Complexity Analysis of Time Series Based on Generalized Fractional Order Refined Composite Multiscale Dispersion Entropy

Based on the dispersion entropy model, combined with multiscale analysis method and fractional order information entropy theory, this paper proposes new models - the generalized fractional order multiscale dispersion entropy (GMDE) and the generalized fractional order refined composite multiscale dispersion entropy (GRCMDE). The new models take the amplitude value information of the sequence itself into consideration, which can make better use of some key information in the sequence and have a higher stability and accuracy. In addition, extending the algorithm to generalized fractional order can make the model better capture the small evolution of the signal data, which is more advantageous for studying the dynamic characteristics of complex systems. This paper verifies the effectiveness of the new models by combining theoretical analysis with empirical research, and further studies the complexity of the financial system and the nature of its multiple time scales. The results show that the proposed GMDE, GRCMDE can better detect the intrinsic nature of financial time series and can distinguish the financial market complexity of different countries.