Penalized estimation of sparse Markov regime-switching vector auto-regressive models

Chavez-Martinez, G., Agarwal, A. , Khalili, A. and Ahmed, S. E. (2023) Penalized estimation of sparse Markov regime-switching vector auto-regressive models. Technometrics, 65(4), pp. 553-563. (doi: 10.1080/00401706.2023.2201336)

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.

• Item Type: Articles
• Additional Information: G. Chavez-Martinez is supported by the Mexican Council of Science and Technology (CONACyT) under the PhD scholarships program. A. Agarwal is supported by the University of Glasgow Early Career Mobility Scheme. A. Khalili and S.E. Ahmed are supported by the Natural Science and Engineering Research Council of Canada (NSERC RGPIN-2020-05011) and (NSERC RGPIN-2017-05228).
• Keywords: EM algorithm, regularization methods, multivariate time series.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Agarwal, Dr Ankush
• Authors: Chavez-Martinez, G., Agarwal, A., Khalili, A., and Ahmed, S. E.
• Subjects: H Social Sciences > HA Statistics; Q Science > QA Mathematics
• College/School: College of Social Sciences > Adam Smith Business School > Economics
• Journal Name: Technometrics
• Publisher: Taylor & Francis
• ISSN: 0040-1706
• ISSN (Online): 1537-2723
• Published Online: 10 April 2023
• Copyright Holders: Copyright © 2023 American Statistical Association and the American Society for Quality
• First Published: First published in Technometrics 65(4):553-563
• Publisher Policy: Reproduced in accordance with the publisher copyright policy