Performance of Model Selection Criteria in Bayesian Threshold VAR (TVAR) Models
研究了贝叶斯阈值VAR模型中多种信息准则（如AIC、BIC、ICOMP等）在不同样本量下的表现，发现这些准则在小样本和大样本中均表现良好，可避免传统方法的计算负担。
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 Akaike , H. ( 1973 ). Information theory and an extension of the maximum likelihood principles . In: Petrov , B. N. , Csaski , F. , eds. Second International Symposium of Information Theory . Budapest : Academia Kiado , pp. 267 – 281 . [Google Scholar]) Information Criterion (AIC), Schwarz (1978 Schwarz , G. ( 1978 ). Estimating the dimension of a model . Annals of Statistics 6 : 461 – 464 .[Crossref], [Web of Science ®] , [Google Scholar]) Bayesian Criterion (SBC), Information Complexity (ICOMP) Criterion of Bozdogan (1990 Bozdogan , H. ( 1990 ). On the information-based measure of covariance complexity and its application to the evaluation of multivariate linear models . Communications in Statistics Theory and Methods 19 ( 1 ): 221 – 278 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar], 1994 Bozdogan , H. ( 1994 ). Mixture-model cluster analysis using model selection criteria and a new informational measure of complexity . In: Bozdogan , H. , ed. Multivariate Statistical Modeling . Proceedings of the First US/Japan Conference on the Frontiers of Statistical Modeling: An Informational Approach . Dordrecht, the Netherlands : Kluwer Academic Publishers , Vol. 2 , pp. 69 – 113 .[Crossref] , [Google Scholar], 2000 Bozdogan , H. ( 2000 ). Akaike's information criterion and recent developments in informational complexity . Journal of Mathematical Psychology 44 : 62 – 91 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), Extended Consistent (AIC) with Fisher Information (CAICF E ), and the new Bayesian Model Selection (BMS) Criterion of Bozdogan and Ueno (2000 Bozdogan , H. , Ueno , M. ( 2000 ). A unified approach to information-theoretic and Bayesian model selection criteria . Paper presented in the Technical Session Track C, The 6th World Meeting of the International Society for Bayesian Analysis , Crete, Greece . [Google Scholar]). 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.