🤖 AI Summary
Modeling state switching in high-dimensional time series—such as those arising in neuroimaging and finance—remains challenging due to computational intractability and statistical inconsistency in existing approaches.
Method: This paper proposes a scalable approximate Expectation-Maximization (EM) algorithm for estimating high-dimensional Markov-switching vector autoregressive (MS-VAR) models. The method integrates high-dimensional statistical inference with state-space estimation techniques, enabling efficient computation while preserving statistical interpretability.
Contribution/Results: We establish, for the first time, consistency guarantees for the approximate EM estimator under high-dimensional asymptotics. Theoretical analysis confirms consistent parameter estimation; simulations demonstrate computational efficiency and robustness to model misspecification and noise. Applied to EEG data from epilepsy patients, the method successfully identifies dynamic brain-state transitions, yielding neurophysiologically interpretable patterns and enhancing practical utility in clinical neuroscience.
📝 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.
