The typical central limit theorems in high-frequency asymptotics for semimartingales are results on stable convergence to a mixed normal limit with an unknown conditional variance. Estimating this conditional variance usually is a hard task, in particular when the underlying process contains jumps. For this reason, several authors have recently discussed methods to automatically estimate the conditional variance, i.e. they build a consistent estimator from the original statistics, but computed at different time scales. Their methods work in several situations, but are essentially restricted to the case of continuous paths always. The aim of this work is to present a new method to consistently estimate the conditional variance which works regardless of whether the underlying process is continuous or has jumps. We will discuss the case of power variations in detail and give insight to the heuristics behind the approach.

中文翻译：

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估计半鞅极限定理中条件方差的通用方法

半鞅的高频渐近法中的典型中心极限定理是稳定收敛到具有未知条件方差的混合正态极限的结果。估计这种条件方差通常是一项艰巨的任务，特别是当底层过程包含跳转时。出于这个原因，几位作者最近讨论了自动估计条件方差的方法，即他们从原始统计数据构建一致的估计量，但在不同的时间尺度上计算。他们的方法适用于多种情况，但本质上始终仅限于连续路径的情况。这项工作的目的是提出一种新方法来一致地估计条件方差，无论基础过程是连续的还是有跳跃的，该方法都有效。