A note on estimation of quarticity based on spot volatility

TL;DR

This paper introduces a new, intuitive estimator for quarticity of continuous Itô semimartingales, establishes its CLT with a specific convergence rate, and compares its asymptotic variance with existing estimators.

Contribution

The paper proposes a novel estimator for quarticity, provides its CLT, and compares its efficiency with classical estimators.

Findings

The new estimator satisfies a CLT with convergence rate 1/√Δn.

The asymptotic variance of the new estimator is compared to existing estimators.

The new estimator is more intuitive than classical methods.

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.