Change Detection by Monitoring Residuals from Time Series Models

Change detection in time series can be approached by fitting a model to the no-change, ordinary background data and then monitoring time series of residuals, where a residual is defined as residual = data - fit. In many applications, models that fit time series data lead to residuals that exhibit no patterns unless the signal of interest is present. Therefore, an effective signal or change detection approach is to first fit a time series model to the background data without any signal and then monitor the time series of residuals for evidence of the signal. This chapter briefly reviews a few time series modeling options and then focuses on statistical tests for monitoring residuals, including Page's cumulative sum (cusum, a type of scan statistic), the ordinary cumulative sum (cumsum), the matched filter (a version of the Neyman-Pearson test statistic), and pattern tests, such as those used in quality control. Simulation and analytical approximation methods are recommended for studying test behavior, as illustrated in three examples.