MONITORING CONSTANCY OF VARIANCE IN CONDITIONALLY HETEROSKEDASTIC TIME SERIES

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.