Estimation of the characteristics of a L\'evy process observed at arbitrary frequency

Johanna Kappus , Markus Reiß

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976),

MSC 2000

62G05 Estimation

62M15 Spectral analysis

Abstract
A L\'evy-process is observed at time points of distance $\Delta$ until time $T$. We construct an estimator of the L\'evy-Khinchine characteristics of the process and derive optimal rates of convergence simultaneously in $\Delta$ and $T$. Thereby, we encompass the usual high- and low-frequency assumptions and obtain also asymptotics in the mid-frequency regime.