Specific Differential Entropy Rate Estimation for Continuous-Valued Time Series

Abstract

We introduce a method for quantifying the inherent unpredictability of a continuous-valued time series via an extension of the differential Shannon entropy rate. Our extension, the specific entropy rate, quantifies the amount of predictive uncertainty associated with a specific state, rather than averaged over all states. We relate the specific entropy rate to popular `complexity' measures such as Approximate and Sample Entropies. We provide a data-driven approach for estimating the specific entropy rate of an observed time series. Finally, we consider three case studies of estimating specific entropy rate from synthetic and physiological data relevant to the analysis of heart rate variability.