Detection of Multiple Structural Breaks in Multivariate Time Series

Philip Preuss, Ruprecht Puchstein and Holger Dette

Journal of the American Statistical Association, 2015, vol. 110, issue 510, 654-668

Abstract: We propose a new nonparametric procedure (referred to as MuBreD) for the detection and estimation of multiple structural breaks in the autocovariance function of a multivariate (second-order) piecewise stationary process, which also identifies the components of the series where the breaks occur. MuBreD is based on a comparison of the estimated spectral distribution on different segments of the observed time series and consists of three steps: it starts with a consistent test, which allows us to prove the existence of structural breaks at a controlled Type I error. Second, it estimates sets containing possible break points and finally these sets are reduced to identify the relevant structural breaks and corresponding components which are responsible for the changes in the autocovariance structure. In contrast to all other methods proposed in the literature, our approach does not make any parametric assumptions, is not especially designed for detecting one single change point, and addresses the problem of multiple structural breaks in the autocovariance function directly with no use of the binary segmentation algorithm. 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 data-driven rules for the selection of all regularization parameters. The results are illustrated by analyzing financial asset returns, and in a simulation study it is demonstrated that MuBreD outperforms the currently available nonparametric methods for detecting breaks in the dependency structure of multivariate time series. Supplementary materials for this article are available online.

Date: 2015
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DOI: 10.1080/01621459.2014.920613

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