The Annals of Statistics

Nonparametric model checks for time series

Hira L. Koul and Winfried Stute

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Abstract

This paper studies a class of tests useful for testing the goodness-of-fit of an autoregressive model. These tests are based on a class of empirical processes marked by certain residuals. The paper first gives their large sample behavior under null hypotheses. Then a martingale transformation of the underlying process is given that makes tests based on it asymptotically distribution free. Consistency of these tests is also discussed briefly.

Article information

Source
Ann. Statist., Volume 27, Number 1 (1999), 204-236.

Dates
First available in Project Euclid: 5 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1018031108

Digital Object Identifier
doi:10.1214/aos/1018031108

Mathematical Reviews number (MathSciNet)
MR1701108

Zentralblatt MATH identifier
0955.62089

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62M30: Spatial processes 62J02: General nonlinear regression

Keywords
Marked empirical process $\psi$-residuals martingale transform tests autoregressive median function

Citation

Koul, Hira L.; Stute, Winfried. Nonparametric model checks for time series. Ann. Statist. 27 (1999), no. 1, 204--236. doi:10.1214/aos/1018031108. https://projecteuclid.org/euclid.aos/1018031108


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