Feature Extraction of Time Series Based on Discrete Information Entropy Theory

This paper introduces a novel methodology for analyzing the complexity of time series using the fractional order dispersion entropy (qDE) and fractional order reverse dispersion entropy (qRDE) plane. Building on the theoretical foundations of dispersion entropy and its transformation, this paper introduces new entropy measures, namely, qDE and qRDE, detailing the computation processes of these entropies and constructing an entropy plane. This new approach offers fresh perspectives and tools for time series complexity analysis. Through theoretical derivations and numerical experiments, including analysis of both simulated and real stock market data, this method has demonstrated strong effectiveness in distinguishing time series of varying complexities, particularly in capturing the trends of financial market outputs over different periods. The results demonstrate that the qDE-qRDE plane can distinctly differentiate time series with varying dynamics and effectively reveal the complexities and cyclical changes in financial markets, showcasing the potential and practical value of this method in time series analysis.