论文标题
使用预先计算的微观结构噪声对斑点波动的内核估计
Kernel Estimation of Spot Volatility with Microstructure Noise Using Pre-Averaging
论文作者
论文摘要
我们首先回顾了使用内核估计器估算ItôSemimartingale的斑点波动的问题。我们证明了一个中央限制定理，对于一般的双面内核，具有最佳收敛速率。接下来，我们引入了一种新的预 - 平均/内核估计器，以进行点波动率，以处理超高频观察的微观结构噪声。我们证明了具有最佳速率的估计误差定理，并研究带宽和内核函数的最佳选择。我们表明，预定/内核估计量的渐近方差对于指数核的差异很小，因此，这表明需要与本工作提出的无限支持的内核合理。我们还开发了具有最佳带宽的提议估计器的可行实现。蒙特卡洛实验证实了设计方法的出色性能。
We first revisit the problem of estimating the spot volatility of an Itô semimartingale using a kernel estimator. We prove a Central Limit Theorem with optimal convergence rate for a general two-sided kernel. Next, we introduce a new pre-averaging/kernel estimator for spot volatility to handle the microstructure noise of ultra high-frequency observations. We prove a Central Limit Theorem for the estimation error with an optimal rate and study the optimal selection of the bandwidth and kernel functions. We show that the pre-averaging/kernel estimator's asymptotic variance is minimal for exponential kernels, hence, justifying the need of working with kernels of unbounded support as proposed in this work. We also develop a feasible implementation of the proposed estimators with optimal bandwidth. Monte Carlo experiments confirm the superior performance of the devised method.
