On Double Smoothed Volatility Estimation of Potentially Nonstationary Jump-Diffusion Model

TL;DR

This paper introduces a double smoothed nonparametric method for estimating the infinitesimal conditional volatility in jump-diffusion models using high-frequency data, ensuring consistency and normality under minimal conditions.

Contribution

It develops a novel double smoothed estimator for jump-diffusion volatility that is consistent and asymptotically normal for various recurrent processes.

Findings

Estimator is strongly consistent as T→∞ and Δn→0

Estimator is asymptotically normal under minimal conditions

Applicable to both Harris recurrent and positive Harris recurrent processes

Abstract

In this paper, we present the double smoothed nonparametric approach for infinitesimal conditional volatility of jump-diffusion model based on high frequency data. Under certain minimal conditions, we obtain the strong consistency and asymptotic normality for the estimator as the time span $T \rightarrow \infty$ and the sample interval $\Delta_{n} \rightarrow 0.$ The procedure and asymptotic behavior can be applied for both null Harris recurrent and positive Harris recurrent processes.