Detecting points of change in time series

A performance comparison study of six time-series change detection procedures via forecast-monitoring simulation is presented. Four of the procedures are due to Brown [1], Page [2], Box and Tiao [3] and Gardner [4]. The other two sequential detection schemes are developed in this paper; the first is based on Bagshaw and Johnson [5], while the second employs a moving-block estimator of innovations autocovariance. Eighty synthetic time series were generated, using an autoregressive model, an integrated-moving average model and a time-regression model having step changes in the parameters. The statistics being employed are based upon cumulative sum (cusum), squared cusum and discounted cusum of the innovations from the corresponding forecasting models. Results of this study indicate that the procedures which employ squared cusum and nondiscounted cusum of innovations yield smaller rates of false detection. The two best change-detection statistics of this study appear to possess good potential for industrial and business forecast monitoring applications.