近日，我院苏涛博士以共同第一作者身份与美国西北大学凯洛格管理学院Torben G. Andersen教授、Viktor Todorov教授以及上海财经大学张志远教授合作的研究论文“Intraday Periodic Volatility Curves”被统计学顶级期刊《Journal of the American Statistical Association》（美国统计学会会刊，JASA）在线发表。JASA是美国统计协会旗下出版的专业性统计期刊，是目前国际统计学界论文质量最高、覆盖领域最广的顶级学术期刊之一。

论文题目：Intraday Periodic Volatility Curves

论文摘要：The volatility of financial asset returns displays pronounced variation over the trading day. Our goal is nonparametric inference for the average intraday volatility pattern, viewed as a function of time-of-day. The functional inference is based on a long span of high-frequency return data. Our setup allows for general forms of volatility dynamics, including time-variation in the intraday pattern. The estimation is based on forming local volatility estimates from the high-frequency returns over overlapping blocks of asymptotically shrinking size, and then averaging these estimates across days in the sample. The block-based estimation of volatility renders the error in the estimation due to the martingale return innovation asymptotically negligible. As a result, the centered and scaled calendar volatility effect estimator converges to a Gaussian process determined by the empirical process error associated with estimating average volatility across the trading day. Feasible inference is obtained by consistently estimating the limiting covariance operator. Simulation results corroborate our theoretical findings. In an application to S&P 500 futures data, we find evidence for a shift in the intraday volatility pattern over time, including a more pronounced role for volatility outside U.S. trading hours in the latter part of the sample.

金融资产回报的波动率在日内表现出明显的变化。本文的目标是对平均日内波动率模式进行非参的推断，将日内波动率视为日内时间的函数。泛函推断是基于长跨度的高频回报数据。本文的模型设定允许广义的波动率变化过程，包括波动率日内变化模式。平均日内波动率的估计量是先从高频回报中得到每天的点波动率估计，然后再把这些点波动率估计平均。点波动率估计的误差主要是由回报中鞅的部分引起的，但该部分可以渐近忽略。因此，标准化的平均日内波动率估计量收敛到一个高斯过程，由平均每天波动率估计的经验过程所确定。通过估计极限协方差算子实现可行的推断。模拟结果验证了理论发现。在对标普500期货数据的应用中，发现日内波动率是随着时间变化的，包括在样本的后一部分，美国交易时间外的波动率对于波动率变化有更明显的作用。