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.