SEQUENTIAL CHANGE-POINT DETECTION IN GARCH(p,q) MODELS
提出一种基于拟似然得分的序列监测方法，用于检测GARCH模型参数变化，无需模型残差，且边界函数可设为常数，渐近控制检验规模。
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.