Bayesian Estimation Of Threshold ARMA Models

Threshold ARMA model is a very important time series model,which has important application value in Economics,Finance and other fields.The traditional maximum likelihood estimation method for threshold ARMA model parameters does not consider the a priori information of the parameters and the posterior distribution of the sample.The Bayesian estimation method is one of the more popular methods for parameter estimation.Bayesian method takes into account the factors of parameter prior information and the value of posterior distribution.Bayesian estimates a more obvious advantage in the estimation of threshold ARMA model parameters.In this paper,the Bayesian method is used to study the threshold ARMA model;the posterior distribution is used to obtain the parameter estimation value by MCMC method.The validity of the threshold ARMA model under Bayesian estimation is verified by the logarithmic yield series of the Shanghai and Shenzhen 300 Index from January 2,2018 to April 8,2019.Firstly,the threshold ARMA model is introduced.The properties of the model parameters are analyzed by the definition of the threshold ARMA model and Two-regime threshold ARMA model.Secondly,the appropriate prior distribution is selected,and the Bayesian estimation of the threshold autoregressive moving average model parameters is carried out by Metropolis-Hastings algorithm and Gibbs sampling method,and the posterior probability density is derived.The MCMC algorithm and specific operational steps are given by describing the Metropolis-Hastings algorithm and the Gibbs sampling method.Finally,we select the Shanghai and Shenzhen 300 Index data from January 2,2018 to April 8,2019,calculate the logarithmic yield of the Shanghai and Shenzhen300 Index,and empirically study the logarithmic yield series of the Shanghai and Shenzhen 300 Index data through the threshold TARMA model.The fluctuation of the logarithmic yield series of the Shanghai and Shenzhen 300 Index.