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Efficient Estimation Of Integrated Volatility Functionals Under General Volatility Dynamics

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  • Li, Jia
  • Liu, Yunxiao

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.

Suggested Citation

  • Li, Jia & Liu, Yunxiao, 2021. "Efficient Estimation Of Integrated Volatility Functionals Under General Volatility Dynamics," Econometric Theory, Cambridge University Press, vol. 37(4), pages 664-707, August.
  • Handle: RePEc:cup:etheor:v:37:y:2021:i:4:p:664-707_2
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    Cited by:

    1. Bollerslev, Tim & Li, Jia & Li, Qiyuan, 2024. "Optimal nonparametric range-based volatility estimation," Journal of Econometrics, Elsevier, vol. 238(1).

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