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 is 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 construct 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. 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是过去二十余年的活跃研究领域。最广为人知且广泛研究的问题之一，是估计含跳跃的伊藤半鞅连续部分二次变差。当跳跃分量为有界变分时，文献中已提出若干速率与方差高效的估计量。然而，截至目前，能处理无界变分跳跃的方法极为有限。通过发展局部稳定列维过程截断矩的新型高阶展开，我们为一类跳跃局部行为类似Blumenthal-Getoor指数 $Y\in (1,8/5)$（即无界变分）稳定列维过程的伊藤半鞅，构造了新的速率与方差高效波动率估计量。所提方法基于过程截断已实现二次变分的两步去偏程序。蒙特卡洛实验表明，在理论框架覆盖的设定下，该方法优于文献中其他高效替代方案。