Nonlinear complexity behaviors of agent-based 3D Potts financial dynamics with random environments. (English) Zbl 1514.91220
Summary: A new microscopic 3D Potts interaction financial price model is established in this work, to investigate the nonlinear complexity behaviors of stock markets. 3D Potts model, which extends the 2D Potts model to three-dimensional, is a cubic lattice model to explain the interaction behavior among the agents. In order to explore the complexity of real financial markets and the 3D Potts financial model, a new random coarse-grained Lempel-Ziv complexity is proposed to certain series, such as the price returns, the price volatilities, and the random time \(d\)-returns. Then the composite multiscale entropy (CMSE) method is applied to the intrinsic mode functions (IMFs) and the corresponding shuffled data to study the complexity behaviors. The empirical results indicate that the 3D financial model is feasible.
MSC:
| 91G80 | Financial applications of other theories |
| 91B80 | Applications of statistical and quantum mechanics to economics (econophysics) |
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
Keywords:
microscopic financial price series dynamics; 3D Potts model; shuffled time series; random coarse-grained Lempel-Ziv complexity; composite multiscale entropy; empirical mode decompositionReferences:
| [1] | Calvet, L. E.; Fisher, A. J., (Multifractal Volatility: Theory, Forecasting, and Pricing. Multifractal Volatility: Theory, Forecasting, and Pricing, Academic Press Advanced Finance (2008), Academic Press) |
| [2] | Amaral, L. A.N.; Buldyrev, S. V.; Havlin, S.; Salinger, M. A.; Stanley, H. E., Power law scaling for a system of interacting units with complex internal structure, Phys. Rev. Lett., 80, 1385-1388 (1998) |
| [3] | Cont, R.; Bouchaud, J. P., Herd behavior and aggregate fluctuations in financial markets, Macroecon. Dyn., 4, 170-196 (1998) · Zbl 1060.91506 |
| [4] | Chen, M. F., From Markov Chains To Non-Equilibrium Particle Systems (2004), World Scientific: World Scientific Singapore · Zbl 1078.60003 |
| [5] | Gabaix, X.; Gopikrishnan, P.; Plerou, V.; Stanley, H. E., A theory of power-law distributions in financial market fluctuations, Nature, 423, 267-270 (2003) |
| [6] | Kantelhardt, J. W.; Zschiegner, S. A.; Koscielny-Bunde, E.; Havlin, S.; Bunde, A.; Stanley, H. E., Multifractal detrended fluctuation analysis of nonstationary time series, Physica A, 316, 87-114 (2002) · Zbl 1001.62029 |
| [7] | Liggett, T. M., Interacting Particle Systems (1985), Springer-Verlag: Springer-Verlag New York · Zbl 0559.60078 |
| [8] | Niu, H. L.; Wang, J., Volatility clustering and long memory of financial time series and financial price model, Digit. Signal Process., 23, 489-498 (2013) |
| [9] | Li, W.; Wang, F.; Havlin, S.; Stanley, H. E., Financial factor influence on scaling and memory of trading volume in stock market, Phys. Rev. E, 84, 046112 (2011) |
| [10] | Bentes, S. R., Forecasting volatility in gold returns under the GARCH, IGARCH and FIGARCH frameworks: New evidence, Physica A, 438, 355-364 (2015) |
| [11] | Sensoy, A.; Tabak, B. M., Time-varying long term memory in the European Union stock markets, Physica A, 436, 147-158 (2015) |
| [12] | Siokis, F. M., Multifractal analysis of stock exchange crashes, Physica A, 392, 1164-1171 (2013) |
| [13] | Li, W.; Bashan, A.; Buldyrev, S. V.; Stanley, H. E.; Havlin, S., Cascading failures in interdependent lattice networks: the critical role of the length of dependency links, Phys. Rev. Lett., 108, 228702 (2012) |
| [14] | Zhang, J. H.; Wang, J., Modeling and simulation of the market fluctuations by the finite range contact systems, Simul. Model. Pract. Theory, 18, 910-925 (2010) |
| [15] | Yuan, Y.; Zhuang, X. T.; Liu, Z. Y., Price-volume multifractal analysis and its application in Chinese stock markets, Physica A, 391, 3484-3495 (2012) |
| [16] | Thompsona, J. R.; Wilson, J. R., Multifractal detrended fluctuation analysis: Practical applications to financial time series, Math. Comput. Simulation, 126, 63-88 (2016) · Zbl 1540.62141 |
| [17] | Li, R.; Wang, J., Interacting price model and fluctuation behavior analysis from Lempel-Ziv complexity and multi-scale weighted-permutation entropy, Phys. Lett. A, 380, 117-129 (2016) |
| [18] | Xu, K. X.; Wang, J., Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics, Phys. Lett. A, 381, 767-779 (2017) · Zbl 1372.94375 |
| [19] | Lu, Y. F.; Wang, J.; Niu, H. L., Agent-based financial dynamics model from stochastic interacting epidemic system and complexity analysis, Phys. Lett. A, 379, 1023-1031 (2015) |
| [20] | Diks, C., The correlation dimension of returns with stochastic volatility, Quant. Finance, 4, 45-54 (2004) · Zbl 1405.91704 |
| [21] | Baxter, R. J., Potts model at the critical temperature, J. Phys. C: Solid State Phys., 6, 445-448 (1973) |
| [22] | Hong, W. J.; Wang, J., Multiscale behavior of financial time series model from Potts dynamic system, Nonlinear Dynam., 78, 1065-1077 (2014) |
| [23] | Zhang, J. H.; Mcburney, P.; Musial, K., Convergence of trading strategies in continuous double auction markets with boundedly-rational networked traders, Rev. Quant. Finance Account. (2017) |
| [24] | Deng, Y.; Blöte, H. W.J.; Nienhuis, B., Backbone exponents of the two-dimensional \(q\)-state Potts model: a Monte Carlo investigation, Phys. Rev. E, 69, 026114 (2004) |
| [25] | Wu, F. Y., The potts model, Rev. Mod. Phys., 54, 235-268 (1982) |
| [26] | Berche, P. E.; Chatelain, C.; Berche, B.; Janke, W., Bond dilution in the 3D Ising model: a Monte Carlo study, Eur. Phys. J. B, 38, 463-474 (2004) |
| [27] | Bazavov, A.; Berg, B. A.; Dubey, S., Phase transition properties of 3D Potts models, Nuclear Phys. B, 802, 421-434 (2008) · Zbl 1190.82017 |
| [28] | Wu, S. D.; Lin, S. G.; Wang, C. C.; Lee, K. Y., Time series analysis using composite multiscale entropy, Entropy, 15, 1069-1084 (2013) · Zbl 1298.65020 |
| [29] | Costa, M.; Goldberger, A. L.; Peng, C. K., Multiscale entropy analysis of complex physiologic time series, Phys. Rev. Lett., 89, 068102 (2002) |
| [30] | Govindan, R. B.; Wilson, J. D.; Eswaran, H.; Lowery, C. L.; Preissl, H., Revisiting sample entropy analysis, Physica A, 376, 158-164 (2007) |
| [31] | Niu, H. L.; Wang, J., Quantifying complexity of financial short-term time series by composite multiscale entropy measure, Commun. Nonlinear Sci. Numer. Simul., 22, 375-382 (2015) · Zbl 1329.91153 |
| [32] | Thuraisingham, R. A.; Gottwald, G. A., On multiscale entropy analysis for physiological data, Physica A, 366, 323-332 (2006) |
| [33] | Wu, S. D.; Wu, C. W.; Lee, K. Y.; Lin, S. G., Modified multiscale entropy for short-term time series analysis, Physica A, 392, 5865-5873 (2013) |
| [34] | Huang, N. E.; Shen, Z.; Long, S. R.; Wu, M. C.; Shih, H. H.; Zheng, Q.; Yen, Nai-Chyuan.; Tung, C. C.; Liu, H. H., The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 454, 903-995 (1998) · Zbl 0945.62093 |
| [35] | Flandrin, P.; Goncalves, P., Empirical mode decompositions as datadriven wavelet-like expansions, Int. J. Wavelets Multiresolution Inf. Process., 2, 477-496 (2004) · Zbl 1092.42502 |
| [36] | Blöte, H. W.J.; Nightingale, M. P., Critical behaviour of the two-dimensional potts model with a continuous number ofstates; a finite size scaling analysis, Physica A, 112, 405-465 (1982) |
| [37] | Karsch, F.; Stickan, S., The three-dimensional, three-state Potts model in an external field, Phys. Lett. B, 488, 319-325 (2000) · Zbl 1050.82509 |
| [38] | Lamberton, D.; Lapeyre, B., Introduction To Stochastic Calculus Applied To Finance (2000), Chapman and Hall/CRC: Chapman and Hall/CRC London · Zbl 0898.60002 |
| [39] | Lempel, A.; Ziv, J., On the complexity of finite sequences, IEEE Trans. Inform. Theory, 22, 75-81 (1976) · Zbl 0337.94013 |
| [40] | Tang, J.; Wang, Y.; Wang, H.; Zhang, S.; Liu, F., Dynamic analysis of traffic time series at different temporal scales: a complex networks approach, Physica A, 405, 303-315 (2014) |
| [41] | Szczepański, J.; Amigó, J. M.; Wajnryb, E.; Sanchez-Vives, M. V., Characterizing spike trains with Lempel-Ziv complexity, Neurocomputing, 58-60, 79-84 (2004) |
| [42] | Ibáñez-Molina, A. J.; Iglesias-Parro, S.; Soriano, M. F.; Aznarte, J. I., Multiscale Lempel-Ziv complexity for EEG measures, Clin. Neurophysiol., 126, 541-548 (2015) |
| [43] | Fernández, A., Lempel-Ziv complexity in shizophrenia: A MEG study, Clin. Neuropharmacol., 122, 2227-2235 (2011) |
| [44] | Abásolo, D.; Hornero, R.; Gómez, C.; García, M.; López, M., Analysis of EEG background activity in Alzheimer’s disease patients with Lempel-Ziv complexity and central tendency measure, Med. Eng. Phys., 28, 315-322 (2006) |
| [45] | Ross, S. M., An Introduction To Mathematical Finance (1999), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0944.91024 |
| [46] | Yu, Y.; Wang, J., Lattice oriented percolation system applied to volatility behavior of stock market, J. Appl. Stat., 39, 785-797 (2012) · Zbl 1514.62217 |
| [47] | Richman, J. S.; Moorman, J. R., Physiological time-series analysis using approximate entropy and sample entropy, Amer. J. Physiol. Heart Circ. Physiol., 278, 2039-2049 (2000) |
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