Markov-Switching Model Selection Using Kullback-Leibler Divergence

UC Davis Agricultural and Resource Economics Working Paper No. 05-001

43 Pages Posted: 2 May 2005

See all articles by Aaron Smith

Aaron Smith

University of California, Davis - Department of Agricultural and Resource Economics

Prasad A. Naik

University of California, Davis

Chih-Ling Tsai

University of California, Davis - Graduate School of Management

Date Written: January 2005

Abstract

In Markov-switching regression models, we use Kullback-Leibler (KL) divergence between the true and candidate models to select the number of states and variables simultaneously. In applying Akaike information criterion (AIC), which is an estimate of KL divergence, we find that AIC retains too many states and variables in the model. Hence, we derive a new information criterion, Markov switching criterion (MSC), which yields a marked improvement in state determination and variable selection because it imposes an appropriate penalty to mitigate the over-retention of states in the Markov chain. MSC performs well in Monte Carlo studies with single and multiple states, small and large samples, and low and high noise. Furthermore, it not only applies to Markov-switching regression models, but also performs well in Markov-switching autoregression models. Finally, the usefulness of MSC is illustrated via applications to the U.S. business cycle and the effectiveness of media advertising.

Keywords: Advertising effectiveness, business cycles, EM algorithm, hidden Markov models, information criterion, Markov-switching regression

JEL Classification: C22, C52

Suggested Citation

Smith, Aaron D. and Naik, Prasad A. and Tsai, Chih-Ling, Markov-Switching Model Selection Using Kullback-Leibler Divergence (January 2005). UC Davis Agricultural and Resource Economics Working Paper No. 05-001, Available at SSRN: https://ssrn.com/abstract=711404 or http://dx.doi.org/10.2139/ssrn.711404

Aaron D. Smith (Contact Author)

University of California, Davis - Department of Agricultural and Resource Economics ( email )

One Shields Avenue
Davis, CA 95616
United States
530-752-2138 (Phone)
530-752-5614 (Fax)

Prasad A. Naik

University of California, Davis ( email )

One Shields Avenue
Apt 153
Davis, CA 95616
United States

Chih-Ling Tsai

University of California, Davis - Graduate School of Management ( email )

One Shields Avenue
Davis, CA 95616
United States

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