光华讲坛——社会名流与企业家论坛第5449期

主题：Principal Component Analysis and Realized Regression with Asynchronous and Noisy High Frequency Data

主讲人：伊利诺伊大学芝加哥分校 陈大川博士

主持人：统计学院统计研究中心 林华珍教授

时间：2019年6月18日（星期二）下午16:00-17:00

地点：西南财经大学柳林校区弘远楼408会议室

主办单位：统计研究中心 统计学院 科研处

主讲人简介：

Dachuan Chen received his Ph.D. degree in Business Administration at University of Illinois at Chicago at 2019. His dissertation advisors are Professor Lan Zhang (from the University of Illinois at Chicago) and Professor Per Mykland (from the University of Chicago). Dachuan’s research interests include financial econometrics and high frequency econometrics. His research papers have been published in several leading journals, including the Journal of Econometrics and IIE Transactions. He received 2018 Stevanovich Student Fellowship from Stevanovich Center for Financial Mathematics, University of Chicago (UoC), as the first recipient from non-UoC universities.

陈大川2019年在伊利诺伊大学芝加哥分校获得工商管理博士学位。他的论文导师是伊利诺伊大学芝加哥分校Lan Zhang教授和芝加哥大学 Per Mykland 教授。陈大川的研究方向包括金融计量经济学和高频计量经济学。有多篇论文发表在Journal of Econometrics、IIE Transactions等计量经济学的顶级期刊上。他还获得了芝加哥大学金融数学中心（UOC）2018年Stevanovich学生奖学金，成为第一位非芝加哥大学学生的获奖者。

主要内容：

We develop the principal component analysis (PCA) and regression tools for high frequency data. As in Northern fairy tales, there are trolls waiting for the explorer. The first three trolls are market microstructure noise, asynchronous sampling times, and edge effects in estimators. To get around these, a robust estimator of spot covariance matrix is developed based on the Smoothed TSRV (Mykland et al. (2017)). The fourth troll is how to pass from estimated time-varying covariance matrix to PCA and realized regression. Under finite dimensionality, we develop this methodology through the estimation of realized spectral functions and time-varying betas. Rates of convergence and central limit theory, as well as an estimator of standard error, are established. The fifth troll is high dimension on top of high frequency, where we also develop PCA and regression techniques. The high-dimensional rates of convergence have been studied for the estimation of large covariance matrix.

In the empirical study, we use the intraday asset returns of the components of the S&P 100 index from TAQ database of NYSE. As an application of PCA, we show that our first principal component (PC) is very close to the iShares S&P 100 ETF after normalization. The empirical study on realized regression explores (i) the validity of time-varying CAPM and (ii) the change in beta around earnings announcements. In the last application, the result suggests that the announcement arrival time is one source of the heterogeneity of the change in beta for large-cap stocks.

我们为高频数据开发了主成分分析（PCA）和回归工具。就像北方的童话里总有巨魔在等着探险家一样，我们在研究中也在不断地攻克着“巨魔”。首先遇到的三个问题是市场微观结构噪声、异步时间采样和估计量中的边缘效应。针对以上问题Mykland等人（2017）提出了一种基于光滑TSRV的点协方差矩阵的稳健估计方法。第四个难题是如何将估计的时变协方差矩阵转化为PCA并实现回归，我们在有限维数下通过估计已实现的谱函数和时变β来推进解决措施，此外还建立了收敛速度和中心极限理论以及标准误差的估计方法。第五个则是高频上的高维问题，对此我们也相应开发了PCA和回归技术，并研究了大协方差矩阵估计的高维收敛速度。

在实证研究中，我们使用了纽约证交所Taq数据库中标准普尔100指数组成部分的日内资产回报率。作为PCA的一个实际应用，我们发现我们的第一主成分（PC）在标准化后非常接近于IShares标准普尔100 ETF。对已实现回归的实证研究探讨了（i）时变资本资产定价模型的有效性和（ii）盈利公告前后的贝塔系数变化。最后一个应用的结果表明，公告到达时间是大型股贝塔系数变化的异质性的一个影响因素。