On the asymptotic properties of multivariate sample autocovariances

Boshnakov, Georgi N. (2005) On the asymptotic properties of multivariate sample autocovariances. Journal of Multivariate Analysis, 92 (1). pp. 42-52. ISSN 0047-259X

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Abstract

We show that if a process can be obtained by filtering an autoregressive process, then the asymptotic distribution of sample autocovariances of the former is the same as the asymptotic distribution of linear combinations of sample autocovariances of the latter. This result is used to show that for small lags the sample autocovariances of the filtered process have the same asymptotic distribution as estimators utilizing more information (observations on the associated autoregression process and knowledge of the parameters of the filter). In particular, for a Gaussian ARMA process the first few sample autocovariances are jointly asymptotically efficient.

Item Type:	Article
Uncontrolled Keywords:	Asymptotic efficiency; Multivariate ARMA; Serial covariances
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes MSC 2010, the AMS's Mathematics Subject Classification > 62 Statistics
Depositing User:	Ms Lucy van Russelt
Date Deposited:	19 Jul 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/400

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