On the analysis tools of turbulent and financial time series

The aim of this work is to give a review on some of the important tools used in analyzing time series. Since turbulence turned out to be a rather complex phenomenon, a variety of different models and analysis tools have been devised to simulate, analyze and address the different questions that are raised by the behaviour of these seemingly very erratic, highly chaotic time series that are gained from the natural phenomena or the models that are supposed to simulate these processes whether natural, financial, ... etc. The most part of the work was dedicated to the stationary time series which are gained from laboratory controlled turbulence experiments, for example, or the models that simulate them e.g. the direct numerical simulation. The main models that were dealt with are the large eddy simulation (LES) and the diffusion equation which is a simplified version of the Navier-Stokes equations (NSE). Then there are tools that are used to extract different information from the time series, like the dimensions, e.g. embedding, fractal, correlation, and the statistical tools like the spectrum, autocorrelation, scaling of the structure function. We have shown that these tools do not say a lot about non-stationary time series and that there are another set of tools e.g. the spectrogram, Wigner-Ville spectrum, wavelets, that define more clearly events that have a beginning and an end but the full interpretation of their results needs more research.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Oldenburg

Year

2007

Author dc:creator

• Mohammed, Amjed

• [Keine Schlagwörter von Autor/in vergeben.]

Repository record source_url

http://oops.uni-oldenburg.de/746

OAI identifier oai:identifier

oai:oops.uni-oldenburg.de:746