In this paper, we study the estimation and forecasting of the quantile threshold autoregressive time series model. By transforming the optimization problem in the quantile regression into a maximum likelihood estimation, we can impose the Metropolis-Hastings method for the Bayesian estimation of the parameters in the model. At the same time, the methodology is applied to the growth of Shanghai composite index data, quantile estimations of the growth data are obtained. The merit of this method is that we need not to propose any distributional assumptions of the data.
