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
Date Written: January 2005
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: Suggested Citation