Complexity Analysis Of Time Series Based On Generalized Fractional Order Dual-Embedded Dimensional Multivariate Multiscale Dispersion Entropy

Based on the theories of multivariate multiscale dispersion entropy, we propose an improved new model — dual-embedded dimensional multivariate multiscale dispersion entropy (mvMDE), and generalize the new model to fractional order (GmvMDE). The mvMDE and GmvMDE simultaneously consider the cross-correlation between multiple channels, and they provide a dynamic complexity measure for measuring the multivariable data observed in one system. We introduce dual embedded dimensions to construct subsequences, which makes the model more flexible and applicable to a variety of application scenarios. Through empirical analysis of simulated data and stock market data, this paper verifies that both mvMDE and GmvMDE can effectively measure and distinguish the sequence complexity, and GmvMDE can better capture the small evolution of sequences, with higher stability and accuracy. On the basis of mvMDE research, we also propose the multiscale system dispersion entropy (MSDE) and its fractional order form (GMSDE). Using the vector-to-vector distance quantization method, the relationship between individuals in the system can be better extracted, and the systemic complexity of financial portfolio can be measured from the time dimension and the space dimension simultaneously. The empirical analysis based on the data of major industries in Chinese stock market shows that MSDE and GMSDE can accurately capture the structural information in the system and effectively distinguish the complexity of financial portfolios.