Multiple-change-point detection for high dimensional time series via sparsified binary segmentation

Abstract: Time series segmentation, a.k.a. multiple change-point detection, is a well-established problem. However, few solutions are designed specifically for high-dimensional situations. In this paper, our interest is in segmenting the second-order structure of a high-dimensional time series. In a generic step of a binary segmentation algorithm for multivariate time series, one natural solution is to combine CUSUM statistics obtained from local periodograms and cross-periodograms of the components of the input time series. However, the standard "maximum" and "average" methods for doing so often fail in high dimensions when, for example, the change-points are sparse across the panel or the CUSUM statistics are spuriously large. In this paper, we propose the Sparsified Binary Segmentation (SBS) algorithm which aggregates the CUSUM statistics by adding only those that pass a certain threshold. This "sparsifying" step reduces the impact of irrelevant, noisy contributions, which is particularly beneficial in high dimensions. In order to show the consistency of SBS, we introduce the multivariate Locally Stationary Wavelet model for time series, which is a separate contribution of this work.