Gilberto Chávez-Martínez, Ankush Agarwal, Abbas Khalili, S. E. Ahmed
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Penalized estimation of sparse Markov regime-switching vector auto-regressive models
Abstract We consider sparse Markov regime-switching vector autoregressive (MSVAR) models in which the regimes are governed by a latent homogeneous Markov chain. In practice, even for moderate values of the number of Markovian regimes and data dimension, the associated MSVAR model has a large parameter dimension compared to a typical sample size. We provide a unified penalized conditional likelihood approach for estimating sparse MSVAR models. We show that our proposed estimators are consistent and recover the sparse structure of the model. We also show that, when the number of regimes is correctly or over-specified, our method provides consistent estimation of the predictive density. We develop an efficient implementation of the method based on a modified Expectation-Maximization (EM) algorithm. We discuss strategies for estimation of the number of regimes. We evaluate finite-sample performance of the method via simulations, and further demonstrate its utility by analyzing a real dataset.
期刊介绍:
Technometrics is a Journal of Statistics for the Physical, Chemical, and Engineering Sciences, and is published Quarterly by the American Society for Quality and the American Statistical Association.Since its inception in 1959, the mission of Technometrics has been to contribute to the development and use of statistical methods in the physical, chemical, and engineering sciences.