Detection and Mode-Identification of Multiple Change Points in Tensor Factor Models

TL;DR

This paper introduces algorithms for detecting multiple change points and identifying affected tensor modes in high-dimensional tensor time series, improving segmentation and mode-wise analysis.

Contribution

It proposes novel methods for change point detection and mode-identification in tensor models, with proven consistency and practical applications.

Findings

Algorithms effectively detect multiple change points in tensor data.

Mode-identification enhances post-segmentation estimation accuracy.

Methods perform well on simulated and real datasets.

Abstract

We study the problems arising from modeling high-dimensional tensor-valued time series under a Tucker decomposition-based factor model with multiple structural change points. First, we propose an algorithm for detecting the multiple change points, which utilizes the low-rank structure of the data for statistical and computational efficiency. Also, the multi-dimensional array setting poses unique challenges, as some changes are associated with a subset of the modes, and the changes in different modes may interact with one another. Recognizing these, we investigate the problem of identifying each change with the tensor modes post-segmentation. To this end, we formalize the mode-identifiability of each change and propose an algorithm for detecting the modes at which the data are undergoing a mode-identifiable shift. We establish the consistency of both change point detection and mode-identification methods under a weak moment condition, and demonstrate their good performance on simulated datasets where, in particular, it is shown that the mode-identification step can improve the post-segmentation estimation of the mode-wise loading space. Additionally we analyze the datasets on New York City taxi usage and Fama--French portfolio returns using the proposed suite of methods.