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ASYMPTOTIC EFFICIENCY OF THE SAMPLE COVARIANCES IN A GAUSSIAN STATIONARY PROCESS
Author(s) -
Kakizawa Yoshihide,
Taniguchi Masanobu
Publication year - 1994
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/j.1467-9892.1994.tb00195.x
Subject(s) - mathematics , asymptotically optimal algorithm , gaussian , variance (accounting) , gaussian process , sample (material) , sample variance , spectral density , derivative (finance) , stationary process , upper and lower bounds , statistics , mathematical analysis , mathematical optimization , chemistry , physics , accounting , chromatography , quantum mechanics , economics , financial economics , business
. 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.