Bayesian Empirical Likelihood Inferences Of Autoregressive Models

The Bayesian statistical inference method is widely used to solve various statistical inference problems.Its advantage is that it can fully consider sample information,overall information and prior information.The empirical likelihood method is a nonparametric statistical inference method.Under the condition of no need to make assumptions about the distribution,the empirical likelihood method can obtain the confidence region based on the data.In this paper,we construct a class of nonparametric likelihood functions which asymptotically obey normal distribution by Taylor expansion of empirical likelihood function,so that Bayesian method and empirical likelihood method can be combined organically.Based on this Bayesian empirical likelihood method,this paper considers the Bayesian empirical likelihood inference problem of two types of time series models.The content is divided into the following two parts:The first part considers the Bayesian empirical likelihood inference problem of a kind of sparse autoregressive model.First,by introducing nonparametric likelihood,the point estimation and interval estimation of model parameters are obtained,as well as the asymptotic properties of the estimation.Then,by introducing a Bayesian hierarchical model with spike-and-slab prior,combined with the Markov Chain Monte Carlo method,the order and non-zero autoregressive coefficients of the model can be accurately determined.Next,numerical simulation shows the superiority of the proposed method.Finally,taking the US industrial production index data set as an example,the application of the model is introduced.The second part considers the Bayesian empirical likelihood inference problem of a kind of sparse threshold autoregressive model.The main methodology is similar to the first part,using the SGS algorithm is used to obtain the estimation of the threshold parameters,and the simulation study is carried out to evaluate the proposed method.Finally,use the growth rate data of the US National Gross data to fit the model analyzed.