Large Volatility Matrix Inference via Combining Low-Frequency and High-Frequency Approaches
Large Volatility Matrix Inference via Combining Low-Frequency and High-Frequency Approaches
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DOI：
10.1198/jasa.2011.tm10276
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发表时间：
2011-09-01
影响因子：
3.7
通讯作者：
Zou, Jian
中科院分区：
文献类型：
--
作者：
Tao, Minjing;Wang, Yazhen;Zou, Jian
在金融经济学中，对资产收益波动率的估计越来越重要。然而，由于对高维矩阵的估计缺乏准确性，大多数可用的方法在涉及的资产数量较大时不能直接适用。因此，减少波动矩阵的有效大小以产生足够的估计和预测是相关的。此外，由于不同资产的高频财务数据通常不是在同一时间点记录的，因此传统的降维技术不能直接适用。为了克服这些困难，我们探索了一种将高频波动矩阵估计与低频动态模型相结合的新方法。提出的方法包括三个步骤：(i)直接基于高频数据估计每日实现的共波动矩阵，（ii）将矩阵因子模型拟合估计的每日共波动矩阵，以及（iii）将向量自回归模型拟合估计的波动因子。我们在允许样本量、资产数量和天数一起趋近无穷大的框架中为所提出的方法建立了渐近理论。我们的理论表明，相关的特征值和特征向量可以一致地估计。我们用2003年177天期间在深圳和上海证券交易所交易的数百只股票的高频价格数据来说明这一方法。我们的方法在日内（高频）和日间（低频）水平上汇集了建模和估计的优势。
It is increasingly important in financial economics to estimate volatilities of asset returns. However, most of the available methods are not directly applicable when the number of assets involved is large, due to the lack of accuracy in estimating high-dimensional matrices. Therefore it is pertinent to reduce the effective size of volatility matrices in order to produce adequate estimates and forecasts. Furthermore, since high-frequency financial data for different assets are typically not recorded at the same time points, conventional dimension-reduction techniques are not directly applicable. To overcome those difficulties we explore a novel approach that combines high-frequency volatility matrix estimation together with low-frequency dynamic models. The proposed methodology consists of three steps: (i) estimate daily realized covolatility matrices directly based on high-frequency data, (ii) fit a matrix factor model to the estimated daily covolatility matrices, and (iii) fit a vector autoregressive model to the estimated volatility factors. We establish the asymptotic theory for the proposed methodology in the framework that allows sample size, number of assets, and number of days go to infinity together. Our theory shows that the relevant eigenvalues and eigenvectors can be consistently estimated. We illustrate the methodology with the high-frequency price data on several hundreds of stocks traded in Shenzhen and Shanghai Stock Exchanges over a period of 177 days in 2003. Our approach pools together the strengths of modeling and estimation at both intra-daily (high-frequency) and inter-daily (low-frequency) levels.