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Regime shifts in high-dimensional time series arise naturally in manyapplications, from neuroimaging to finance. This problem has receivedconsiderable attention in low-dimensional settings, with both Bayesian andfrequentist methods used extensively for parameter estimation. The EM algorithmis a particularly popular strategy for parameter estimation in low-dimensionalsettings, although the statistical properties of the resulting estimates havenot been well understood. Furthermore, its extension to high-dimensional timeseries has proved challenging. To overcome these challenges, in this paper wepropose an approximate EM algorithm for Markov-switching VAR models that leadsto efficient computation and also facilitates the investigation of asymptoticproperties of the resulting parameter estimates. We establish the consistencyof the proposed EM algorithm in high dimensions and investigate its performancevia simulation studies.

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