引入联跳的中国股市协方差预测——基于多元HAR模型  

The Role of Cojumps in Forecasting Covariance Matrices in Chinese Stock Markets:A Study Based on the Multivariate HAR Model

作　　者：瞿慧[1] 纪萍[1] 

机构地区：[1]南京大学工程管理学院,南京210093

出　　处：《管理科学》2016年第6期28-38,共11页Journal of Management Science

基　　金：国家自然科学基金(71671084;71201075);教育部高等学校博士学科点专项科研基金(20120091120003)~~

摘　　要：金融资产的时变协方差矩阵是投资组合配置、风险管理等实务活动的关键参数。早期的协方差预测模型研究使用日数据或者更低频数据,但大多存在参数估计困难和维数灾难等问题。运用日内高频数据可以构建协方差矩阵的后验非参数估计量,使其从隐变量转变为可以直接建模的可观测变量,降低协方差模型估计的复杂性并增强模型的高维适用性。进一步的,利用高频数据还可以识别多个金融资产的价格在日内同一采样间隔内发生的跳跃,即多资产联跳。针对联跳多由宏观经济新闻公告和政策制度等的发布引起,这些信息终将被吸收并体现在协方差矩阵中,联跳可能蕴含着对协方差预测有益的信息,因此识别联跳并将其引入协方差预测模型。将异质自回归模型扩展至多元形式,作为协方差非参数估计量的基准模型,并将取值0/1的联跳指示变量与Hawkes模型估计出的联跳强度分别及同时引入多元形式模型,构建3种扩展模型。选择均方误差和平均绝对误差这两种常用统计意义损失函数,采用Diebold Mariano检验,评价各扩展模型的样本外预测性能相对于基准模型是否有所改进,并采用模型置信集检验并挑选最佳扩展模型。此外,比较各种预测模型用于全局最小方差投资组合策略的效果。基于上证50指数成分股中不同行业5只高流动性个股分钟高频价格数据进行实证,研究结果表明,(1)相对于联跳指示变量,联跳强度对协方差矩阵的预测有更显著的贡献;(2)引入联跳强度可以显著提升对协方差的拟合优度和样本外预测精度;(3)同时引入联跳强度和联跳指示变量,且采用矩阵对数变换,确保正定性的扩展多元形式模型在统计和经济意义上都是最优模型。研究结论肯定了在协方差预测模型中引入联跳的重要价值,并揭示了宏观信息对协方差预测的贡献,对于金融管理者和投资者�The time-varying covariance matrix of the financial assets is the key for financial applications such as portfolio alloca- tion and risk management. Previous studies on covariance matrix forecasting use daily or even lower frequency data, causing the problems of parameter estimation difficulty and curse of dimensionality. With intraday high-frequency data, non-parametric estimators of the covariance matrix can be constructed. This turns the co- variance matrix from hidden to an observable variable that can be directly modeled, thus reducing the complexity of eovariance model estimation and increasing the applicability of covariance models in high-dimension applications. Furthermore, with high- frequency data, cojumps can be identified, which refers to jumps of multiple asset prices in the same intraday sampling interval. Cojumps are often triggered by macr0economic news announcements and policy releases, and such macro-information will eventu- ally be absorbed and reflected in the covariance matrix. Thus, we argue that cojumps may contain information beneficial for co- variance forecasting and propose to identify cojumps and use them in the covariance forecasting models. The multivariate heterogeneous autoregressive（MHAR） model is used as the benchmark model for the nonparametric covari- ance matrix estimator. The cojump indicators and the cojump intensities estimated by the Hawkes model are included as addition- al predictors, first separately and then simultaneously. Based on the mean squared error and the mean absolute error criteria, the three extended MHAR models are each compared with the benchmark using the Diebold Mariano test in terms of their out-of-sam- ple forecast performance. The model confidence set test is then used to identify the best models. Besides, the out-of-sample fore- casts are used in the global minimum variance portfolio strategy to justify the economic value of the extended models. We consider five high liquidity stocks from different sectors of the SSE 50 index and employ their

关 键 词：协方差预测 联跳 多元异质自回归模型 Hawkes模型 模型置信集检验 全局最 小方差投资组合 

分 类 号：F830.91[经济管理—金融学]