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.