Research On The Order Of The Two-threshold Variable Autoregressive Model Based On Bayesian Inference

The linear model occupies an important position in the field of classical econometrics,and it is the basis of other econometric models.However,in practice,most economic time series exhibit nonlinear characteristics.The research on this characteristic makes the nonlinear model develop rapidly.One of the important models for studying the nonlinear dynamic adjustment of economic variables is the threshold autoregressive(TAR)model.Since the TAR model has only one threshold variable,when it needs two or more threshold variables in real data analysis,then further expansion of the TAR model is needed.In literature,classical statistical methods have been used for researching on the autoregressive models with two threshold variables.This paper analyzes the two-threshold variable autoregressive(TTV-AR)model using Bayesian statistical methods.This paper studies how to determine the order of TTV-AR model,since it is an important parameter for establishing TTV-AR model.We applied the reversible jump Markov Monte Carlo(RJMCMC)method to determine the order of the TTVAR model,and used the Bayesian method to estimate other parameters of the model.In order to verify the validity of the method,a simulation experiment was conducted.It was found that the model order can be evaluated correctly.Meanwhile,the values of the parameters estimated by Beyesian method were also very close to the real ones.In the empirical analysis,the Hang Seng Index time series from January 2,2007 to December 30,2016 was used.Taking into account the relationship between stock prices and stock price fluctuations and trading volume,one of the threshold variables is set for the stock price.Another threshold variable is set as a variable with respect to the volume.Finally,a four-segment dual-threshold autoregressive model is established,and the parameters of the model are estimated using MCMC method.It can be seen that the order of TTV-AR model is estimated as(6,5,5,6)by RJMCMC method,and the standard deviations of the parameters are small.The final results indicate that the established model is good.