A Surrogate Test for Pseudo-periodic Time Series Data

Standard (linear) surrogate methods are only useful for time series exhibiting no pseudoperiodic structure. We describe a new algorithm that can distinguish between a noisy periodic orbit and deterministic non-periodic inter-cycle dynamics. Possible origins of deterministic nonperiodic inter-cycle dynamics include: non-periodic linear or nonlinear dynamics, or chaos. This new algorithm is based on mimicking the large-scale dynamics with a local model, but obliterating the fine scale features with dynamic noise. We demonstrate the application of this method to artificial data and experimental time series, including human electrocardiogram (ECG) recordings during sinus rhythm and ventricular tachycardia (VT). The method is able to successfully differentiate between the chaotic Rossler system and a pseudo periodic realization of the Rossler equations with dynamic noise. Application to ECG data demonstrates that both sinus rhythm and VT exhibit nontrivial inter-cycle dynamics.