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高维金融数据的波动性因子分析:方法与理论

国家自然科学基金青年科学基金项目(项目号: 71601131)

    李委明老师的课题《高维金融数据的波动性因子分析:方法与理论》,获得获得国家自然科学基金青年科学基金的资助(项目号:71601131,资助额度17万元),执行期限为2017年1月至2019年12月。
    在实证中,时间序列的条件方差往往随时间而变化,我们称之为波动率或条件异方差,这是时间序列分析的重要内容,对譬如金融定价、风险管理、证券监管、资产组合、对冲基金等都有重要意义。对于单变量条件异方差模型,文献已经进行了充分研究,得到了一系列完整理论与体系。然而,研究者们普遍认为宏观或金融变量应该建立向量模型,将多个变量放一起进行建模,这就需要对多变量的条件协方差矩阵服从的随机过程进行研究。从单变量模型向多变量模型推广,在概念上并没什么难度,但在实践操作中却遇到了巨大困难,譬如 “维数诅咒”。本项目构建一个因子模型框架,对高维数据的波动过程进行建模。首先应用主成分分析法对高维数据进行降维,得到主导其波动率的主波动成分,然后构建一个低维多变量GARCH模型,进一步得到其中的模型参数。本项目还将得到参数估计量的渐近结果,用以统计推断。无论是中国或国际的宏观或金融数据,本项目的理论都具有广阔应用前景。
    Empirical time series always exhibit the feature of time varying conditional covariances, known as volatility or conditional heteroscedasticity, which plays a very important role in financial pricing, risk management, securities regulations, portfolio allocation and hedging. While a number of statistical models as sell as the associated inference methods and theory have been well developed for modeling and forecasting univariate volatilities, almost all real macro and financial applications require to specify the volatilities for multiple series jointly. This calls for the modeling of conditional variance-covariance matrix processes. Though there is little conceptual difficulty in extending most univariate volatility models to multivariate cases, the estimation and the implementation for multivariate volatility models are of great technical challenge, including the curse of dimensionality. Since it is believed that the volatilities of many financial assets are often driven by a few common latent factors, we propose in the project a factor structure to model the high dimensional volatility processes. Principal component analysis is used at the first stage to reduce the dimension of the volatility space and to estimate to so-called principal volatility components. A lower-dimensional multivariate GARCH model is employed to estimate the structural coefficients for the volatility factors. Asymptotic results and statistical inference will be established. The proposed method and theory can be applied to macro and financial data in Chinese market as well as international market.   
 

(日期:2016-08-30 作者:李委明 来源:)