In Markov-switching regression models, Professors Prasad Naik, Chih-Ling Tsai and co-author Aaron Smith from the UC Davis Department of Agricultural and Resource Economics use Kullback–Leibler (KL) divergence between the true and candidate models to select the number of states and variables simultaneously.

Specifically, the authors derive a new information criterion, Markov switching criterion (MSC), which is an estimate of KL divergence. MSC imposes an appropriate penalty to mitigate the over retention of states in the Markov chain, and it performs well in Monte Carlo studies with single and multiple states, small and large samples, and low and high noise.

The authors illustrate the usefulness of MSC via applications to the U.S. business cycle and to media advertising. In Markov-switching regression models, they use Kullback–Leibler (KL) divergence between the true and candidate models to select the number of states and variables simultaneously.