日间模式是否足以解释日内波动变化？一种非参数评估
Is the diurnal pattern sufficient to explain intraday variation in volatility? A nonparametric assessment
AI总结：
本文提出非参数方法检验日间模式是否能解释日内波动变化，发现日间模式解释了显著部分，但异方差性仍存在。
摘要：
在本文中，我们提出了一种非参数方法来检验时间变化的日内波动性是否仅由确定性和重复的日间模式引起。我们假设可以获取噪声高频数据，这些数据来自离散采样跳跃扩散过程。测试基于资产回报率，这些回报率被季节性成分抵消，因此在原假设下是同方差的。为了构建我们的检验统计量，我们通过截断装置将预平均双功率变异的概念扩展到一般的Itô半鞅设置中。我们证明了该统计量的中心极限定理，并构造了一个正定估计的渐近协方差矩阵。t统计量（在预平均和跳跃截断后）在存在随机波动性时会发散，否则服从标准正态分布。我们证明将真实的日间因素替换为无模型跳跃和噪声鲁棒估计器不会影响渐近理论。蒙特卡洛模拟也显示这种替换在有限样本中没有明显影响。然而，测试受到小无限活动价格跳跃的扭曲。为了改进推断，我们提出了一种新的自助法，这导致几乎正确大小的原假设检验。我们应用开发的框架到大量股票高频数据，并发现日间模式解释了日内波动变化相当大的比例，但数据中仍然存在重要的异方差性来源。
英文摘要：
In this paper, we propose a nonparametric way to test the hypothesis that time-variation in intraday volatility is caused solely by a deterministic and recurrent diurnal pattern. We assume that noisy high-frequency data from a discretely sampled jump-diffusion process are available. The test is then based on asset returns, which are deflated by the seasonal component and therefore homoskedastic under the null. To construct our test statistic, we extend the concept of pre-averaged bipower variation to a general Itô semimartingale setting via a truncation device. We prove a central limit theorem for this statistic and construct a positive semi-definite estimator of the asymptotic covariance matrix. The $t$-statistic (after pre-averaging and jump-truncation) diverges in the presence of stochastic volatility and has a standard normal distribution otherwise. We show that replacing the true diurnal factor with a model-free jump- and noise-robust estimator does not affect the asymptotic theory. A Monte Carlo simulation also shows this substitution has no discernable impact in finite samples. The test is, however, distorted by small infinite-activity price jumps. To improve inference, we propose a new bootstrap approach, which leads to almost correctly sized tests of the null hypothesis. We apply the developed framework to a large cross-section of equity high-frequency data and find that the diurnal pattern accounts for a rather significant fraction of intraday variation in volatility, but important sources of heteroskedasticity remain present in the data.
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