Nonparametric estimation of the jump component in financial time series

In this thesis, we analyze nonparametric estimation of Lévy-based
models using wavelets methods. As the considered class is
restricted to pure-jump Lévy processes, it is sufficient to
estimate their Lévy densities. For implementing a wavelet density
estimator, it is necessary to setup a preliminary histogram
estimator. Simulation studies show that there is an improvement of
the wavelet estimator by invoking an optimally selected histogram.
The wavelet estimator is based on block-thresholding of empirical
coefficients. We conclude with two empirical applications which
show that there is a very high arrival rate of small jumps in
financial data sets.