Sequential monitoring for changes from stationarity to mild non-stationarity

We develop and study sequential testing procedures á la Chu et al. (1996) for on-line detection of changes in a time series from stationarity to mild forms of non-stationarity. The proposed tests are based on sequential CUSUM and KPSS-type detector processes, and are shown to provide consistent detection under a wide range of change point models, including changes in the parameters of ARMA and GARCH series from values within the model’s stationarity parameter region to values close (converging) to the stationarity boundary. Local asymptotic results are established giving precise descriptions of the time to detection under several of these models, which show that such procedures are powerful to detect a wide range of non-stationary characteristics, including changes in mean, volatility, and unit root behaviour. The proposed methods are investigated by means of a simulation study and in applications to monitoring for changes in trend and unit root behaviour in macroeconomic production series, and to detect changes in volatility of the S&P-500 stock market index.