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March, 1976 The Asymptotic Distribution of Serial Covariances
E. J. Hannan
Ann. Statist. 4(2): 396-399 (March, 1976). DOI: 10.1214/aos/1176343415


A central limit theorem is proved for the sample serial covariances of an ergodic, stationary, purely nondeterministic process whose linear innovations have their first four moments as for a sequence of independent random variables. The necessary and sufficient condition for the theorem is then that the spectra be square integrable.


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E. J. Hannan. "The Asymptotic Distribution of Serial Covariances." Ann. Statist. 4 (2) 396 - 399, March, 1976.


Published: March, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0328.62059
MathSciNet: MR398029
Digital Object Identifier: 10.1214/aos/1176343415

Primary: 62M10
Secondary: 60G10

Keywords: central limit theorem , serial covariances , stationary process

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 2 • March, 1976
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