论文标题
一种通用方法，用于估计半明星限制定理的条件差异
A universal approach to estimate the conditional variance in semimartingale limit theorems
论文作者
论文摘要
半明星高频渐近性中的典型中心极限定理是稳定收敛到混合正常极限的结果，并具有未知的条件差异。估计条件差异通常是一项艰巨的任务，特别是当基础过程包含跳跃时。因此，几位作者最近讨论了自动估计条件差异的方法，即它们从原始统计数据中构建了一致的估计器，但在不同的时间范围内进行了计算。它们的方法在几种情况下起作用，但基本上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，以始终如一地估计有条件差异的方法，无论基础过程是连续还是跳跃。我们将详细讨论功率变化的案例，并深入了解该方法背后的启发式方法。
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 various 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.
