Local SIML estimation of some Brownian and jump functionals under market micro-structure noise

Abstract

This paper is a contribution to a special issue on Data Science: Present and Future, because the main topic has been and will be in an active area of contemporary data science. High-frequency financial data are commonly available by now. To estimate Brownian and jump functionals from high-frequency financial data under market micro-structure noise, we introduce a new local estimation method of the integrated volatility and higher order variation of Ito’s semi-martingale processes. Although extending the realized volatility (RV) estimation to the general diffusion-jump processes without micro-market noise is straightforward, estimating Brownian and jump functionals in the presence of micro-market noise may not be easy. In this study, we develop the local SIML (LSIML) method, which is an extension of the separating information maximum likelihood (SIML) method proposed by Kunitomo et al. (Separating information maximum likelihood method for high-frequency financial data, 2018) and Kunitomo and Kurisu (Jpn J Stat Data Sci (JJSD) 4(1):601–641, 2021). The new LSIML method is simple, and the LSIML estimator has some desirable asymptotic properties and reasonable finite sample properties.