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

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.