On the cusum of squares test for variance change in nonstationary and nonparametric time series models

In this paper we consider the problem of testing for a variance change in nonstationary and nonparametric time series models. The models under consideration are the unstable AR(q) model and the fixed design nonparametric regression model with a strong mixing error process. In order to perform a test, we employ the cusum of squares test introduced by Inclan and Tiao (1994, J. Amer. Statist. Assoc., 89, 913-923). It is shown that the limiting distribution of the test statistic is the sup of a standard Brownian bridge as seen in iid random samples. Simulation results are provided for illustration.