We investigate price duration variance estimators that have long been neglected in the literature. In particular, we consider simple-to-construct non-parametric duration estimators, and parametric price duration estimators using autoregressive conditional duration specifications. This paper shows (i) how price duration estimators can be used for the estimation and forecasting of the integrated variance of an underlying semi-martingale price process and (ii) how they are affected by discrete and irregular spacing of observations, market microstructure noise, and finite price jumps. Specifically, we contribute to the literature by constructing the asymptotic theory for the non-parametric estimator with and without the presence of bid/ask spread and time discreteness. Further, we provide guidance about how our estimators can best be implemented in practice by appropriately selecting a threshold parameter that defines a price duration event, or by averaging over a range of non-parametric duration estimators. We also provide simulation and forecasting evidence that price duration estimators can extract relevant information from high-frequency data better and produce more accurate forecasts than competing realized volatility and option-implied variance estimators, when considered in isolation or as part of a forecasting combination setting.

中文翻译：

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基于价格持续时间的波动率估计和预测

我们研究了长期以来在文献中被忽视的价格久期方差估计量。特别是，我们考虑了易于构建的非参数持续时间估计器，以及使用自回归条件持续时间规范的参数价格持续时间估计器。本文展示了（i）价格持续时间估计量如何用于估计和预测基础半鞅价格过程的综合方差，以及（ii）它们如何受到离散和不规则的观察间隔、市场微观结构噪声、和有限的价格跳跃。具体来说，我们通过为存在和不存在买卖价差和时间离散性的非参数估计量构建渐近理论来为文献做出贡献。进一步，we provide guidance about how our estimators can best be implemented in practice by appropriately selecting a threshold parameter that defines a price duration event, or by averaging over a range of non-parametric duration estimators. 我们还提供了模拟和预测证据，证明价格持续时间估计器可以更好地从高频数据中提取相关信息，并产生比竞争的已实现波动率和期权隐含方差估计器更准确的预测，当单独考虑或作为预测组合设置的一部分时。