B1480
Title: On the finite sample behaviour of the cusum test
Authors: Alexander Duerre - TU Dortmund (Germany) [presenting]
Abstract: The cusum test is a very popular tool in nonparametric change point analysis. It is applied to decide whether an observed time series remains stationary or exhibits a structural change. Under the null hypothesis of no change, the cusum trajectory converges under very general conditions against a Brownian bridge. If there is one level shift, the trajectory gets more triangular shaped and attains larger absolute values, which is the reason one usually looks at the maximal absolute value of the cusum trajectory. This value converges to the Kolmogorov-Smirnov distribution. However, the test statistic is seriously biased which leads to conservative tests under the null hypothesis and a loss of power under the alternative. We show that this distortion, under independent normally distributed random variables, is of order $n^{(-1/2)}$ where $n$ is the sample size. There is a straightforward correction, and we show that this correction is also reasonable in case of other symmetric distributions. Serial dependence results in even more conservative behaviour. We investigate the error under autoregressive processes.
