Complexity and uncertainty analysis of financial stock markets based on entropy of scale exponential spectrum
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Research on complexity and uncertainty of nonlinear signals has great significance in dynamic system analysis. In order to further analyze the detailed information from the financial data to acquire deeper insight into the complex system and improve the ability of prediction, we propose the entropy of scale exponential spectrum (EOSES) as a new measure. Combined with multiscale theory, we get multiscale EOSES. The scale exponential spectrum (SES) is derived from the scale exponent of detrended fluctuation analysis. As for the entropy, we choose Rényi entropy and fractional cumulative residual entropy to compare and analyze the results. Simulated data and financial time series are used to obtain further in-depth information on the EOSES. Compared with traditional methods, we find that Rényi EOSES over moving window can provide more details of complexity which include fractal structure and scale properties. Also, it reduces the influence of degree of fitting polynomial and has higher noise immunity. In addition, through the SES and EOSES, we can better research the properties and stages of stock markets and distinguish stock markets with different characteristics.
KeywordsComplexity Rényi entropy Scale exponent Financial time series
The financial support from the Fundamental Research Funds for the Central Universities (Grant No. 2018JBZ104) and the National Natural Science Foundation of China (Grant No. 61771035) are gratefully acknowledged.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest concerning the publication of this manuscript.
- 1.Akbaba-Altun, S.: Complexity of integrating computer technologies into education in Turkey. J. Educ. Technol. Soc. 9(1), 176–187 (2006)Google Scholar
- 7.Kim, Dai-Jin, et al.: An estimation of the first positive Lyapunov exponent of the EEG in patients with schizophrenia. Psychiatry Res. Neuroimaging 98, 177–189 (2000)Google Scholar
- 11.Bialynicky-Birula, I., Mycielski, J.: Relations for information entropy in wave mechanics. Commun. Math. Phys. 44, 129–132 (1975)Google Scholar
- 17.Szita, István, Lörincz, András: Learning Tetris using the noisy cross-entropy method. Neural Comput. 18(12), 2936–2941 (2006)Google Scholar
- 30.He, L.Y., Chen, S.P.: Nonlinear bivariate dependency of pricevolume relationships in agricultural commodity futures markets: a perspective from multifractal detrended cross-correlation analysis. Phys. A Stat. Mech. Appl. 390, 297–308 (2010). https://doi.org/10.1016/j.physa.2010.09.018 Google Scholar
- 34.Qian, B., Rasheed, K.: Hurst exponent and financial market predictability. In: Proceedings of the Second IASTED International Conference on Financial Engineering and Applications, pp. 203–209 (2004)Google Scholar
- 41.Gorenflo, R., Mainardi, F.: Fractional calculus: integral and differential equations of fractional order. arXiv preprint arXiv:0805.3823 (2008)