Model Specification in Multivariate Time Series

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Abstract
We propose a method to specify an appropriate yet parsimonious vector autoregressive moving average (ARMA) model for a given multivariate time series. By considering contemporaneous linear transformations of the vector process, we introduce the concept of scalar component models within the vector ARMA framework (a) to reveal possibly hidden simplifying structures of the process, (b) to achieve parsimony in parameterization and (c) to identify the exchangeable models. The simplifying structures are of particular importance in the analysis of multivariate time series because they are often not obvious from the observed data but can be used to gain insights to the process under study. The analytical tool used to search for scalar component models is a canonical correlation analysis of vector processes and the proposed procedures are illustrated via two real examples.