  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.
