RELIABLE DETECTION OF NONLINEARITY IN EXPERIMENTAL TIME-SERIES WITH STRONG PERIODIC COMPONENTS

Testing with phase-randomised surrogate signals has been used extensiv ely to search for interesting nonlinear dynamical structure in experim ental time series. In this paper we argue that, in the case of experim ental time series with strong periodic components, the method of phase -randomised surrogate data may not be particularly suitable to test fo r nonlinearity, since construction of such surrogates by FFT requires a time series whose length is a power of 2. We demonstrate that, in th e case of (nearly) periodic signals, this approach will almost always produce spurious detection of nonlinearity. This error can be fixed by adjusting the length of the time series such that it becomes an integ er multiple of the dominant periodicity. The resulting time series wil l not be a power of 2, and requires the use of a DFT to generate surro gate data. DFT-based surrogates no longer detect spurious nonlinearity , but cannot be used to detect periodic nonlinearity. We propose a new test, nonlinear cross-prediction (NLCP), which avoids some of the pro blems associated with phase-randomised surrogate data, and which allow s reliable detection of both periodic and aperiodic nonlinearity. In t he test the original data are used to construct a nonlinear model to p redict the original data set as well as amplitude-inverted and time-re versed versions of the original data. Lower predictability of the ampl itude-inverted or time-reversed copies reflect, respectively, an asymm etric amplitude distribution and time irreversibility. Both of these i ndicate nonlinearity in the data set.