Asymptotic Normality and Finite-Sample Robustness of the Fourier Spot Volatility Estimator in the Presence of Microstructure Noise
研究了高频价格受微观结构噪声污染时，傅里叶瞬时波动率估计量的有效性和稳健性，证明了其渐近正态性并给出了最优收敛速度，同时提出了切割频率的可行选择方法。
We study the efficiency and robustness of the Fourier spot volatility estimator when high-frequency prices are contaminated by microstructure noise. First, we show that the estimator is consistent and asymptotically efficient in the presence of additive noise, establishing a Central Limit Theorem (CLT) with the optimal rate of convergence n1/8. Additionally, we complete the asymptotic theory in the absence of noise, obtaining a CLT with the optimal rate of convergence n1/4. Feasible CLTs with the optimal convergence rate are also obtained, by proving the consistency of the Fourier estimators of the spot volatility of volatility and the quarticity in the presence of noise. Second, we introduce a feasible method for selecting the cutting frequencies of the estimator in the presence of noise, based on the optimization of the integrated asymptotic variance. Finally, we provide support to the accuracy and robustness of the method by means of a numerical study and an empirical exercise, which is conducted using tick-by-tick prices of three U.S. stocks with different liquidity.