Regression and time series model selection using variants of the Schwarz information criterion

The Schwarz (1978) information criterion, SIC, is a widely-used tool in model selection, largely due to its computational simplicity and effective performance in many modeling frameworks. The derivation of SIC (Schwarz, 1978) establishes the criterion as an asymptotic approximation to a transformation of the Bayesian posterior probability of a candidate model. In this paper, we investigate the derivation for the identification of terms which are discarded as being asymptotically negligible, but which may be significant in small to moderate sample-size applications. We suggest several SIC variants based on the inclusion of these terms. The results of a simulation study show that tile variants improve upon the performance of SIC in two important areas or application: multiple linear regression and time series analysis.