Performance analysis of four nonlinearity analysis methods using a model with variable complexity and application to...

Several measures have been proposed to detect nonlinear characteristics in time series. Results on time series, multiple surrogates and their z-score are used to statistically test for the presence or absence of non-linearity. The z-score itself has sometimes been used as a measure of nonlinearity. The sensitivity of nonlinear methods to the nonlinearity level and their robustness to noise have rarely been evaluated in the past. While surrogates are important tools to rigorously detect nonlinearity, their usefulness for evaluating the level of nonlinearity is not clear. In this paper we investigate the performance of four methods arising from three families that are widely used in non-linearity detection: statistics (time reversibility), predictability (sample entropy, delay vector variance) and chaos theory (Lyapunov exponents). We used sensitivity to increasing complexity and the mean square error (MSE) of Monte Carlo instances for quantitative comparison of their performances. These methods were applied to a Henon nonlinear synthetic model in which we can vary the complexity degree (CD). This was done first by applying the methods directly to the signal and then using the z-score (surrogates) with and without added noise. The methods were then applied to real uterine EMG signals and used to distinguish between pregnancy and labor contraction bursts. The discrimination performances were compared to linear frequency based methods classically used for the same purpose such as mean power frequency (MPF), peak frequency (PF) and median frequency (MF). The results show noticeable difference between different methods, with a clear superiority of some of the nonlinear methods (time reversibility, Lyapunov exponents) over the linear methods. Applying the methods directly to the signals gave better results than using the z-score, except for sample entropy.