Estimating spot volatility under infinite variation jumps with dependent market microstructure noise
针对高频金融数据中同时存在无限变异性跳跃和序列相关噪声的难题，提出一种混合预平均技术和经验特征函数的瞬时波动率估计量，并证明其一致性和渐近正态性。
Summary Jumps and market microstructure noise are stylized features of high-frequency financial data. It is well known that they introduce bias in the estimation of volatility (including integrated and spot volatilities) of assets, and many methods have been proposed to deal with this problem. When the jumps are intensive with infinite variation, the efficient estimation of spot volatility under serially dependent noise is not available and is thus in need. For this purpose, we propose a novel estimator of spot volatility with a hybrid use of the pre-averaging technique and the empirical characteristic function. Under mild assumptions, the results of consistency and asymptotic normality of our estimator are established. Furthermore, we show that our estimator achieves an almost efficient convergence rate with optimal variance when the jumps are either less active or active with symmetric structure. Simulation studies verify our theoretical conclusions. We apply our proposed estimator to empirical analyses, such as estimating the weekly volatility curve using second-by-second transaction price data.