Detection of multiple structural breaks in multivariate time series
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Date
2013-09-17
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Abstract
We propose a new 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 identifies 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 time series and consists of
three steps: it starts with a consistent test, which allows to prove the existence of
structural breaks at a controlled type I error. Secondly, 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 which have been 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 returns, and in a simulation study it is demonstrated that the new procedure
outperforms the currently available nonparametric methods for detecting breaks in the
dependency structure of multivariate time series.
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Keywords
Multiple structural breaks, Cusum test, Empirical process, Nonparametric spectral estimates, Multivariate time series