A Test for Detecting Changes in Mean

In the classical time series analysis, a process is often modeled as three additive components: long-time trend, seasonal effect and background noise. Then the trend superimposed with the seasonal effect constitutes the mean part of the process. The issue of mean stationarity, which is generically called change-point problem, is usually the first step for further statistical inference. In this paper we develop testing theory for the existence of a long-time trend. Applications to the global temperature data and the Darwin sea level pressure data are discussed. Our results extend and generalize previous ones by allowing dependence and general patterns of trends.