Phase-randomized surrogates can produce spurious identifications of non-random structure

Calculations with surrogate variants of original data are used to validate results obtained in dynamical analysis. Three classes of surrogates are now in use: random-shuffle surrogates, random-phase surrogates and Gaussian-scaled random-phase surrogates. In this paper we present an example based on a natural source of random numbers (radioactive decay) in which random-shuffle and Gaussian-scaled random-phase surrogates both correctly identify the random nature of the data while random-phase surrogates give a dramatic, and totally spurious, identification of non-random structure. The application of random-phase surrogates by themselves, without confirmatory calculations using Gaussian-scaled random-phase surrogates, is becoming increasingly common. The results presented here argue against this practice. The first step in the application of symbolic analysis to dynamical data is the partitioning of the data into a finite symbol alphabet. These results also show that appropriately constructed surrogates can be used as a protection against spurious results caused by defective partitioning.