Entropic Analysis of Time Series through Kernel Density Estimation

This work presents a novel framework for time series analysis using entropic measures based on the kernel density estimate (KDE) of a time series' Takens' embedding in two dimensions. Using this framework we introduce two distinct analytical tools: (1) a multi-scale KDE entropy metric, denoted as $\Delta\text{KE}$, which quantifies the evolution of time series complexity across different delay time scales by measuring changes in entropy, and (2) a sliding baseline method that employs the Kullback-Leibler (KL) divergence to detect changes in time series structure through changes in KDEs. The $\Delta{\rm KE}$ metric offers insights into the information content and ''unfolding'' properties of the time series' Takens' embedding well-suited to the analysis of dynamical systems, while the KL-divergence-based approach provides a noise and outlier robust measure for identifying time series change points well-suited to the detection of injected radio frequency (RF) signals in noisy backgrounds. We demonstrate the effectiveness and versatility of these tools through a set of experiments across several science and technology domains. In the case of RF communications, we achieve accurate detection of injected signals under varying noise and interference conditions comparable with tools of the art and without the need for training. Secondly, we apply our methodology to electrocardiography (ECG) data, successfully identifying instances of ventricular fibrillation with high accuracy. Finally, we demonstrate the potential of our tools for identifying anomalous intermittent chaotic regimes within a signal in dynamical systems.