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June, 1989 Consistency of Akaike's Information Criterion for Infinite Variance Autoregressive Processes
Keith Knight
Ann. Statist. 17(2): 824-840 (June, 1989). DOI: 10.1214/aos/1176347145

Abstract

Suppose $\{X_n\}$ is a $p$th order autoregressive process with innovations in the domain of attraction of a stable law and the true order $p$ unknown. The estimate $\hat{p}$ of $p$ is chosen to minimize Akaike's information criterion over the integers $0, 1, \cdots, K$. It is shown that $\hat{p}$ is weakly consistent and the consistency is retained if $K \rightarrow \infty$ as $N \rightarrow \infty$ at a certain rate depending on the index of the stable law.

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Keith Knight. "Consistency of Akaike's Information Criterion for Infinite Variance Autoregressive Processes." Ann. Statist. 17 (2) 824 - 840, June, 1989. https://doi.org/10.1214/aos/1176347145

Information

Published: June, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0672.62092
MathSciNet: MR994270
Digital Object Identifier: 10.1214/aos/1176347145

Subjects:
Primary: 62M10
Secondary: 60G10, 62F12

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 2 • June, 1989
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