Detecting periods in which a time series model fails to predict the observed volatility

The cumulative sums of squares (CUSUMSQ) provide a means for detecting change points in the volatility (variance) of time series. In this paper a new method for detecting such change points is proposed. The method is based on a combination of two existing algorithms and is intended to combine their positive features in a single algorithm. The results of a simulation experiment to compare the performance of the algorithms are presented and, as an example, the algorithm is applied to the CUSUMSQ of pseudo-residuals. This provides a method of detecting periods in which a time series model fails to predict the observed volatility.