Multiple Change Point Detection in Reduced Rank High Dimensional Vector Autoregressive Models

TL;DR

This paper develops methods for detecting multiple change points in high-dimensional VAR models with low rank plus sparse transition matrices, providing theoretical guarantees and practical algorithms.

Contribution

It introduces a two-step algorithm for multiple change point detection in high-dimensional VAR models with low rank and sparse structures, including error bounds and computational strategies.

Findings

The algorithms accurately detect change points in synthetic data.

The methods are effective on real-world datasets.

Theoretical error bounds are established for the detection accuracy.

Abstract

We study the problem of detecting and locating change points in high-dimensional Vector Autoregressive (VAR) models, whose transition matrices exhibit low rank plus sparse structure. We first address the problem of detecting a single change point using an exhaustive search algorithm and establish a finite sample error bound for its accuracy. Next, we extend the results to the case of multiple change points that can grow as a function of the sample size. Their detection is based on a two-step algorithm, wherein the first step, an exhaustive search for a candidate change point is employed for overlapping windows, and subsequently, a backward elimination procedure is used to screen out redundant candidates. The two-step strategy yields consistent estimates of the number and the locations of the change points. To reduce computation cost, we also investigate conditions under which a surrogate VAR model with a weakly sparse transition matrix can accurately estimate the change points and their locations for data generated by the original model. This work also addresses and resolves a number of novel technical challenges posed by the nature of the VAR models under consideration. The effectiveness of the proposed algorithms and methodology is illustrated on both synthetic and two real data sets.