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

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