Abstract: This paper systematically analyzes the mathematic model and conditional likelihood function of time series model with AR(p) error,and constructs conjugate prior distribution of parameters on the basis of the statistical structure of the function.In the condition of normal-mixed Γ prior distribution，the paper studies the Bayesian inference of the model,including the statistical inference of the parameter of the  kernel estimation of trend and the prior parameters of posterior distribution.

Key words: Bayesian estimation, AR(p) error, Gibbs sampling