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.

中文翻译：

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基于广义分数阶细化复合多尺度离散熵的时间序列复杂度分析

本文基于色散熵模型，结合多尺度分析方法和分数阶信息熵理论，提出了新模型——广义分数阶多尺度色散熵（GMDE）和广义分数阶细化复合多尺度色散熵（GRCMDE）。新模型考虑了序列本身的幅值信息，可以更好地利用序列中的一些关键信息，具有更高的稳定性和准确性。此外，将算法扩展到广义分数阶，可以使模型更好地捕捉信号数据的微小演化，更有利于研究复杂系统的动态特性。本文将理论分析与实证研究相结合，验证了新模型的有效性，并进一步研究了金融系统的复杂性及其多时间尺度的性质。结果表明，提出的GMDE、GRCMDE能够更好地检测金融时间序列的内在本质，能够区分不同国家金融市场的复杂性。