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Multiple Time Series Identification

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V.III.1 Multiple Time Series Identification

Define the stable vector autoregressive (VAR(p)) model as

Multiple Time Series Identification

(V.III.1-1)

If a VAR model is stable it can be written in MA representation

(V.III.1-2)

The stable and invertible VARMA(p,q) process is defined by

(V.III.1-3)

Note that the stability condition ensures that the VARMA process can be written in pure MA form, whereas the invertibility condition enables a pure VAR representation.

Numerous identification procedures for VAR, and VARMA models have been considered in literature. Two main groups of identification strategies can be found: the strategies based on model selection criteria such as AIC (c.q. a trial and error strategy), and the strategies using some kind of correlation measure. To date, however, no one method has become the standard procedure (unlike in the univariate case where the Box-Jenkins approach can be considered to be the standard).
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