Grey dispersion entropy based on truncated Gaussian whitenization function: a novel time series complexity measure

Time series originate from different systems, and analyzing their complexity provides insights into the system’s core characteristics. Dispersion entropy (DE) is now regarded as one of the most powerful entropy methods for quantifying the complexity of a time series. However, DE is often sensitive to noise, thus a novel grey dispersion entropy (GDE) is suggested to alleviate this problem. Specifically, the truncated grey Gaussian whitenization function is substituted for the primary round function in DE, based on a notion of grey number whitening in grey theory. Furthermore, we also advocate using dynamic grey dispersion entropy (DGDE) to enhance the mapping outcome by means of a dynamic truncated grey Gaussian function. Simulation Experiments reveal that, when compared to DE, the proposed GDE and DGDE have lower noise sensitivity, reliable entropy calculation outcomes, and can detect both amplitude and frequency changes. Last but not least, real-world datasets from the biological, mechanical, and financial domains are used to apply GDE and DGDE. It has been found that GDE and DGDE are able to identify different states of the real signal and detect subtle dynamic sequence changes.