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October 2008 Residual empirical processes for long and short memory time series
Ngai Hang Chan, Shiqing Ling
Ann. Statist. 36(5): 2453-2470 (October 2008). DOI: 10.1214/07-AOS543

Abstract

This paper studies the residual empirical process of long- and short-memory time series regression models and establishes its uniform expansion under a general framework. The results are applied to the stochastic regression models and unstable autoregressive models. For the long-memory noise, it is shown that the limit distribution of the Kolmogorov–Smirnov test statistic studied in Ho and Hsing [Ann. Statist. 24 (1996) 992–1024] does not hold when the stochastic regression model includes an unknown intercept or when the characteristic polynomial of the unstable autoregressive model has a unit root. To this end, two new statistics are proposed to test for the distribution of the long-memory noises of stochastic regression models and unstable autoregressive models.

Citation

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Ngai Hang Chan. Shiqing Ling. "Residual empirical processes for long and short memory time series." Ann. Statist. 36 (5) 2453 - 2470, October 2008. https://doi.org/10.1214/07-AOS543

Information

Published: October 2008
First available in Project Euclid: 13 October 2008

zbMATH: 1205.62128
MathSciNet: MR2458194
Digital Object Identifier: 10.1214/07-AOS543

Subjects:
Primary: 62G30
Secondary: 62M10

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 5 • October 2008
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