A note on estimation of quarticity based on spot volatility

Abstract

In this paper, we aim at estimating the quarticity of continuous It\^{o} semimartingales. Instead of using some classical estimators, we introduce a more intuitive one and establish a central limit theorem (CLT) for it, with a convergence rate of $1/\sqrt{\Delta_n}$ in the sense of stable convergence. Moreover, we compare the asymptotic variance of this estimator with that of other existing estimators.