Detection of Multiple Structural Breaks in Multivariate Time Series

• Activity Number: 90
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Philip Preuss*+
• Companies: Ruhr-University Bochum
• Keywords: multiple structural breaks ; cusum test ; empirical process

Abstract

We propose an integrative nonparametric procedure for the detection and estimation of multiple structural breaks in the autocovariance function of a multivariate (second-order) piecewise stationary process, which also identifies the components of the series where the breaks occur. The new method is based on a comparison of the estimated spectral distribution on different segments of the observed times series and consists of three steps: it starts with a consistent bootstrap test, which allows to prove the existence of structural breaks at a controlled type I error. Secondly, it estimates a set of possible break points and finally this set is reduced to identify the relevant structural breaks and corresponding components which are responsible for these breaks. We prove that the new procedure detects all components and the corresponding locations where structural breaks occur with probability converging to one as the sample size increases and provide a data-driven rule for the selection of regularization parameters. In a comprehensive simulation study it is shown that the proposed test cleary outperforms the well know CUSUM procedure if more than one break point is present.