Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than two decades. One of the most well-known and widely studied problems has been the estimation of the quadratic variation of the continuous component of an It\^o semimartingale with jumps. Several rate- and variance-efficient estimators have been proposed in the literature when the jump component is of bounded variation. However, to date, very few methods can deal with jumps of unbounded variation. By developing new high-order expansions of the truncated moments of a locally stable L\'evy process, we propose a new rate- and variance-efficient volatility estimator for a class of It\^o semimartingales whose jumps behave locally like those of a stable L\'evy process with Blumenthal-Getoor index $Y\in (1,8/5)$ (hence, of unbounded variation). The proposed method is based on a two-step debiasing procedure for the truncated realized quadratic variation of the process and can also cover the case $Y<1$. Our Monte Carlo experiments indicate that the method outperforms other efficient alternatives in the literature in the setting covered by our theoretical framework.

翻译：基于高频观测数据的随机过程统计推断已活跃研究二十余年。其中最具代表性的经典问题之一，是估计带跳Itô半鞅连续分量的二次变差。当跳分量为有界变差时，文献中已提出多种速率及方差高效的估计量。然而，目前能处理无界变差跳的方法极为有限。通过建立局部稳定Lévy过程截断矩的新型高阶展开，本文针对一类局部跳行为类似于稳定Lévy过程且Blumenthal-Getoor指数$Y\in (1,8/5)$（即无界变差）的Itô半鞅，提出一种新的速率与方差高效的波动率估计量。该方法基于对过程截断实现二次变差的两步去偏技术，并同时覆盖$Y<1$的情形。蒙特卡洛实验表明，在理论框架所涵盖的设定下，该方法优于文献中的其他高效替代方案。