8.3 Vector Moving-Average Models

A vector moving-average model of order q, or VMA(q), is in the form

where is a k-dimensional vector, are k × k matrices, and is the MA matrix polynomial in the back-shift operator B. Similar to the univariate case, VMA(q) processes are weakly stationary provided that the covariance matrix of exists. Taking expectation of Eq. (8.23), we obtain that . Thus, the constant vector is the mean vector of for a VMA model.

Let be the mean-corrected VAR(q) process. ...

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