The Annals of Statistics

Residual empirical processes for long and short memory time series

Ngai Hang Chan and Shiqing Ling

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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.

Article information

Source
Ann. Statist., Volume 36, Number 5 (2008), 2453-2470.

Dates
First available in Project Euclid: 13 October 2008

Permanent link to this document
https://projecteuclid.org/euclid.aos/1223908099

Digital Object Identifier
doi:10.1214/07-AOS543

Mathematical Reviews number (MathSciNet)
MR2458194

Zentralblatt MATH identifier
1205.62128

Subjects
Primary: 62G30: Order statistics; empirical distribution functions
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Keywords
Empirical process long-memory time series residuals unit root weak convergence

Citation

Chan, Ngai Hang; Ling, Shiqing. Residual empirical processes for long and short memory time series. Ann. Statist. 36 (2008), no. 5, 2453--2470. doi:10.1214/07-AOS543. https://projecteuclid.org/euclid.aos/1223908099


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