Inference on the Lévy measure in case of noisy observations
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Date
2013-04-23
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Abstract
In this paper we are concerned with inference on the Lévy measure of a Lévy
process in case of noisy high frequency observations. It is known that standard techniques
for denoising, developed for diffusion settings, do not work in this case. For
this reason, we provide an extension of the pre-averaging method which allows for
a consistent estimation of the Lévy distribution function even under microstructure
noise. Interestingly, the asymptotic behaviour of the novel estimator is the same as in
the no-noise case. This is in sharp contrast to what is known for diffusions.
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Keywords
Lévy process, microstructure noise, nonparametric statistics, weak convergence