Fourier phase randomization Can anybody please explain or point to an online resource that explains the Fourier phase randomization technique? I encountered it in the context of comparing the cross-correlation of two signals before and after Fourier phase randomization. What does it mean when the cross-correlation disappears after Fourier phase randomization? Thank you.
 A: So, the original paper that describes the method is the following: Theiler, J., Eubank, S., Longtin, A., Galdrikian, B., & Doyne Farmer, J. (1992). Testing for nonlinearity in time series: the method of surrogate data. Physica D: Nonlinear Phenomena, 58(1), 77-94. As the title suggests, it is a test of nonlinearity in time series. As the abstract of the paper explains: 

The method first specifies some linear process as a null hypothesis,
  then generates surrogate data sets which are consistent with this null
  hypothesis, and finally computes a discriminating statistic for the
  original and for each of the surrogate data sets. If the value
  computed for the original data is significantly different than the
  ensemble of values computed for the surrogate data, then the null
  hypothesis is rejected and nonlinearity is detected.

A more detailed explanation from Podobnik, B., Fu, D. F., Stanley, H. E., & Ivanov, P. C. (2007). Power-law autocorrelated stochastic processes with long-range cross-correlations. The European Physical Journal B, 56(1), 47-52.:

The procedure creates a surrogate data with the same correlation
  properties as the original signal. Following the procedure, one
  performs a Fourier transform on the original time series, preserving
  the Fourier amplitudes but randomizing the Fourier phases. Finally,
  one performs an inverse Fourier transform to create surrogate data.

I hope this helps other people who encountered the method in a context where it was not properly explained.
