Abstract
In this chapter, the canonical structure of vector ARMA model representations is briefly discussed through the introduction of the concepts of Kronecker indices and McMillan degree of a vector process {Yt}, and the echelon canonical form of the vector ARMA model is presented in particular. Canonical correlation structure for stationary vector ARMA processes is examined, and the relation between canonical correlation structure and the associated notion of scalar component models, introduced by Tiao and Tsay (1989) to specify simplifying structure for the vector ARMA model parameterization, is discussed. The partial correlation matrices and partial canonical correlations of a stationary vector process, and their special features for pure AR models, are also considered.
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© 1993 Springer-Verlag New York, Inc.
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Reinsel, G.C. (1993). Canonical Structure of Vector ARMA Models. In: Elements of Multivariate Time Series Analysis. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0198-1_3
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DOI: https://doi.org/10.1007/978-1-4684-0198-1_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-0200-1
Online ISBN: 978-1-4684-0198-1
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