dorsal/arxiv
View SchemaDetecting non-linearities in data sets. Characterization of Fourier phase maps using the Weighted Scaling Indices
| Authors | Roberto A. Monetti, Wolfram Bunk, Ferdinand Jamitzky, Christoph Raeth, Gregor Morfill |
|---|---|
| Categories | |
| ArXiv ID | physics/0405130 |
| URL | https://arxiv.org/abs/physics/0405130 |
Abstract
We present a methodology for detecting non-linearities in data sets based on the characterization of the structural features of the Fourier phase maps. A Fourier phase map is a 2D set of points $M= \{(\phi_{\vec{k}}, \phi_{\vec{k} + \vec{\Delta}})\}$, where $ \phi_{\vec{k}}$ is the phase of the $k$-mode of the Fourier transform of the data set and $\vec{\Delta}$ a phase shift. The information thus rendered on this space is analyzed using the spectrum of weighted scaling indices to detect phase coupling at any scale $\vec{\Delta}$. We propose a statistical test of significance based on the comparison of the properties of phase maps created from both the original data and surrogate realizations. We have applied our method to the Lorenz system and the logarithmic stock returns of the Dow Jones index. Applications to higher dimensional data are straightforward. The results indicate that both the Lorenz system and the Dow Jones time series exhibit significant signatures of non-linear behavior.
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"abstract": "We present a methodology for detecting non-linearities in data sets based on\nthe characterization of the structural features of the Fourier phase maps. A\nFourier phase map is a 2D set of points $M= \\{(\\phi_{\\vec{k}}, \\phi_{\\vec{k} +\n\\vec{\\Delta}})\\}$, where $ \\phi_{\\vec{k}}$ is the phase of the $k$-mode of the\nFourier transform of the data set and $\\vec{\\Delta}$ a phase shift. The\ninformation thus rendered on this space is analyzed using the spectrum of\nweighted scaling indices to detect phase coupling at any scale $\\vec{\\Delta}$.\nWe propose a statistical test of significance based on the comparison of the\nproperties of phase maps created from both the original data and surrogate\nrealizations. We have applied our method to the Lorenz system and the\nlogarithmic stock returns of the Dow Jones index. Applications to higher\ndimensional data are straightforward. The results indicate that both the Lorenz\nsystem and the Dow Jones time series exhibit significant signatures of\nnon-linear behavior.",
"arxiv_id": "physics/0405130",
"authors": [
"Roberto A. Monetti",
"Wolfram Bunk",
"Ferdinand Jamitzky",
"Christoph Raeth",
"Gregor Morfill"
],
"categories": [
"physics.data-an"
],
"title": "Detecting non-linearities in data sets. Characterization of Fourier phase maps using the Weighted Scaling Indices",
"url": "https://arxiv.org/abs/physics/0405130"
},
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