I have a set of time series, more specifically velocity components (u, v), of which their phase relation determines the rotational motion of the surrounding water. The clockwise and counterclowise motion is found by taking the Fourier transform of the complex form of the components, f.ex. z = u + i*v, the so-called rotary spectra (e.g. Gonella, 1972).
The phase relation between these two vectors is essential, as by just randomly creating independent surrogates of the components does affect the energy spectrum and we lose information of the real state. I used an IAAFT approach for this, but the results diverge from the expected values even for synthetic time series.
My question is thus the following: Is there an approach for creating surrogates for a pair of time series in which their phase relation property is conserved?
Thanks in advance.