Estimation of quarticity with high frequency data

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

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. © 2012 Copyright Taylor and Francis Group, LLC.