贝叶斯柔性密度方法及其在高维金融数据中的应用

项目名称： 贝叶斯柔性密度方法及其在高维金融数据中的应用

项目编号： No.11501587

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 李丰

作者单位： 中央财经大学

项目金额： 18万元

中文摘要： 贝叶斯高维密度柔性建模是贝叶斯方法论的热点和难点课题。然而目前多元密度建模方法的研究成果往往限定在对单一的或者连续或者离散型变量下密度特征的静态研究中，而且实际可操作性停留在响应变量维度小于十的低维情况，尚不能实现有效全面地描述复杂高维数据中关联性尤其是尾部关联性。基于申请者前期研究成果，本课题拟首先从混合有连续边际和离散边际的二维Copula密度的贝叶斯柔性建模出发，以密度估计理论为支撑，利用并改进MCMC抽样技术、结合贝叶斯变量选择理论、深入研究混合离散和连续边际的Copula协变量相依的动态相依性和尾部相依性。其次利用贝叶斯条件独立性、以及基于预测的贝叶斯模型比较理论，将二维Copula柔性密度理论扩展到混合连续边际和离散边际的高维贝叶斯柔性密度的高效构建和估计中。本课题理论成果将为混合有文本信息的高维金融数据建模等复杂数据应用领域提供有效的解决工具。

中文关键词： 柔性密度建模；MCMC方法；Copula函数；高维数据；多元模型

英文摘要： Bayesian Flexible modeling of high dimensional density is the state-of-the-art topic in Bayesian methodology. Financial data have the unique feature such as time-dependent, high-dimensional, non-Gaussian and heavy correlated among variables. Tremendous research has been done on continuous financial data in low-dimensions. Recent research also has found the importance of textual data interfering financial events. Unfortunately there is still lack of research on modeling high-dimensional data combining with textual data and continuous data. This is partially because that constructing high-dimensional density that can be modeled with continuous and discrete margins is not yet efficient. Usual statistical inference tools are less likely to be successful in that setting because of the curse of dimensionality, especially when there are more than a couple of margins...In this project, we propose a general approach for modeling data features in high-dimensional density with flexible continuous and discrete marginal densities. Our approach begins with a two-dimensional copula density where the rank correlation and tail-dependence coefficients are connected with covariates via smooth functions, in which the two marginal densities are from finite mixture of student-t densities and Poisson densities, respectively. We propose a highly efficient MCMC algorithm that updates all the marginal and joint density features jointly. And we also propose an efficient stochastic searching margins permutation algorithm that effectively constructs a high-dimensional flexible copula density with flexible bivariate copulas. Unlike the usual reversible jump MCMC used in the literature which is heavily dependent by the choice of prior and can only update one margin per time. Our algorithm jointly update the joint multivariate density with an efficient propose of margin combinations by Bayesian model comparison techniques based on out of sample predictive performance that eliminates the effect from the prior...Our proposed Bayesian approach is applied to high dimensional stock market data with additional text information provided by Bloomberg.

英文关键词： Flexible Density Modeling;MCMC;Copula;High Dimensional;Multivariate Modeling