Weak convergence of the empirical truncated distribution function of the Lévy measure of an Itos semimartingale
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Date
2015
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Abstract
Given an Ito semimartingale with a time-homogeneous jump part observed
at high frequency, we prove weak convergence of a normalized truncated empirical
distribution function of the Levy 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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Keywords
empirical distribution function, weak convergence, Lévy measure, Ito semimartingale, high-frequency statistics