A New Look at the Change-point Problem

Tuesday, November 13, 2001 - 11:00am - 12:00pm
Keller 3-180
Wei Wu (University of Chicago)
In classical time series analysis, processes are often modelled as three additive components: long-time trend, seasonal effect and background noise. Then the trend superimposed with the seasonal effect constitute the mean part of the process. The issue of mean stationarity is usually the first step for further statistical inference. In this talk, we present testing and estimation theory for the existence of a monotonic trend and the identification of seasonal effects. The associated statistical inference is generically called change-point problem, or probabilistic diagnostics, which has been one of the central issues of statistics for several decades. Change-point problem initially arose in quality control assessment. It includes, for example, the testing for changes in weather patterns and disease rates. Here we mainly consider a posteriori testing. We apply the isotonic regression to test and estimate the trend, and the spectral analysis to determine periodic components.

A distinctive feature of our approach is that these two problems can be treated simultaneously. The isotonic regression gives estimators for the long-time trend with negligible influence from the seasonal effect.