Weak convergence of the empirical truncated distribution function of the Lévy measure of an Itō semimartingale

2015/06/24 by Michael Hoffmann, Hoffmann, Michael, Mathias Vetter +2 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability and Risk Models #Statistical Methods and Inference #Statistics Theory (math.ST) #Stochastic processes and financial applications #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1506.07404

arxiv created 2015/06/24 · openalex publication_date 2015/06/24 · arxiv updated 2015/06/25 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

Given an Itō semimartingale with a time-homogeneous jump part observed at high frequency, we prove weak convergence of a normalized truncated empirical distribution function of the Lévy measure to a Gaussian process. In contrast to competing procedures, our estimator works for processes with a non-vanishing diffusion component and under simple assumptions on the jump process.

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