The Annals of Statistics

Weak Convergence of the Residual Empirical Process in Explosive Autoregression

Hira L. Koul and Shlomo Levental

Full-text: Open access

Abstract

This paper proves the weak convergence of the residual empirical process in an explosive autoregression model to the Brownian bridge. As an application the Kolmogorov-Smirnov goodness-of-fit test for testing that the errors have a specified distribution is shown to be asymptotically distribution-free.

Article information

Source
Ann. Statist., Volume 17, Number 4 (1989), 1784-1794.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347395

Digital Object Identifier
doi:10.1214/aos/1176347395

Mathematical Reviews number (MathSciNet)
MR1026313

Zentralblatt MATH identifier
0695.60042

JSTOR
links.jstor.org

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Keywords
Brownian bridge goodness-of-fit test asymptotically distribution-free exponential inequality

Citation

Koul, Hira L.; Levental, Shlomo. Weak Convergence of the Residual Empirical Process in Explosive Autoregression. Ann. Statist. 17 (1989), no. 4, 1784--1794. doi:10.1214/aos/1176347395. https://projecteuclid.org/euclid.aos/1176347395


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