A note on estimation of quarticity based on spot volatility

In this paper, we aim at estimating the quarticity of continuous Itô 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 $1\mathrm{/}\sqrt{{\mathrm{\Delta }}_n}$ in the sense of stable convergence. Moreover, we compare the asymptotic variance of this estimator with that of other existing estimators.