Model selection in the presence of nonstationarity

This paper studies model selection methods in the presence of nonstationarity. We focus on the Bayesian model selection rule and compare it with other criteria that are frequently used in econometric practice. First, we derive each of these criteria in the presence of nonstationarity. In particular, we study the Bayesian model selection rule in detail and derive three alternative forms of it in the presence of nonstationarity. One important feature of the Bayesian model selection criterion (BMSC) is that BMSC gives different weights to the stationary and nonstationary components of a model while the other criteria do not. This feature of BMSC is a desirable property for a model selection rule in the presence of possible nonstationarity. Second, we compare these criteria with regard to parsimony and power. We have found that BMSC shows the highest parsimony, AIC is the second, and Cp and R̄2, having the same level of parsimony, are the third. With regard to power, the order is not clearly established. However, for the size adjusted power BMSC becomes dominant as the sample size increases. Without size adjustment the order in the power is exactly the opposite to that in parsimony. Also, we find that BMSC is a consistent selection rule while the other criteria are not. Third, we consider four different cases of practical interest for which BMSC with some of the other criteria is applicable. We discuss how our BMSC can be used in these cases of practical interest. Results of an extensive Monte Carlo simulation for models in these four cases show that overall the BMSC outperforms other criteria.