Estimation of High-Dimensional Markov-Switching VAR Models with an Approximate EM Algorithm

TL;DR

This paper introduces an approximate EM algorithm for high-dimensional Markov-switching VAR models, enabling efficient estimation and analysis of regime shifts in complex time series data, with proven consistency and practical application to EEG data.

Contribution

It develops a novel approximate EM algorithm tailored for high-dimensional Markov-switching VAR models, addressing computational and theoretical challenges.

Findings

Algorithm is consistent in high dimensions

Simulation studies validate performance

Applied successfully to EEG seizure data

Abstract

Regime shifts in high-dimensional time series arise naturally in many applications, from neuroimaging to finance. This problem has received considerable attention in low-dimensional settings, with both Bayesian and frequentist methods used extensively for parameter estimation. The EM algorithm is a particularly popular strategy for parameter estimation in low-dimensional settings, although the statistical properties of the resulting estimates have not been well understood. Furthermore, its extension to high-dimensional time series has proved challenging. To overcome these challenges, in this paper we propose an approximate EM algorithm for Markov-switching VAR models that leads to efficient computation and also facilitates the investigation of asymptotic properties of the resulting parameter estimates. We establish the consistency of the proposed EM algorithm in high dimensions and investigate its performance via simulation studies. We also demonstrate the algorithm by analyzing a brain electroencephalography (EEG) dataset recorded on a patient experiencing epileptic seizure.