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EFFICIENT ESTIMATION OF INTEGRATED VOLATILITY FUNCTIONALS UNDER GENERAL VOLATILITY DYNAMICS

Published online by Cambridge University Press:  17 July 2020

Jia Li  and
Yunxiao Liu
Jia Li*
Affiliation:
Duke University
Yunxiao Liu
Affiliation:
University of North Carolina at Chapel Hill
*
Address correspondence to Jia Li, Department of Economics, Duke University, Durham, NC 27708, USA; e-mail: jl410@duke.edu.
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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.

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 4 , August 2021 , pp. 664 - 707
Copyright
© Cambridge University Press 2020

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Footnotes

We are grateful for comments from a co-editor and two anonymous referees, which have greatly improved the paper. We also thank Tim Bollerslev, Peter Hansen, Andrew Patton, Vladas Pipiras, George Tauchen, and Jean Jacod for helpful comments. J.L.’s research was partially supported by NSF Grant SES-1326819.

References

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