Wavelet Analysis on Stochastic Time Series

Wavelet analysis is a method to decompose a time series into time-frequency space. This view offers interesting insights into the dominant modes of a time series and how those modes vary over time.

The aim of this paper is to give an introduction into the field of wavelets by using a rather visual approach.

Two types of financial time series will be examined.

First, artificial time series that were generated by including trends and disturbances into a random process and second, real world long term financial time series that date back until the time before the great depression. For all those time series wavelet spectras were calculated and visualized. To understand what kind of information a wavelet spectrum is providing, it very much helps to visualize those spectras in an appealing way.

Of course the wavelet spectrum can only be fully understood by examining the theory behind it. Therefore a description on how the wavelet spectras in this paper were cal-

culated will be given; along with a description on how we can interpret the values of such a spectrum from a mathematical point of view. The theory may only cover a small part of the whole field of wavelet theory. But is should be enough to get a solid base on which further and more complex work can be developed, such as strategies for financial trading.