分位数回归的贝叶斯估计与应用研究
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摘要
分位数回归是现代计量经济学研究的前沿之一,采用贝叶斯分析方法对其进行研究比频率学派方法有无可比拟的优势。本文对分位数回归的贝叶斯估计方法进行了探索性研究,同时,应用该方法对股票市场风险和黄金的对冲作用进行了实证分析。
本文内容由七部分构成。第一章为绪论,在阐述本文的写作依据和研究意义之后,对分位数回归的贝叶斯参数估计方法和非(半)参数估计方法的相关文献进行回顾,并对本文的研究内容和创新点进行归纳总结。第二章介绍分位数回归的基本思想,以及传统分位数估计方法和相关渐近理论,同时对贝叶斯估计的基本原理进行回顾。第三章介绍分位数回归的贝叶斯估计原理,分析不同先验分布设定和贝叶斯抽样算法对估计量性质的影响,并对贝叶斯分位数回归方法和传统频率学派的分位数回归方法在参数估计的有效性和假设检验的准确性方面进行比较。与第三章针对连续因变量的贝叶斯分位数回归方法不同,第四章将该方法扩展到离散因变量的情形,对二元选择分位数回归和删失分位数回归的贝叶斯估计方法进行探索性研究。本文主要研究参数化的贝叶斯分位数回归方法,而非(半)参数的贝叶斯分位数回归方法作为参数方法的有益补充,二者既相关又有差异,因而在第五章对主要的非(半)参数贝叶斯分位数回归方法进行了分析。第六章运用连续因变量和离散因变量的贝叶斯分位数回归估计方法对现实问题进行了研究。第七章总结本文的研究结论,并进一步展望未来的研究方向。
本文以分位数回归的贝叶斯估计方法研究为主,在理论方面的创新主要体现在以下方面：(1)在贝叶斯分析软件WinBUGS中实现对非标准分布——非对称拉普拉斯分布似然函数的表达,从而为贝叶斯分位数回归方法在WinBUGS由得以实施奠定了基础。(2)将贝叶斯分位数回归方法中非对称拉普拉斯分布的尺度(scale)参数进行参数化,并通过Gibbs抽样算法得到其后验分布。实验结果表明,与未参数化时相比,参数化后Gibbs抽样算法得到的估计量统计性质更好。(3)针对连续因变量的贝叶斯分位数回归估计方法,首先,模拟不同先验分布设定和不同抽样算法对参数估计量统计性质的影响,实验结果表明,合适的先验分布可以提高Gibbs抽样估计量的统计性质；Gibbs抽样与M-H抽样相比,得到的估计量偏误和标准差更小。其次,比较频率学派和贝叶斯学派对分位数回归模型估计量的有效性和假设检验的准确性,模拟实验的结果表明,采用贝叶斯分位数回归方法得到的参数估计量的统计性质(偏误更小,精度更高)普遍优于传统内点法得到的统计性质,且前者检验功效更高。(4)针对离散因变量,对二元Probit分位数回归和Tobit分位数回归模型进行贝叶斯分析,模拟不同先验分布设定、不同抽样算法、不同估计方法对估计量的影响。
在实证研究部分,本文以我国股票市场和黄金市场为研究对象,采用贝叶斯分位数回归方法对股票市场风险来源和黄金的风险对冲功能进行了研究。实证结果表明：(1)我国上证A股、上证B股、H股的极端风险均受国际市场的影响。其中,上证B股、H股受到的影响最大；而对于上证A股的极端风险则主要来自于自身市场。最后给出我国股市应对大风险应采取的措施。(2)对于短期的投资者,投资黄金不能对冲通货膨胀和股票市场的风险。而从长期来看,只要投资者愿意长期持有黄金,黄金可以作为对冲通货膨胀和股票市场风险的有效工具。但是,在经济大萧条或者股市动荡时期,黄金不是股市和通胀的安全“避风港”。
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".
本文内容由七部分构成。第一章为绪论,在阐述本文的写作依据和研究意义之后,对分位数回归的贝叶斯参数估计方法和非(半)参数估计方法的相关文献进行回顾,并对本文的研究内容和创新点进行归纳总结。第二章介绍分位数回归的基本思想,以及传统分位数估计方法和相关渐近理论,同时对贝叶斯估计的基本原理进行回顾。第三章介绍分位数回归的贝叶斯估计原理,分析不同先验分布设定和贝叶斯抽样算法对估计量性质的影响,并对贝叶斯分位数回归方法和传统频率学派的分位数回归方法在参数估计的有效性和假设检验的准确性方面进行比较。与第三章针对连续因变量的贝叶斯分位数回归方法不同,第四章将该方法扩展到离散因变量的情形,对二元选择分位数回归和删失分位数回归的贝叶斯估计方法进行探索性研究。本文主要研究参数化的贝叶斯分位数回归方法,而非(半)参数的贝叶斯分位数回归方法作为参数方法的有益补充,二者既相关又有差异,因而在第五章对主要的非(半)参数贝叶斯分位数回归方法进行了分析。第六章运用连续因变量和离散因变量的贝叶斯分位数回归估计方法对现实问题进行了研究。第七章总结本文的研究结论,并进一步展望未来的研究方向。
本文以分位数回归的贝叶斯估计方法研究为主,在理论方面的创新主要体现在以下方面：(1)在贝叶斯分析软件WinBUGS中实现对非标准分布——非对称拉普拉斯分布似然函数的表达,从而为贝叶斯分位数回归方法在WinBUGS由得以实施奠定了基础。(2)将贝叶斯分位数回归方法中非对称拉普拉斯分布的尺度(scale)参数进行参数化,并通过Gibbs抽样算法得到其后验分布。实验结果表明,与未参数化时相比,参数化后Gibbs抽样算法得到的估计量统计性质更好。(3)针对连续因变量的贝叶斯分位数回归估计方法,首先,模拟不同先验分布设定和不同抽样算法对参数估计量统计性质的影响,实验结果表明,合适的先验分布可以提高Gibbs抽样估计量的统计性质；Gibbs抽样与M-H抽样相比,得到的估计量偏误和标准差更小。其次,比较频率学派和贝叶斯学派对分位数回归模型估计量的有效性和假设检验的准确性,模拟实验的结果表明,采用贝叶斯分位数回归方法得到的参数估计量的统计性质(偏误更小,精度更高)普遍优于传统内点法得到的统计性质,且前者检验功效更高。(4)针对离散因变量,对二元Probit分位数回归和Tobit分位数回归模型进行贝叶斯分析,模拟不同先验分布设定、不同抽样算法、不同估计方法对估计量的影响。
在实证研究部分,本文以我国股票市场和黄金市场为研究对象,采用贝叶斯分位数回归方法对股票市场风险来源和黄金的风险对冲功能进行了研究。实证结果表明：(1)我国上证A股、上证B股、H股的极端风险均受国际市场的影响。其中,上证B股、H股受到的影响最大；而对于上证A股的极端风险则主要来自于自身市场。最后给出我国股市应对大风险应采取的措施。(2)对于短期的投资者,投资黄金不能对冲通货膨胀和股票市场的风险。而从长期来看,只要投资者愿意长期持有黄金,黄金可以作为对冲通货膨胀和股票市场风险的有效工具。但是,在经济大萧条或者股市动荡时期,黄金不是股市和通胀的安全“避风港”。
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".
引文
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