Surrogate data pathologies and the false-positive rejection of the null hypothesis

It is shown that inappropriately constructed random phase surrogates can gi ve false-positive rejections of the surrogate null hypothesis. Specifically , the procedure erroneously indicated the presence of deterministic, nonlin ear structure in a time series that was constructed by linearly filtering n ormally distributed random numbers. It is shown that the erroneous identifi cation was due to numerical errors in the estimation of the signal's Fourie r transform. In the example examined here, the introduction of data windowi ng into the algorithm eliminated the false-positive rejection of the null h ypothesis. Additional guidelines for the use of surrogates are considered, and the results of a comparison test of random phase surrogates, Gaussian s caled surrogates and iterative surrogates are presented.