Segmentation of High-Dimensional Matrix-Variate Time Series

Abstract

In this chapter, we introduce a new segmentation method for high-dimensional matrix-variate time series. Specifically, we look for linear transformations to segment the matrix into many small sub-matrices for which each of them is uncorrelated with the others both contemporaneously and serially, thus they can be analyzed separately, which will greatly reduce the number of parameters to be estimated in terms of modeling. To overcome the identification issue, we propose a two-step and more structured procedure to segment the rows and columns separately. When the dimension is large in relation to the sample size, we assume the transformation matrices are sparse and use threshold estimators for the (auto) covariance matrices. Unlike principal component analysis (PCA) for independent data, we cannot guarantee that the required linear transformation exists. When it does not, the proposed method provides an approximate segmentation, which may be useful for forecasting. The proposed method is illustrated with simulated data examples.