The Bayesian Estimation Of The Parameters Of The Seemingly Unrelated Model With Error Autoregressive

Nowadays,with the advent of the information technology and the era of big data,Large data capacity,diverse content,complex form,intensive correlation,and the correlation research between things has been paid more and more people's attention.People can no longer explain the phenomena existing in society and nature with a single independent perspective.The classical Linear Regression Models can't explain all aspects of life in a reasonable way in many fields.It seems that the emergence of the Seemingly Unrelated Regression model(SUR)breaks the understanding that the Error Model satisfying the Gauss Markov's hypothesis.The error closely links the models which appear to be unrelated.Later,the scholars' research on the SUR model has penetrated into the fields of economy,environment,ecology and health.these all illustrate that the model has a good explanatory and a wide range of application prospects.For the research of panel data,the spatial effects are widely concerned by the public.If at the same time section,the main research is about the heterogeneity of spatial location and the correlation between regions;In a specific geographical location,the observations are presented in time series.the Error Covariance Matrix established in this paper is an Error Autoregressive model which are related to time series,that is to study some interaction between same locations at different times.The problem of spatial heterogeneity is generally characterized by the Geographically Weighted Regression model.This paper proposes the Time-Correlated Error Autoregressive Seemingly Unrelated model and The Geographical Weighted Seemingly Unrelated Regression model with Error Autoregressive.The model is used to better describe the dynamic process of the relationship between explanatory variables and interpreted variables and to solve the problem of spatial and temporal heterogeneity and correlation.For the estimation of SUR model parameters,domestic and foreign scholars provide a variety of methods,like Generalized Least Squares estimation method,Maximum Likelihood method,Generalized Moment method,Linear Bayesian method,etc.In this paper,The Linear Bayesian estimation method is used to estimate the parameters of the Time-Correlated Error Autoregressive Seemingly Unrelated model.and obtained the unbiasedness and effectiveness of the method.In the simulation,the Mean Square Error and the Mean of Absolute Bias are used as the test indicators to obtain the superiority of the linear Bayes method compared with the GLS method.Based on the Bayesian statistical inference and the information prior distribution of the multivariate parameters,obtaining the posterior distribution of the parameters of the Autoregressive Geographically Weighted Seemingly Unrelated model,Through simulation,Combined with Gibbs sampling method,The Bayesian estimation value is obtained by using the posterior mean value as the parameter of the model.The Residual Sum of Squares,the Mean Square Error and the Mean of Absolute Bias are used as test indicators,compared with the Generalized Locally Weighted Least Squares estimation method,Thus,which shows the better interpretability of this model and the effectiveness of the estimation methods.