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SEQUENTIAL CHANGE-POINT DETECTION IN GARCH(p,q) MODELS

Published online by Cambridge University Press:  01 December 2004

István Berkes ,
Edit Gombay ,
Lajos Horváth  and
Piotr Kokoszka
István Berkes
Affiliation:
Hungarian Academy of Sciences
Edit Gombay
Affiliation:
University of Alberta
Lajos Horváth
Affiliation:
University of Utah
Piotr Kokoszka
Affiliation:
Utah State University
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Abstract

We suggest a sequential monitoring scheme to detect changes in the parameters of a GARCH(p,q) sequence. The procedure is based on quasi-likelihood scores and does not use model residuals. Unlike for linear regression models, the squared residuals of nonlinear time series models such as generalized autoregressive conditional heteroskedasticity (GARCH) do not satisfy a functional central limit theorem with a Wiener process as a limit, so its boundary crossing probabilities cannot be used. Our procedure nevertheless has an asymptotically controlled size, and, moreover, the conditions on the boundary function are very simple; it can be chosen as a constant. We establish the asymptotic properties of our monitoring scheme under both the null of no change in parameters and the alternative of a change in parameters and investigate its finite-sample behavior by means of a small simulation study.This research was partially supported by NSF grant INT-0223262 and NATO grant PST.CLG.977607. The work of the first author was supported by the Hungarian National Foundation for Scientific Research, grants T 29621, 37886; the work of the second author was supported by NSERC Canada.

Type
Research Article
Information
Econometric Theory , Volume 20 , Issue 6 , December 2004 , pp. 1140 - 1167
Copyright
© 2004 Cambridge University Press

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