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.