波动率泛函的估计：一个平方根n窗口的情形
Estimation of volatility functionals: the case of a square root n window
摘要：
考虑在[0，t]上以1/Δ n的高频率正则采样的多维Ito半鞅，其中Δ n趋于零.本文的目的是提供一个估计的积分在[0，t]上的一个给定的函数的波动率矩阵，具有最佳率1/ \sqrt{Δ_n}和最小的渐近方差。为了实现这一点，我们使用基于长度为k_nΔ_n的时间间隔内的观测值的现货波动率估计。在文献[5]中，k_n趋于无穷大，k_n \sqrt{Δ_n}趋于0，并在适当去偏后给出了一个中心极限定理。这里我们对阶数为1/ \sqrt{Δ_n}的k_n做同样的事情。这导致较小的偏差，尽管更难以消除。
英文摘要：
We consider a multidimensional Ito semimartingale regularly sampled on [0,t] at high frequency 1/Δ_n, with Δ_n going to zero. The goal of this paper is to provide an estimator for the integral over [0,t] of a given function of the volatility matrix, with the optimal rate 1/\sqrt{Δ_n} and minimal asymptotic variance. To achieve this we use spot volatility estimators based on observations within time intervals of length k_nΔ_n. In [5] this was done with k_n tending to infinity and k_n\sqrt{Δ_n} tending to 0, and a central limit theorem was given after suitable de-biasing. Here we do the same with k_n of order 1/\sqrt{Δ_n}. This results in a smaller bias, although more difficult to eliminate.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
