The Annals of Statistics

The Asymptotic Distribution of Serial Covariances

E. J. Hannan

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 4, Number 2 (1976), 396-399.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343415

Digital Object Identifier
doi:10.1214/aos/1176343415

Mathematical Reviews number (MathSciNet)
MR398029

Zentralblatt MATH identifier
0328.62059

JSTOR
links.jstor.org

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 60G10: Stationary processes

Keywords
Stationary process serial covariances central limit theorem

Citation

Hannan, E. J. The Asymptotic Distribution of Serial Covariances. Ann. Statist. 4 (1976), no. 2, 396--399. doi:10.1214/aos/1176343415. https://projecteuclid.org/euclid.aos/1176343415


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