带非参数分布的GARCH模型的贝叶斯统计分析

GARCH model is important models for describing financial asset returns. Recently GARCH model is based on the assumption that the conditional distribution is a kind of parameteric distributions with the characteristics, such as fat-tails and lepkutosis. The reason is that just the modified GARCH models still can''t fully descirbe the characteristics, more attentions are needed to study the conditional distribution. However, the emprical results show that GARCH models with one kind parametric distribution also can''t capture the characteristics of returns, and it is hard to decide which distribuion is better. Therefore, this project proposes to use nonparametric distribution to descirbe the conditional distribution and the GARCH model with nonparametric distribution, and use Bayesian theory to study problem including parameter estimation and model selection. This project an effective MCMC algorithms combining the ideas of retrospective sampling, the slice sampling and the Griddy-Gibbs sampling, and use data augmentation techniques and numerical integration methods such that all the conditional distributions are easy to sample. And proposes to use the modified DIC to study model selection. Lastly we will compile the coresponding code before the end of this project, and can provide it for practical users.

GARCH模型是研究金融资产收益的重要工具，由于仅靠改进其结构形式不能全面地解释金融资产收益尖峰厚尾等特性，需要将越来越多的注意力转移到条件分布研究中。然而现有文献多集中于参数化条件分布，而对于非参数化条件分布的研究尚不多见。本项目拟采用非参数分布来描述条件分布特性，进而建立带非参数分布的GARCH模型，并运用贝叶斯方法对模型进行分析，包括参数估计和模型选择。由于模型结构复杂，因此分析的难点在于如何从后验分布中有效地抽取样本以得到未知参数的后验估计。本项目在贝叶斯方法的框架下，拟利用回溯抽样、切片抽样、Griddy-Gibbs抽样、数据增广和数值积分方法来解决这一问题。另外，本项目还会利用改进的偏差信息准则（DIC）来研究模型比较问题。最后，我们会编写分析模型的程序，在本项目结束之时，我们会发布这一程序以供有需要的研究者使用。

本项目研究成果包括两方面内容：（1）带非参数分布的 GARCH模型的模型设定和参数估计；（2）带非参数分布的 GRACH模型的比较研究。.在第一个方面，利用 Dirichlet 过程混合模型去描述 GARCH 模型的条件分布，建立带非参数分布的 GARCH 模型；利用切片抽样（Sclice sampling）、数据增广和Griddy-Gibbs抽样等MCMC抽样技术估计模型参数。项目在半参数GARCH 模型的参数估计研究中取得了重要成果。.在第二方面，利用改进的偏差信息准则（DIC）研究参数和半参数GARCH模型的比较问题。研究结果表明，半参数GARCH模型可更好地刻画金融资产收益特性。