There are two major reasons why one might want to read this thesis - or in
general study nonlinear methods in time series analysis: to improve predictions
and to enhance the data quality of a nonlinear dynamics experiment.

For a given signal processing task (eg a prediction problem) there might be
hope that a nonlinear algorithm gives superior results. For example the human
electro-encephalogram (EEG) assumes a characteristic shape a few moments
before an epileptic seizure occurs. The dynamics seems to be neither periodic
nor completely random. Can nonlinear dynamics help predicting or even
preventing a possible seizure?

On the other hand the theory of nonlinear dynamics has inspired many
experiments which explore phenomena related to deterministic chaos. Nonlinear
methods are essential for the understanding the data from such experiments. As
usual, one wants to filter the data in order to reduce the noise before any
quantities are evaluated. However, traditional filters do not only fail to
reduce noise in chaotic data, they even distort essential features of the
signal. Nonlinear noise reduction, which forms one of the main subjects of this
work, can enhance data precision considerably while the nonlinear structure in
the data is preserved.