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Performance of model selection criteria in Bayesian threshold VAR (TVAR) models. (English) Zbl 1482.62093

Summary: 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 Information Criterion (AIC) [H. Akaike, in: 2nd internat. Sympos. Inform. Theory, Tsahkadsor 1971, 267–281 (1973; Zbl 0283.62006)], Schwarz Bayesian Criterion (SBC) [G. Schwarz, Ann. Stat. 6, 461–464 (1978; Zbl 0379.62005)], Information Complexity (ICOMP) Criterion of H. Bozdogan [Commun. Stat., Theory Methods 19, No. 1, 221–278 (1990; Zbl 0900.62041); J. Math. Psychol. 44, No. 1, 62–91 (2000; Zbl 1047.62501)], Extended Consistent (AIC) with Fisher Information (CAICF\(_{\text{E}}\)), and the new Bayesian Model Selection (BMS) Criterion of H. Bozdogan and M. Ueno [“A unified approach to information-theoretic and Bayesian model selection criteria”, in: The 6th World Meeting of the International Society for Bayesian Analysis (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.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62B10 Statistical aspects of information-theoretic topics
62F15 Bayesian inference
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