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Analysis of Financial Time Series, Third Edition by RUEY S. TSAY

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8.3 Vector Moving-Average Models

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

8.23 8.23

where Inline is a k-dimensional vector, Inline are k × k matrices, and Inline 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 Inline of Inline exists. Taking expectation of Eq. (8.23), we obtain that Inline. Thus, the constant vector Inline is the mean vector of Inline for a VMA model.

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

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