Markov regime-switching vector auto-regressives are frequently used for modelling heterogeneous and complex relationships between variables in multivariate time series analysis. Applications include analyzing macroeconomic time series such as manufacturing activities, consumer price indices, and housing and asset prices. The most common method of estimation in these models is maximum likelihood estimation (MLE). However, even for moderate data dimension and number of regimes, the MLE becomes unstable. In this talk, we present regularization-based estimators when the number of regimes in the model is correctly or over-specified. We also discuss theoretical and finite-sample performances of the methods,
including forecasting, and conclude with a real data analysis.