Closed-form expression for finite predictor coefficients of multivariate ARMA processes

Inoue Akihiko

Journal of Multivariate Analysis

We derive a closed-form expression for the finite predictor coefficients of multivariate ARMA (autoregressive moving-average) processes. The expression is given in terms of several explicit matrices that are of fixed sizes independent of the number of observations. The significance of the expression is that it provides us with a linear-time algorithm to compute the finite predictor coefficients. In the proof of the expression, a correspondence result between two relevant matrix-valued outer functions plays a key role. We apply the expression to determine the asymptotic behavior of a sum that appears in the autoregressive model fitting and the autoregressive sieve bootstrap. The results are new even for univariate ARMA processes.

Finite predictor coefficients

Multivariate ARMA processes

Closed-form expression

Linear-time algorithm

eng

Elsevier

© 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

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[ISSN] 0047-259X

[DOI] 10.1016/j.jmva.2019.104578

[DOI] https://doi.org/10.1016/j.jmva.2019.104578