非参数动态混合Copula模型：估计、推断及应用

On account of new problems in financial risk management ,and the drawbacks of dynamic mixture Copula in risk management applications, this research project is to combine mixture Copula and nonparametric method to solve the problems of how to choose Copula and how to model dynamic parameters,and then propose a new model specification test to check the applicability of nonparametric models. The research topics in the project include: (1) The theoretical modeling of local linearly time-varying Copula and single index Copula within two dimensions , the former is a function of time t, and the latter is a function of linear combination of external variables. (2) The modeling methods of bivariate Copulas such as time-varying nonparametric model and single index model are extended to C and D vine Copulas. The asymptotic normality, the principles of choosing optimal bandwidth, and Monte Carlo simulations are studied in Case (1) and (2). Finally, the performances of the proposed models with traditional dynamic mixture Copula are compared. (3 )Model specification test is proposed to test constancy of dependence in mixture Copula.(4)The application of the proposed models to measure market dynamic risk value in Chinese financial markets such as future and spot stock markets, exchange rate markets as well as interest rate markets. Some perceptive suggestions will be proposed to investors and financial regulatory authorities.

针对目前金融风险管理中新出现的问题，以及针对动态Copula模型在风险管理应用中所存在的缺陷，本项目将混合Copula模型与非参数方法相结合来解决Copula模型的选择和参数的动态化问题，并提出新的模型适用性检验方法。具体包括：（1）二元混合Copula的局部线性时变模型和单指数模型。前者把参数设为时间t的函数，后者把参数设为外生变量的线性组合函数。（2）把二元下的局部线性和单指数型扩展到较为流行的多元C型和D型藤状Copula模型。在（1）和（2）中，我们将考察非参数估计量的渐近统计性质以及带宽选择的影响，研究有限样本下的Monte Carlo 模拟表现，并与传统各类参数模型进行比较,评价其优越性。（3）构建非参数动态混合Copula模型适用性的检验方法。（4）运用新发展的模型来考察包括我国股指期货、现货市场、汇率市场以及利率市场的风险时变特征。

如何正确地刻画金融变量间的相依性对金融资产的投资组合具有重要意义。Copula方法是近年来发展起来的用以研究变量间非正态、非线性相依结构的最有效方法之一。然而，目前Copula建模方法仍存在较多局限性，如主要停留在静态参数模型阶段，只能同时刻画某种相依特征。本项目针对传统Copula建模所存在的缺陷，提出了动态混合非参数建模方法。第一种为时变型，即不对模型的参数进行任何形式的设定，而假设权重系数以及Copula参数为时间的函数；第二种为单指数型，即假设权重系数与相依参数的变动由外生变量的线性组合驱动。我们运用局部极大似然估计法来对参数进行估计。我们推导出了非参数估计量的渐近正态性质， 讨论估计量的偏差与方差的大小， 并运用交叉验证法给出最优带宽的选择。另外，为了检验所提出的动态混合Copula的模型的适用性，我们在广义似然比框架下，构建混合Copula模型非参数估计的模型诊断、检验和识别方法。最后，我们把新发展的方法用于研究中国A、B、H股票市场间尾部相依性的长期变化趋势。