PREVIOUS SEMINAR - 4th June 2021
Speaker: Abolfazl Safikhani (University of Florida)
Title: Multiple Change Point Detection in Reduced Rank High Dimensional Vector Autoregressive Models
Abstract: In this talk, we discuss 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 backwards 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. The effectiveness of the proposed algorithms and methodology is illustrated on both synthetic and real data sets. This is a joint work with Peiliang Bai and George Michailidis.