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Note on the Asymptotic Efficiency of Sample Covariances in Gaussian Vector Stationary Processes
Author(s) -
Kakizawa Yoshihide
Publication year - 1999
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00156
Subject(s) - autocovariance , mathematics , gaussian , gaussian process , zero (linguistics) , asymptotically optimal algorithm , sample (material) , mathematical analysis , mathematical optimization , fourier transform , physics , linguistics , philosophy , quantum mechanics , thermodynamics
In this note certain results obtained by Porat ( J. Time Ser. Anal. 8 (1987), 205–20) and Kakizawa and Taniguchi ( J. Time Ser. Anal. 15 (1994), 303–11) concerning the asymptotic efficiency of sample autocovariances of a zero‐mean Gaussian stationary process are extended to the case of m ‐vector processes. It is shown that, for Gaussian vector AR( p ) processes, the sample autocovariance matrix at lag k is asymptotically efficient if 0 ≤ k ≤ p . Further, none of the sample autocovariance matrices is asymptotically efficient for Gaussian vector MA( q ) processes.