Many methods for estimating integrated volatility and related functionals of semimartingales in the presence of jumps require specification of tuning parameters for their use. In much of the available theory, tuning parameters are assumed to be deterministic, and their values are specified only up to asymptotic constraints. However, in empirical work and in simulation studies, they are typically chosen to be random and data-dependent, with explicit choices in practice relying on heuristics alone. In this paper, we consider novel data-driven tuning procedures for the truncated realized variations of a semimartingale with jumps, which are based on a type of stochastic fixed-point iteration. Being effectively automated, our approach alleviates the need for delicate decision-making regarding tuning parameters, and can be implemented using information regarding sampling frequency alone. We show our methods can lead to asymptotically efficient estimation of integrated volatility and exhibit superior finite-sample performance compared to popular alternatives in the literature.

翻译：许多估计存在跳跃的半鞅积分波动率及相关泛函的方法需要指定调谐参数以供使用。在现有的大部分理论中，调谐参数被假定为确定性的，且其值仅需满足渐近约束。然而，在实证研究和模拟分析中，这些参数通常被选为随机的且依赖于数据，实际中的明确选择仅依赖启发式方法。本文针对含跳跃半鞅的截断已实现变差，研究了一种基于随机固定点迭代的新型数据驱动调谐程序。该方法实现了自动化调谐，消除了关于调谐参数的细致决策需求，且仅需利用采样频率信息即可实施。我们证明：该方法能实现积分波动率的渐近有效估计，并在有限样本性能上优于文献中的主流替代方案。