  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.
