Regensburg 2004 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 20: Fractals and Nonlinearity I
DY 20.6: Vortrag
Dienstag, 9. März 2004, 11:00–11:15, H2
Detecting non-linearities in data sets. Characterization of Fourier phase maps using the Weighting Scaling Indices. — •Roberto Monetti, Wolfram Bunk, Ferdinand Jamitzky, Christoph Raeth, and Gregor Morfill — CIPS, Max-Planck-Inst. f. extraterr. Physik, Gaching
The analysis of the linear properties (LP) (power spectrum, etc) is the first step in the characterization of data sets. However, given an image for instance one can generate a new one by shuffling the Fourier phases. The new image looks different though the phase shuffling process keeps the LP. Then, the Fourier phases contain information beyond the LP called non-linear properties (NLP). A challenging problem is the characterization of the information contained in the Fourier phases. We present a method to detect NLP in arbitrary data sets. With a set of Fourier phases { φk→ } and a phase shift Δ→, we represent the phase information on a 2D space via the phase maps M= { (φk→, φk→ + Δ→) }. The information rendered on this space is analyzed using the spectrum of weighting scaling indices to detect phase coupling at any scale Δ→. We have applied our method to the time series of the logarithmic stock returns of the Dow Jones. Applications to higher dimensional data are straighforward. The results indicate that the Dow Jones time series exhibits highly significant signatures of a strong non-linear behavior.