英文文献：Bipower-type estimation in a noisy diffusion setting-噪声扩散环境下的双类型估计
英文文献作者：Mark Podolskij,Mathias Vetter
英文文献摘要：
We consider a new class of estimators for volatility functionals in the setting of frequently observed It? diffusions which are disturbed by i.i.d. noise. These statistics extend the approach of pre-averaging as a general method for the estimation of the integrated volatility in the presence of microstructure noise and are closely related to the original concept of bipower variation in the no-noise case. We show that this approach provides efficient estimators for a large class of integrated powers of volatility and prove the associated (stable) central limit theorems. In a more general It? semimartingale framework this method can be used to define both estimators for the entire quadratic variation of the underlying process and jump-robust estimators which are consistent for various functionals of volatility. As a by-product we obtain a simple test for the presence of jumps in the underlying semimartingale.

摘要研究了一类新的易变泛函的估计量，这些估计量在常观测的Ito扩散受噪声干扰的情况下存在。这些统计量扩展了预平均方法作为估计微结构噪声中综合波动率的一般方法，并与无噪声情况下双功率变化的原始概念密切相关。证明了该方法提供了一类挥发性积分幂的有效估计，并证明了相应的(稳定)中心极限定理。在更一般的Ito半鞅框架中，该方法可用于定义基础过程整个二次变差的估计量和对各种波动泛函一致的跳稳健估计量。作为一个副产品，我们获得了一个简单的测试，用于测试底层半马拉加ale中是否存在跳转。