金融高频高维数据的波动率矩阵估计:基于GARCH-Ito分组因子模型

High-dimensional volatility matrix estimation with high-frequency financial data:The GARCH-Ito grouped factor model

在高频金融数据分析中,高维波动率矩阵的估计和预测十分具有挑战性,当金融资产存在自然的分组结构时,此问题尤为突出.为此,本文提出一种新的GARCH-Ito分组因子模型,将对数价格序列表示为共同因子、分组因子以及异质项,并通过将离散的广义自回归条件异方差(generalized autoregressive conditional heteroskedasticity,GARCH)结构嵌入特征值过程的波动率中,实现刻画数据波动率动态的目的.本文利用伪极大似然法得到模型的参数估计,建立极限理论,模拟研究表明其良好的有限样本性质.在实证研究中,利用上海证券交易所主板及深圳证券交易所创业板的股票高频价格数据,对比了不分组的模型及波动率矩阵的非参数多尺度已实现波动率(multi-scale realized volatility,MSRV)估计,对比结果显示本文模型具有更好的波动率预测效果.

In the research area of the high-frequency financial data analysis,estimation and prediction of the high-dimensional volatility matrix are challenging problems,especially when the assets of interest have a naturally given group structure.In order to address this issue,we propose a novel GARCH-Ito grouped factor model,in which we present the log price series of grouped assets with common factors,group-specific factors,and an assetspecific error term.We then embed the discrete GARCH structure into the volatility of the eigenvalue processes to capture the volatility dynamics of the observed price data.We propose a quasi maximum likelihood method for parameter estimation,establish its asymptotic properties and illustrate its good finite-sample performance with simulation.In real data analysis,we compare our method with the ungrouped factor model and the nonparametric high-frequency volatility estimator MSRV using the data from the SSE Main Board and the SZSE Chi Next market,where the proposed method outperforms its competitors in terms of prediction of the volatility matrix.