(LAGS,1),...,PHI(LAGS,LAGS).