On the asymptotic properties of multivariate sample autocovariances

  • Authors:

  • Georgi N. Boshnakov

  • Affiliations:

  • Mathematics Department, University of Manchester Institute of Science and Technology, P. O. Box 88, Manchester M60 1QD, UK

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2005

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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.