Changepoint detection in a nonparametric time series regression model

A weakly dependent time series is considered, for which we develop a strategy to detect whether the nonparametric conditional mean function is stable in time. The strategy allows for autoregressive effects and heteroscedasticity. Our proposal is based on a modified CUSUM-type test procedure, which uses a sequential marked empirical process of residuals. We show weak convergence of the considered process to a centered Gaussian process under the null ”mt(·) = m(·) for all t” and a stationarity assumption. This requires some sophisticated arguments for sequential empirical processes of weakly dependent variables. As a consequence we obtain the convergence of Kolmogorov-Smirnov
and Cramér-von Mises type test statistics. The procedure acquires a very simple limiting distribution and nice consistency properties against changepoint alternatives, features from which related tests are lacking. Further considerations include a bootstrap procedure as well as a test for change in the conditional variance function. Finally, a simulation study is conducted to investigate the finite sample performance of our tests.