A Self-Normalized Approach to Testing for Change Points in Time Series

• Activity Number: 545
• Type: Invited
• Date/Time: Wednesday, August 3, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Xiaofeng Shao*+
• Companies: University of Illinois at Urbana-Champaign
• Keywords: change point ; cusum ; invariance principle ; self-normalization

Abstract

In this talk, we introduce a new class of change point test statistics in the time series setting. To test for a mean shift, the traditional Kolmogorov-Smirnov CUSUM-based test statistic involves a consistent long run variance estimator, which is needed to make the limiting null distribution free of nuisance parameters. The commonly used long run variance estimator requires to choose a bandwidth parameter and its selection is a difficult task in practice. The bandwidth that is a fixed function of the sample size is not adaptive to the magnitude of the dependence in the series, whereas the data-dependent bandwidth could lead to nonmonotonic power. To circumvent the difficulty, we propose a self-normalization (SN) based Kolmogorov-Smirnov test, where the formation of the self-normalizer takes the change point alternative into account. The resulting test statistic is asymptotically distr