Estimating the distribution of dynamic invariants: Illustrated with an application to human photo-plethysmographic time series

Dynamic invariants are often estimated from experimental time series with the aim of differentiating between different physical states in the underlying system. The most popular schemes for estimating dynamic invariants are capable of estimating confidence intervals, however such confidence intervals do not reflect variability in the underlying dynamics. In this communication we propose a surrogate based method to estimate the expected distribution of values under the null hypothesis that the underlying deterministic dynamics are stationary. We demonstrate the application of this method by considering four recordings of human pulse waveforms in differing physiological states and provide conclusive evidence that correlation dimension is capable of differentiating between three (but not all four) of these states.