EFFICIENT ESTIMATION OF INTEGRATED VOLATILITY FUNCTIONALS UNDER GENERAL VOLATILITY DYNAMICS

Jia Li and Yunxiao Liu

Econometric Theory, 2021, vol. 37, issue 4, 664-707

Abstract: We provide an asymptotic theory for the estimation of a general class of smooth nonlinear integrated volatility functionals. Such functionals are broadly useful for measuring financial risk and estimating economic models using high-frequency transaction data. The theory is valid under general volatility dynamics, which accommodates both Itô semimartingales (e.g., jump-diffusions) and long-memory processes (e.g., fractional Brownian motions). We establish the semiparametric efficiency bound under a nonstandard nonergodic setting with infill asymptotics, and show that the proposed estimator attains this efficiency bound. These results on efficient estimation are further extended to a setting with irregularly sampled data.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:cup:etheor:v:37:y:2021:i:4:p:664-707_2

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