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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:176

Article

Inoue, Akihiko¹ 

[1] Hiroshima Univ, Dept Math, Higashihiroshima 7398526, Japan

关键词: Finite predictor coefficients;    Multivariate ARMA processes;    Closed-form expression;    Linear-time algorithm;   

DOI  :  10.1016/j.jmva.2019.104578

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free