Detecting autocovariance change in time series

A new test to detect changes in the covariance structure of a time series is developed. The test does not involve direct fitting of an assumed model for the time series. It is based on detecting changes in autocovariances calculated in a moving window through the series. The use of standard tests of time series change points is inappropriate because of the correlations imposed by the moving windows. This requires the development of new adjustments to existing time series change point tests. The ability of this moving window technique to detect changes in the lag one autocovariance of autoregressive and moving average time series is studied. We compare the performance of the moving window technique with seven parametric techniques for detecting change points in time series. We show that for long time series, the moving window technique outperforms these methods. Simulation results are used to determine appropriate number and width of windows and overlap percentage between two successive windows. We illustrate the application of this new test on UK treasury bill rates and airline travel data. The changes in covariances detected coincide with identifiable economic events that might have caused these changes.