A Method For Detecting Changes In Long Time Series

Abstract Modern scientific activities, both physical and computational can result in time series of many thousands or even millions of data values. Here we describe a statistically motivated algorithm for quick screening of very long time series data for the presence of potentially interesting but arbitrary changes. The basic data model is a stationary Gaussian stochastic process, and the approach to detecting a change is the comparison of two predictions of the series at a time point or contiguous collection of time points. One prediction is a "forecast", i.e. based on data from earlier times, while the other a "backcast", i.e. based on data from later times. The statistic is the absolute value of the log-likelihood ratio for these two predictions, evaluated at the observed data. A conservative procedure is suggested for specifying critical values for the statistic under the null hypothesis of "no change". - vii - 1. Introduction By "time series", we generally mean a sequence of da..