This paper analyzes the benefits of sampling intraday returns in intrinsic time for the realized variance (RV) estimator. We theoretically show in finite samples that depending on the permitted sampling information, the RV estimator is most efficient under either hitting time sampling that samples whenever the price changes by a pre-determined threshold, or under the new concept of realized business time that samples according to a combination of observed trades and estimated tick variance. The analysis builds on the assumption that asset prices follow a diffusion that is time-changed with a jump process that separately models the transaction times. This provides a flexible model that allows for leverage specifications and Hawkes-type jump processes and separately captures the empirically varying trading intensity and tick variance processes, which are particularly relevant for disentangling the driving forces of the sampling schemes. Extensive simulations confirm our theoretical results and show that for low levels of noise, hitting time sampling remains superior while for increasing noise levels, realized business time becomes the empirically most efficient sampling scheme. An application to stock data provides empirical evidence for the benefits of using these intrinsic sampling schemes to construct more efficient RV estimators as well as for an improved forecast performance.

翻译：本文分析了在内在时间中对日内收益率进行抽样对已实现方差（RV）估计量的益处。我们在有限样本中从理论上证明，根据所允许的抽样信息，RV估计量在以下两种情况下效率最高：要么是在价格变化达到预定阈值时进行抽样的击中时间抽样法下，要么是在根据观察到的交易和估计的报价变动方差相结合进行抽样的新概念——已实现业务时间抽样法下。该分析基于资产价格遵循一个扩散过程的假设，该扩散过程由一个跳跃过程进行时间变换，该跳跃过程单独对交易时间进行建模。这提供了一个灵活的模型，允许纳入杠杆效应设定和霍克斯型跳跃过程，并分别捕捉了经验上变化的交易强度过程和报价变动方差过程，这对于厘清不同抽样方案的驱动因素尤为重要。大量的模拟实验证实了我们的理论结果，并表明在低噪声水平下，击中时间抽样法仍然更优；而在噪声水平增加时，已实现业务时间抽样法成为经验上最有效的抽样方案。对股票数据的应用提供了经验证据，表明使用这些内在抽样方案来构建更高效的RV估计量以及获得改进的预测性能是有益的。