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In this article, we introduce two quantile autoregressive models with explanatory variables. The Bayesian quantile estimation method is considered in estimating the model parameters based on an asymmetric Laplace likelihood. By introducing the latent variables, we developed the two Gibbs sampling algorithms for the proposed models. The numerical simulation implies that the Gibbs sampling algorithms converges fast and the Bayesian quantile estimators are robust. A real example is given to discuss the relationship of the gold price and three exogenous variables. Both the simulations and the data example indicate that the proposed methods are feasible, reliable and appropriate for analyzing the gold price time series.

Bayesian inference for quantile autoregressive model with explanatory variables