Bayesian Quantile Regression Analysis For Bivariate Vector Autoregressive Models With Applications

With the rapid development of the economy and the continuous progress of science and technology,more and more scholars have found that traditional least squares estimation methods only focus on the impact of covariates on the mean of response variables,and cannot comprehensively analyze the relationship between covariates and response variables,which has certain limitations.The quantile regression method considers the influence of covariates on response variables at different quantile levels.When researchers are interested in the overall information of conditional distribution of dependent variables,quantile regression can provide a good analytical idea,and can also provide a good model explanation,which greatly expands the flexibility of parametric and nonparametric regression methods.Compared with classical statistical methods,Bayesian quantile regression is more robustness.Bayesian statistical inference methods are widely used to solve various statistical inference problems.Its advantage is that sample information,overall information and prior information can be fully considered.Markov chain Monte Carlo(MCMC)method has been proved to be a useful tool for many branches of statistics.Bayesian quantile method combines Bayesian method with quantile regression,giving full play to their advantages,and providing a new idea for parameter estimation methods of quantile regression.Due to the complex structure of vector autoregressive models,the Bayesian quantile method is still an unresolved problem for such models.Based on this Bayesian quantile method,this paper considers the Bayesian quantile inference of two vector autoregressive models.The full text is divided into two parts:The first part considers the problem of Bayesian quantile estimation of bivariate vector autoregression(VAR)model.By introducing an asymmetric Laplacian distribution into the likelihood function,a complete data likelihood is obtained.On this basis,the full conditional distribution of each parameter can be obtained.Subsequently,numerical simulations were conducted to demonstrate the superiority of the proposed method.Finally,the application of the model was introduced using Canada’s US dollar exchange rate data and annual interest rate data as examples.The second part of this paper studies the Bayesian quantile estimation problem of binary threshold vector autoregression(TVAR)model.The difference between its main methodology and the first part is that it considers the correlation between the components of the Error term and constructs the likelihood function by introducing a binary asymmetric Laplace function.When estimating the threshold parameters,the M-H sampling algorithm is used to obtain the estimation of the threshold parameters,and the MCMC algorithm is evaluated through simulation and real data examples.Finally,an empirical analysis was conducted on the datasets of the Shanghai Composite Index and the S&P 500 Index in the United States.