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June, 1986 Limit Theory for the Sample Covariance and Correlation Functions of Moving Averages
Richard Davis, Sidney Resnick
Ann. Statist. 14(2): 533-558 (June, 1986). DOI: 10.1214/aos/1176349937

Abstract

Let $X_t = \sum^\infty_{j=-\infty} c_jZ_{t-j}$ be a moving average process where the $Z_t$'s are iid and have regularly varying tail probabilities with index $\alpha > 0$. The limit distribution of the sample covariance function is derived in the case that the process has a finite variance but an infinite fourth moment. Furthermore, in the infinite variance case $(0 < \alpha < 2)$, the sample correlation function is shown to converge in distribution to the ratio of two independent stable random variables with indices $\alpha$ and $\alpha/2$, respectively. This result immediately gives the limit distribution for the least squares estimates of the parameters in an autoregressive process.

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Richard Davis. Sidney Resnick. "Limit Theory for the Sample Covariance and Correlation Functions of Moving Averages." Ann. Statist. 14 (2) 533 - 558, June, 1986. https://doi.org/10.1214/aos/1176349937

Information

Published: June, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0605.62092
MathSciNet: MR840513
Digital Object Identifier: 10.1214/aos/1176349937

Subjects:
Primary: 62M10
Secondary: 60F05, 62E20

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 2 • June, 1986
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