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June, 1989 Strong Consistency of the PLS Criterion for Order Determination of Autoregressive Processes
E. M. Hemerly, M. H. A. Davis
Ann. Statist. 17(2): 941-946 (June, 1989). DOI: 10.1214/aos/1176347154

Abstract

This note concerns the problem of order determination for autoregressive models. Rissanen's "Predictive least squares principle" prescribes that one should choose as order estimate $\hat{k}(n)$ at time $n$ the order of the model which has given the least mean square prediction error up to that time. We show that this procedure is strongly consistent, that is, that $\hat{k}(n) \rightarrow p$ a.s. as $n \rightarrow \infty$ when the data are generated by an AR process of order $p$, given an upper bound $p^\ast$.

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E. M. Hemerly. M. H. A. Davis. "Strong Consistency of the PLS Criterion for Order Determination of Autoregressive Processes." Ann. Statist. 17 (2) 941 - 946, June, 1989. https://doi.org/10.1214/aos/1176347154

Information

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

zbMATH: 0675.62061
MathSciNet: MR994279
Digital Object Identifier: 10.1214/aos/1176347154

Subjects:
Primary: 62M10
Secondary: 60F15, 62M20, 93E12

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 2 • June, 1989
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