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.