Estimation of quarticity with high-frequency data

Abstract

We propose a new methodology based on Fourier analysis to estimate the fourth power of the volatility function (spot quarticity) and, as a byproduct, the integrated function. We prove the consistency of the proposed estimator of the integrated quarticity. Further, we analyse its efficiency in the presence of microstructure noise, from both a theoretical and empirical viewpoint. Extensions to higher powers of volatility and to the multivariate case are also discussed.

Keywords:

• Volatility
• Covariance
• Quarticity
• Microstructure
• Fourier analysis

JEL Classification:

• C13
• C14
• C58
• G10

Acknowledgements

We wish to thank Neil Shephard, Dobrislav Dobrev, Frederi Viens and an anonymous referee for their insightful comments and remarks.