Changepoint Detection in Periodic and Autocorrelated Time Series

Abstract

Undocumented changepoints (inhomogeneities) are ubiquitous features of climatic time series. Level shifts in time series caused by changepoints confound many inference problems and are very important data features. Tests for undocumented changepoints from models that have independent and identically distributed errors are by now well understood. However, most climate series exhibit serial autocorrelation. Monthly, daily, or hourly series may also have periodic mean structures. This article develops a test for undocumented changepoints for periodic and autocorrelated time series. Classical changepoint tests based on sums of squared errors are modified to take into account series autocorrelations and periodicities. The methods are applied in the analyses of two climate series.