Bayesian Quantile Regression And Application

Quantile regression is an advanced research topic in modern econometrics. It has unparalleled advantage for Bayesian method to analyze quantile regression than Frequency method. This dissertation made an exploratory study in Bayesian quantile regression theory, at the same time, made an empirical analysis in risk of stock market and gold hedging role with this theory.The dissertation consists of seven parts. Chapter1is foreword, which introduced the writing background and the research significance of the paper, the reviews of the Bayesian quantile regression estimation method and non-(semi-) parameter estimation methods, then summarized the organization and innovations of this dissertation. Chapter2described the basic idea of quantile regression, as well as traditional quantile estimation methods and asymptotic theory, and reviewed the basic principles of Bayesian estimation. Chapter3introduced the Bayesian quantile regression theory, and analyzed the impacts of different prior distribution and sampling algorithm to properties of estimators. At the same time, we compared effectiveness of the estimators and accuracy of hypothesis test of different methods belongs to Bayes School and Frequency School. In Chapter3, Bayesian quantile regression method was based on continuous variable, while Chapter4extended the method to discrete dependent variable, and made exploratory research on binary quantile regression, as well as censored data. This paper mainly studied parameterized Bayesian quantile regression method, while non-(semi-) parameterized Bayesian quantile regression method is a useful complement to parametric approach, although they are differences. Therefore, in Chapter5we introduced major non-(semi-) parametric Bayesian quantile regression methods. Chapter6we used continuous and discrete dependent variable Bayesian quantile regression estimation method to solve real problem, then summarized the conclusions of this study and pointed out the directions for further research.This dissertation mainly focused on Bayesian quantile regression estimation method and the innovations of theory are reflected in the following aspects:(1) We expressed likelihood function of Non-standard distribution——asymmetric Laplace distribution, which laid the foundation for Bayesian quantile regression method to be implemented in Bayesian analysis software WinBUGS.(2) Asymmetric Laplace distribution is basis of Bayesian quantile regression method, which scale (scale) variable was parameterized, and got the posterior distribution by Gibbs sampling algorithm. Experimental results showed that, compared with no parameterization, the statistical properties of the estimator are better.(3) For continuous variables, firstly, we analyzed the effects of different algorithms and prior specifications on the properties of the Bayesian quantile regression estimators. Experimental results showed that the appropriate prior distribution can improve the statistical properties of the estimator. And compared with MH sampling, the estimator had a smaller bias and smaller standard deviation by Gibbs sampling. Secondly, we compared quantile regression model in estimator validity and accuracy of hypothesis testing between Frequency and Bayes School. Simulation results showed that estimator statistical properties were better (smaller bias, more accurate) using Bayesian quantile regression method than traditional interior point method, and the former had higher test power.(4) For discrete dependent variable, we estimated Bayesian Binary Probit quantile regression and Tobit quantile regression models, and simulated the effects of different prior specifications, sampling algorithms and estimate methods on the properties of estimators.In the part of empirical researches, we analyzed the sources of stock market risk and the hedging role of gold in China using Bayesian quantile regression method. Empirical results showed that:(1) the extreme risk of Shanghai A shares, Shanghai B shares and H shares were subject to international markets. Specifically, the Shanghai B shares and H shares were impacted greatly; Extreme risk for the Shanghai A shares were mainly from their own market. Then we gave corresponding measures to deal with risks.(2) For short-term investors, investing in gold cannot hedge against inflation and stock market risk. In the long run, as long as investors are willing to hold gold, it can be used as an effective tool to hedge against inflation and stock market risk. However, when economic situation was in the Great Depression or the stock market was in turbulent times, gold is not a "safe haven".