Parameter Estimation Of Threshold Auto-Regressive Models By Gibbs Sampling

Threshold auto-regressive model is a typical nonlinear time series model,it adds additional constraints to the autoregressive model,Its essence is a kind of nonlinear time series model that adopt the way of linear time series to solve nonlinear problems.Based on the assumptions of the random part is normal distribution,taking the kdimensional model as an example,we give some properties of threshold auto-regressive model.It is proved that time series of Threshold auto-regressive model have Markov chain with stable transition probability in appropriate sets.Using Bayesian statistical inference method and Select appropriate prior distribution,computing conditional posterior distribution of each parameter by Bayes formula and some properties of conjugate Prior.Based on the method of the stochastic simulation,with the use of the MCMC and Gibbs sampling algorithms that Sample and generate samples in conditional posterior distribution,estimating and evaluating the parameters of threshold auto-regressive model with posterior mean and variance.At last,we its numerical simulation results are given.It proves that this arithmetic is concise and effective to solve parameter estimation of Threshold auto-regressive model problem by farther analysis.