Detection of multiple structural breaks in multivariate time series

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 struc-tural breaks and corresponding components which are responsible for the changes in the autocovariance structure. In contrast to all other methods which have been pro-posed in the literature, our approach does not make any parametric assumptions, is not especially designed for detecting one single change point and addresses the prob-lem 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 prob-ability converging to one as the sample size increases and provide data-driven rules for 1 a