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Computation of vector ARMA autocovariances. (English) Zbl 1417.62253
Summary: This note describes an algorithm for computing the autocovariance sequence of a VARMA process, without requiring the intermediary step of determining the Wold representation. Although the recursive formula for the autocovariances is well-known, the initialization of this recursion in standard treatments (such as [P. J. Brockwell and R. A. Davis, Time series: theory and methods. 2nd ed. Berlin etc.: Springer-Verlag (1991; Zbl 0709.62080); H. Lütkepohl, New introduction to multiple time series analysis. Corrected 2nd printing. Berlin: Springer (2006; Zbl 1141.62071)] is slightly nuanced; we provide explicit formulas and algorithms for the initial autocovariances.
MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
65C50 Other computational problems in probability (MSC2010)
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