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

arXiv: https://arxiv.org/abs/2210.07456 · HTML: https://mlsanity.com/paper/2210.07456/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 41 references that are in the map.
- First posted on arXiv 14 Oct 2022.

## Builds on (most cited first, 5 of 5)

- [Statistical guarantees for the EM algorithm: From population to sample-based analysis](https://mlsanity.com/paper/1408.2156/) (2014)
- [Regularized estimation in sparse high-dimensional time series models](https://mlsanity.com/paper/1311.4175/) (2013)
- [Regularized EM Algorithms: A Unified Framework and Statistical Guarantees](https://mlsanity.com/paper/1511.08551/) (2015)
- [Simultaneous Clustering and Estimation of Heterogeneous Graphical Models](https://mlsanity.com/paper/1611.09391/) (2016)
- [Estimating the error variance in a high-dimensional linear model](https://mlsanity.com/paper/1712.02412/) (2017)

## Abstract (arXiv)

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.