Semiparametric Estimation in Continuous-Time: Asymptotics for Integrated Volatility Functionals with Small and Large Bandwidths

This article studies the estimation of integrated volatility functionals, which is a semiparametric two-step estimation problem in the nonstationary continuous-time setting. We generalize the asymptotic normality results of Jacod and Rosenbaum to a wider range of bandwidths. Moreover, we employ matrix calculus to obtain a new analytical bias correction and variance estimation method. The proposed method gives more succinct expressions than the element-by-element analytical method of the above cited article. In addition, it has a computational advantage over the jackknife/simulation-based method proposed by Li, Liu, and Xiu. Comprehensive simulation studies demonstrate that our method has good finite sample performance for a variety of volatility functionals, including quadraticity, determinant, continuous beta, and eigenvalues.