Performance of Model Selection Criteria in Bayesian Threshold VAR (TVAR) Models

Abstract

This article presents a new Bayesian modeling and information-theoretic model selection criteria for threshold vector autoregressive (TVAR) models. The analytical framework of Bayesian modeling for threshold VAR models are developed. Markov Chain Monte Carlo (MCMC) simulation and importance/rejection sampling methods are used to estimate the parameters of the model and to obtain posterior samples. We propose reliable modeling procedures using Bayes factor, and the information-theoretic model selection criteria such as, Akaike's (1973) Information Criterion (AIC), Schwarz (1978) Bayesian Criterion (SBC), Information Complexity (ICOMP) Criterion of Bozdogan (1990, 1994, 2000), Extended Consistent (AIC) with Fisher Information (CAICF E ), and the new Bayesian Model Selection (BMS) Criterion of Bozdogan and Ueno (2000). We study the performance of these criteria under different design of the simulation protocol with varying sample sizes in TVAR models. Our results show that these criteria perform well in small sample as well as large samples to avoid heavy computational burden in conventional procedures.