ASYMPTOTIC EFFICIENCY OF THE SAMPLE COVARIANCES IN A GAUSSIAN STATIONARY PROCESS

Yoshihide Kakizawa, Masanobu Taniguchi

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Abstract. This paper deals with the asymptotic efficiency of the sample autocovariances of a Gaussian stationary process. The asymptotic variance of the sample autocovariances and the Cramer–Rao bound are expressed as the integrals of the spectral density and its derivative. We say that the sample autocovariances are asymptotically efficient if the asymptotic variance and the Cramer–Rao bound are identical. In terms of the spectral density we give a necessary and sufficient condition that they are asymptotically efficient. This condition is easy to check for various spectra.

Original languageEnglish
Pages (from-to)303-311
Number of pages9
JournalJournal of Time Series Analysis
Volume15
Issue number3
DOIs
Publication statusPublished - 1994
Externally publishedYes

Keywords

  • Asymptotic efficiency
  • Cramer–Rao bound
  • Gaussian stationary process
  • sample autocovariance
  • spectral density
  • Toeplitz matrix

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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