Comparison of entropy rate measures for the evaluation of time series complexity: Simulations and application to heart rate and respiratory variability

Abstract

Most real-world systems are characterised by dynamics and correlations emerging at multiple time scales, and are therefore referred to as complex systems. In this work, the complexity of time series produced by complex systems was investigated in the frame of information theory computing the entropy rate via the conditional entropy (CE) measure. A comparative investigation of several CE estimators, based on linear parametric and non-linear model-free representations of the process dynamics, was performed considering simulated linear autoregressive (AR) and mixed non-linear deterministic and linear stochastic dynamics processes, as well as physiological time series reflecting short-term cardiorespiratory dynamics. In simulations, the estimated CE values decreased when reducing the system complexity through an increase in the pole radius of the AR process or with the predominance of the deterministic behaviour in the mixed dynamics. In the application to cardiorespiratory dynamics, a reduction in physiological complexity was observed resulting from a regularization of the time series of heart rate and respiratory volume when decreasing the breathing rate. Our results evidence how simple and fast approaches based on linear parametric or permutation-based model-free estimators allow efficient discrimination of complexity changes in the short-term evolution of complex dynamic systems. However, in the presence of non-linear dynamics, the superiority of the more general but computationally expensive nearest-neighbour method is highlighted. These findings have implications for the assessment of complex dynamics both in clinical settings and in physiological monitoring.