Specific Differential Entropy Rate Estimation for Continuous-Valued Time Series

TL;DR

This paper proposes a novel method to estimate the specific differential entropy rate of continuous-valued time series, enabling state-specific unpredictability analysis, with applications demonstrated on synthetic and physiological data.

Contribution

It introduces the concept of specific entropy rate, extending traditional entropy measures to quantify predictive uncertainty for individual states in time series.

Findings

The method effectively estimates specific entropy rates from data.

Application to heart rate variability data demonstrates practical utility.

The approach relates to existing complexity measures like Approximate and Sample Entropies.

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.