Shrinkage estimation and order selection in threshold autoregressive models via Bayesian empirical likelihood

Abstract

Threshold autoregressive models have a wide range of applications in the field of econometrics. This paper considers the Bayesian empirical likelihood (BEL) shrinkage estimation and order selection for a class of sparse threshold autoregressive models. With the help of Taylor explanation, a “normally distributed” nonparametric likelihood is obtained. Based on this likelihood, the BEL estimation is well addressed. By using the Markov Chain Monte Carlo (MCMC) techniques under a Bayesian hierarchical model, the order and the non-zero autoregressive coefficients of the model can be accurately determined. Some simulation studies are conducted to show the performances of the proposed methods. Finally, an application to the US gross national product data set is provided.