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MONITORING CONSTANCY OF VARIANCE IN CONDITIONALLY HETEROSKEDASTIC TIME SERIES

Published online by Cambridge University Press:  15 March 2006

Lajos Horváth ,
Piotr Kokoszka  and
Aonan Zhang
Lajos Horváth
Affiliation:
University of Utah
Piotr Kokoszka
Affiliation:
Utah State University
Aonan Zhang
Affiliation:
Bank of America
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Abstract

We propose several methods of on-line detection of a change in unconditional variance in a conditionally heteroskedastic time series. We follow the paradigm of Chu, Stinchcombe, and White (1996, Econometrica 64, 1045–1065) in which the first m observations are assumed to follow a stationary process and the monitoring scheme has asymptotically controlled probability of falsely rejecting the null hypothesis of no change. Our theory is applicable to broad classes of GARCH-type time series and relies on a strong invariance principle that holds for the squares of observations generated by such models. Practical implementation of the procedures, which uses a bandwidth selection procedure of Andrews (1991, Econometrica 59, 817–858), is proposed, and the performance of the methods is investigated by a simulation study.This research was partially supported by NSF grants INT-0223262 and DMS-0413653 and NATO grant PST.EAP.CLG 980599.

Type
Research Article
Information
Econometric Theory , Volume 22 , Issue 3 , June 2006 , pp. 373 - 402
Copyright
© 2006 Cambridge University Press

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