Bayesian Subset Selection For Two Threshold Variables Autoregressive Models

As a class of nonlinear time series analysis model,threshold autoregressive(TAR)model explains the change of time series better,compared with the linear time series model.It has better properties in the practical application of fitting and forcasting.With the continuous development of the era of data,threshold autoregressive model with single threshold variable can not meet the requirements of time series analysis.Two threshold variables autoregressive(TTV-AR)model arises at the historic moment,which is more suitable for the analysis of practical problems.In this paper,we propose and study an effective Bayesian subset selection method for TTV-AR models.It can select the best subset model by MCMC technique of stochastic search idea and estimate all the parameters at the same time.Compared to model with single threshold variable,the complexity of TTV-AR model selection is increased by capturing the uncertainty of two unknown threshold levels and two unknown delay lags.By deducing the Bayesian inference of parameters in the model,using Gibbs sampler and Metropolis-Hastings(M-H)algorithm of MCMC techniques and the stochastic search idea,we can identify the best subset model from a large number of possible choices.And we can estimate all the parameters simultaneously,without fixing the two unknown threshold levels and two unknown delay lags in advance.Simulation experiments show that the proposed method works very well.It successfully identify the best subset model from thousands of possible choices and estimate the parameters accurately.In the application to Hang Seng index from January 2,2007 to December 30,2016,by using Bayesian subset selection method,we can distinguish the best subset TTV-AR model successfully.Compared the best subset model we selected in the application with model which obtained by classical statistics,AIC value and BIC value show that the former is more desirable.