Abstract
To model the nonlinear and complex dynamics of financial systems, a new model for the formation of financial prices is developed, taking into account heterogeneity in the communication range of market agents. Specifically, one type of agents can potentially gather and disseminate information via additional long-distance contacts compared to the other type, and interactions among these agents are imitated by the contact process. The financial price series of the model are simulated, analysed, and compared with multiple major stock indices in nonlinear fluctuation behaviours. To better investigate the complexity structure of the financial time series, a generalization of the multiscale entropy method is developed to consider various moments in coarse graining. Overall, the modelled series are found to follow a fat-tail distribution and a pattern of complexity structure over both moments and time scales similar to real market data. This similarity is also shown by applying alternative complexity measure, matching energy method. Moreover, the wealth inequality among agents is found to increase over time within each type as well as across two types, further revealing nonlinear price and welfare dynamics of the model.
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Azami, H., Fernández, A., Escudero, J.: Refined multiscale fuzzy entropy based on standard deviation for biomedical signal analysis. Med. Biol. Eng. Comput. 55(11), 2037–2052 (2017)
Azami, H., Li, P., Arnold, S.E., Escudero, J., Humeau-Heurtier, A.: Fuzzy entropy metrics for the analysis of biomedical signals: assessment and comparison. IEEE Access 7, 104833–104847 (2019)
Bandt, C., Pompe, B.: Permutation entropy: a natural complexity measure for time series. Phys. Rev. Lett. 88(17), 174102 (2002)
Bouchaud, J.-P., Potters, M.: Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management, 2nd edn. Cambridge University Press, Cambridge and New York (2003)
Calvet, L., Fisher, A.: Forecasting multifractal volatility. J. Econom. 105(1), 27–58 (2001)
Chakraborti, A., Toke, I.M., Patriarca, M., Abergel, F.: Econophysics review: I. empirical facts. Quant. Finance 11(7), 991–1012 (2011)
Chatterjee, A., Ghosh, A., Inoue, J., Chakrabarti, B.K.: Social inequality: from data to statistical physics modeling. In: Statphys-Kolkata VIII, volume 638 of Journal of Physics Conference Series, 2015. 8th International Conference on Statistical Physics (Statphys), Kolkata, India, Dec 01–05 (2014)
Chen, W., Wang, Z., Xie, H., Wangxin, Y.: Characterization of surface EMG signal based on fuzzy entropy. IEEE Trans. Neural Syst. Rehabilit. Eng. Publ. IEEE Eng. Med. Biol. Soc. 15(2), 266–272 (2007)
Chen, W., Zhuang, J., Wangxin, Y., Wang, Z.: Measuring complexity using FuzzyEn, ApEn, and SampEn. Med. Eng. Phys. 31(1), 61–68 (2009)
Chiang, H.-S., Chen, M.-Y., Huang, Y.-J.: Wavelet-based EEG processing for epilepsy detection using fuzzy entropy and associative petri net. IEEE Access 7, 103255–103262 (2019)
Costa, M., Goldberger, A.L., Peng, C.: Multiscale entropy analysis of complex physiologic time series. Phys. Rev. Lett. 89(6), 068102 (2002)
Costa, M., Goldberger, A.L., Peng, C.: Multiscale entropy analysis of biological signals. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 71(2 Pt 1), 021906 (2005)
Costa, M.D., Goldberger, A.L.: Generalized multiscale entropy analysis: application to quantifying the complex volatility of human heartbeat time series. Entropy 17(3), 1197–1203 (2015)
Costa, M.D., Peng, C.-K., Goldberger, A.L.: Multiscale analysis of heart rate dynamics: entropy and time irreversibility measures. Cardiovasc. Eng. 8(2), 88–93 (2008)
Fang, W., Wang, J.: Effect of boundary conditions on stochastic ising-like financial market price model. Bound. Value Probl. 2012(1), 549 (2012)
Fang, W., Wang, J.: Statistical properties and multifractal behaviors of market returns by ising dynamic systems. Int. J. Mod. Phys. C 23(03), 1250023 (2012)
Fouda, J.S.A.E.: The matching energy: a novel approach for measuring complexity in time series. Nonlinear Dyn. 86(3), 2049–2060 (2016)
Gabaix, X., Gopikrishnan, P., Plerou, V., Eugene Stanley, H.: A theory of power-law distributions in financial market fluctuations. Nature 423(6937), 267–270 (2003)
Garofalo, F., Iudice, F.L., Napoletano, E.: Herding as a consensus problem. Nonlinear Dyn. 92(1), 25–32 (2018)
Hong, H., Kubik, J.D., Stein, J.C.: Social interaction and stock-market participation. J. Finance 59(1), 137–163 (2004)
Hong, W., Wang, J.: Multiscale behavior of financial time series model from Potts dynamic system. Nonlinear Dyn. 78(2), 1065–1077 (2014)
Ilinski, K.: Physics of Finance: Gauge Modelling in Non-Equilibrium Pricing. Wiley Finance Series. Wiley, Chichester (2001)
Ivković, Z., Weisbenner, S.: Information diffusion effects in individual investors’ common stock purchases: covet thy neighbors’ investment choices. Rev. Financ. Stud. 20(4), 1327–1357 (2007)
Krawiecki, A.: Microscopic spin model for the stock market with attractor bubbling and heterogeneous agents. Int. J. Mod. Phys. C 16(04), 549–559 (2005)
Li, P., Liu, C., Li, K., Zheng, D., Liu, C., Hou, Y.: Assessing the complexity of short-term heartbeat interval series by distribution entropy. Med. Biol. Eng. Comput. 53(1), 77–87 (2015)
Li, Y., Pan, W., Li, K., Jiang, Q., Liu, G.: Sliding trend fuzzy approximate entropy as a novel descriptor of heart rate variability in obstructive sleep apnea. IEEE J. Biomed. Health Inform. 23(1), 175–183 (2019)
Liggett, T.M.: Interacting Particle Systems. Springer, New York (1985)
Liggett, T.M.: Stochastic Interacting Systems: Contact, Voter and Exclusion Processes. Springer, Berlin and London (1999)
Lu, Y., Wang, J.: Nonlinear dynamical complexity of agent-based stochastic financial interacting epidemic system. Nonlinear Dyn. 86(3), 1823–1840 (2016)
Niu, H., Wang, J.: Volatility clustering and long memory of financial time series and financial price model. Digit. Signal Process. 23(2), 489–498 (2013)
Niu, H., Wang, J.: Multifractal and recurrence behaviors of continuum percolation-based financial price dynamics. Nonlinear Dyn. 83(1–2), 513–528 (2016)
Ormos, M., Zibriczky, D.: Entropy-based financial asset pricing. PloS One 9(12), e115742 (2014)
Ozsoylev, H.N., Walden, J., Deniz Yavuz, M., Bildik, R.: Investor networks in the stock market. Rev. Financ. Stud. 27(5), 1323–1366 (2014)
Pincus, S.M.: Approximate entropy as a measure of system complexity. Proc. Natl. Acad. Sci. U.S.A. 88(6), 2297–2301 (1991)
Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral, L.A.N., Eugene Stanley, H.: Econophysics: financial time series from a statistical physics point of view. Phys. A Stat. Mech. Appl. 279(1–4), 443–456 (2000)
Polanco-Martínez, J.M.: Dynamic relationship analysis between NAFTA stock markets using nonlinear, nonparametric, non-stationary methods. Nonlinear Dyn. 97(1), 369–389 (2019)
Richman, J.S., Randall Moorman, J.: Physiological time-series analysis using approximate entropy and sample entropy. Am. J. Physiol. Heart Circ. Physiol. 278, H2039–H2049 (2000)
Rossi, A.G., Blake, D., Timmermann, A., Tonks, I., Wermers, R.: Network centrality and delegated investment performance. J. Financ. Econ. 128(1), 183–206 (2018)
Rostaghi, M., Azami, H.: Dispersion entropy: a measure for time-series analysis. IEEE Signal Process. Lett. 23(5), 610–614 (2016)
Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27(4), 623–656 (1948)
Shiller, R.J., Pound, J.: Survey evidence on diffusion of interest and information among investors. J. Econ. Behav. Org. 12(1), 47–66 (1989)
Stauffer, D., Penna, T.J.P.: Crossover in the Cont–Bouchaud percolation model for market fluctuations. Phys. A Stat. Mech. Appl. 256(1–2), 284–290 (1998)
Szuminski, W.: Integrability analysis of chaotic and hyperchaotic finance systems. Nonlinear Dyn. 94(1), 443–459 (2018)
Tacha, O.I., Munoz-Pacheco, J.M., Zambrano-Serrano, E., Stouboulos, I.N., Pham, V.T.: Determining the chaotic behavior in a fractional-order finance system with negative parameters. Nonlinear Dyn. 94(2), 1303–1317 (2018)
Tenreiro Machado, J.A., Duarte, F.B., Duarte, G.M.: Analysis of financial data series using fractional fourier transform and multidimensional scaling. Nonlinear Dyn. 65(3), 235–245 (2011)
Tenreiro Machado, J.A.: Complex dynamics of financial indices. Nonlinear Dyn. 74(1–2), 287–296 (2013)
Tenreiro Machado, J.A.: Relativistic time effects in financial dynamics. Nonlinear Dyn. 75(4), 735–744 (2014)
Tenreiro Machado, J.A., Lopes, A.M.: Relative fractional dynamics of stock markets. Nonlinear Dyn. 86(3), 1613–1619 (2016)
Wang, J., Wang, J.: Measuring the correlation complexity between return series by multiscale complex analysis on Potts dynamics. Nonlinear Dyn. 89(4), 2703–2721 (2017)
Wang, J., Wang, Q., Shao, J.: Fluctuations of stock price model by statistical physics systems. Math. Comput. Model. 51(5–6), 431–440 (2010)
Wu, Z., Zhang, W.: Fractional refined composite multiscale fuzzy entropy of international stock indices. Entropy 21(9), 914 (2019)
Xiao, D., Wang, J.: Modeling stock price dynamics by continuum percolation system and relevant complex systems analysis. Phys. A Stat. Mech. Appl. 391(20), 4827–4838 (2012)
Xiao, D., Wang, J.: Graph based and multifractal analysis of financial time series model by continuum percolation. Int. J. Nonlinear Sci. Numer. Simul. 15(5), 265–277 (2014)
Xiao, D., Wang, J., Niu, H.: Volatility analysis of financial agent-based market dynamics from stochastic contact system. Comput. Econ. 48(4), 607–625 (2016)
Yang, G., Wang, J., Deng, W.: Nonlinear analysis of volatility duration financial series model by stochastic interacting dynamic system. Nonlinear Dyn. 80(1–2), 701–713 (2015)
Yao, Y., Wang, J.: Lattice-oriented percolation system applied to volatility behavior of stock market. J. Appl. Stat. 39(4), 785–797 (2012)
Zhang, J., Wang, J., Shao, J.: Finite-range contact process on the market return intervals distributions. Adv. Complex Syst. 13(5), 643–657 (2010)
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This work was supported by Humanities and Social Sciences Foundation of Ministry of Education of China No. 20YJCZH184.
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Xiao, D., Wang, J. Complexity behaviours of agent-based financial dynamics by hetero-distance contact process. Nonlinear Dyn 100, 3867–3886 (2020). https://doi.org/10.1007/s11071-020-05734-z
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DOI: https://doi.org/10.1007/s11071-020-05734-z