论文标题
在存在无限变化的情况下，有效的综合波动率估计通过伪造的截断已实现的变化跳跃
Efficient Integrated Volatility Estimation in the Presence of Infinite Variation Jumps via Debiased Truncated Realized Variations
论文作者
论文摘要
基于高频观察的随机过程的统计推断已成为一个活跃的研究领域，已有二十多年了。最著名和最广泛研究的问题之一是估计具有跳跃的ItôSemimartingale连续成分的二次变化。当跳跃成分有界限时，在文献中提出了几种速率和方差估计器。但是，迄今为止，很少有方法可以处理无界变化的跳跃。通过为本地稳定的Lévy过程的截断瞬间开发新的高级扩展，我们为一类ItôSemimartingales提供了一个新的速率和差异波动性估计器，其跳跃在本地的行为与Blumenthal-Getoor-Getoor intex $ y y in（1,1,8/5）$ y Unbecound（Hence）的稳定lévy流程的行为一样。所提出的方法是基于对该过程的截断已实现的二次变化的两步偏数程序，还可以覆盖案例$ y <1 $。我们的蒙特卡洛实验表明，该方法在我们的理论框架所涵盖的环境中的文献中优于文献中的其他有效替代方案。
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 Itô 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 Lévy process, we propose a new rate- and variance-efficient volatility estimator for a class of Itô semimartingales whose jumps behave locally like those of a stable Lévy 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.
