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

Xiye Yang

Journal of Business & Economic Statistics, 2021, vol. 39, issue 3, 793-806

Abstract: 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.

Date: 2021
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DOI: 10.1080/07350015.2020.1733583

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