  Testing for nonlinearity is one of the most important preprocessing steps in
nonlinear time series analysis. Typically, this is done by means of the linear
surrogate data methods. But it is a known fact that the validity of the results
heavily depends on the stationarity of the time series. Since most
physiological signals are non-stationary, it is easy to falsely detect
nonlinearity using the linear surrogate data methods. In this document, we
propose a methodology to extend the procedure for generating constrained
surrogate time series in order to assess nonlinearity in non-stationary data.
The method is based on the band-phase-randomized surrogates, which consists
(contrary to the linear surrogate data methods) in randomizing only a portion
of the Fourier phases in the high frequency band. Analysis of simulated time
series showed that in comparison to the linear surrogate data method, our
method is able to discriminate between linear stationarity, linear
non-stationary and nonlinear time series. When applying our methodology to
heart rate variability (HRV) time series that present spikes and other kinds of
nonstationarities, we where able to obtain surrogate time series that look like
the data and preserves linear correlations, something that is not possible to
do with the existing surrogate data methods.
