Modified tests for variance changes in autoregressive regression

In this paper, we consider the problem of testing for variance changes in the linear autoregressive processes including AR(p) processes meanwhile autoregressive parameters shifts occur. In performing a test, we employ the conventional residual CUSUM of squares test (RCUSQ) statistic. The RCUSQ test is based on the bootstrap method introduced to eliminate the influence caused by the autoregressive parameters shifts. It is shown that under regularity conditions, the test statistic behaves asymptotically the function of a standard Brownian bridge. Simulation results as to AR(1) processes and an example of real data analysis are provided for illustration.