Specific Differential Entropy Rate Estimation for Continuous-Valued Time Series
This work addresses the need for more precise unpredictability measures in time series analysis, particularly for physiological data like heart rate variability, but it appears incremental as it extends existing entropy concepts.
The paper tackles the problem of quantifying unpredictability in continuous-valued time series by introducing a specific entropy rate that measures predictive uncertainty for specific states, rather than averaging over all states, and demonstrates its application in synthetic and physiological heart rate variability data.
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.