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 practice. 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 often relying entirely on heuristics. In this paper, we consider novel data-driven tuning procedures for the truncated realized variations of a semimartingale with jumps based on a type of random fixed-point iteration. Being effectively automated, our approach alleviates the need for delicate decision-making regarding tuning parameters in practice 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：许多在跳跃存在下估计半鞅积分波动率及相关泛函的方法，在实际应用时需要指定调优参数。在现有理论中，调优参数通常被假定为确定性的，且其值仅通过渐近约束加以规定。然而，在实证研究与模拟分析中，这些参数往往被选择为随机的且依赖于数据，其具体选择常完全依赖于启发式方法。本文针对含跳跃半鞅的截断实现变分，提出一种基于随机定点迭代的新型数据驱动调优程序。该方法实现了自动化处理，避免了实践中针对调优参数的精细决策需求，且仅需利用采样频率信息即可实施。我们证明该方法能够实现积分波动率的渐近有效估计，并在有限样本表现上优于文献中主流替代方法。