Nonlinear fluctuation behaviors of complex voter financial price dynamics on small-world network

To simulate the price fluctuation dynamics of financial markets, a novel financial price model is developed by the voter dynamic system on the Watts-Strogtz small-world network and the random jump process. The voter system is a classical statistical physics system, which describes the dynamics of voters’ attitudes towards a certain topic in the mutual influence. The Watts-Strogtz small-world network is a special kind of complex networks, which can be used to study the transmission dynamics of different things in complex and real-world systems. The paper first attempts to use the voter dynamic system on the small-world network to reproduce the micro-mechanism of price fluctuations caused by the interaction among different investors in financial markets, where investors can potentially disseminate information and interact via additional long-distance contacts. Moreover, considering that external macro environments have the impact on price fluctuations in financial markets, this paper introduces the random jump process in the price model. The effectiveness of the proposed model can be verified by comparing price returns generated by the model with returns of several important stock indexes in terms of nonlinear fluctuation behaviors. First, some statistical behaviors of the fluctuation dynamics are explored, including distribution characteristics and autocorrelation. Moreover, based on the ensemble empirical mode decomposition method, multifractal behaviors and complexity behaviors of returns and the first three intrinsic mode functions are investigated. The empirical results show that the dynamical model can well simulate these nonlinear fluctuation behaviors of real markets.

[1]  S. Redner,et al.  Voter model on heterogeneous graphs. , 2004, Physical review letters.

[2]  J. Kwapień,et al.  Physical approach to complex systems , 2012 .

[3]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[4]  Claudio Castellano,et al.  Incomplete ordering of the voter model on small-world networks , 2003 .

[5]  Weiting Chen,et al.  Measuring complexity using FuzzyEn, ApEn, and SampEn. , 2009, Medical engineering & physics.

[6]  Chun-Chieh Wang,et al.  Time Series Analysis Using Composite Multiscale Entropy , 2013, Entropy.

[7]  Stephen L Taylor.  Conjectured models for trends in financial prices, tests and forecasts , 1980 .

[8]  Co-Movements and Asymmetric Volatility in the Portuguese and U.S. Stock Markets , 2006 .

[9]  H. Lilliefors.  On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown , 1967 .

[10]  Xavier Gabaix,et al.  Power Laws in Economics and Finance , 2009 .

[11]  Rifat Hacioglu,et al.  Prediction of Bitcoin prices with machine learning methods using time series data , 2018, 2018 26th Signal Processing and Communications Applications Conference (SIU).

[12]  Yasmine Hayek Kobeissi.  Multifractal Financial Markets: An Alternative Approach to Asset and Risk Management , 2012 .

[13]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[14]  Jun Wang,et al.  Nonlinear analysis of volatility duration financial series model by stochastic interacting dynamic system , 2015 .

[15]  Rosario N. Mantegna,et al.  Book Review: An Introduction to Econophysics, Correlations, and Complexity in Finance, N. Rosario, H. Mantegna, and H. E. Stanley, Cambridge University Press, Cambridge, 2000. , 2000 .

[16]  Daniele Vilone,et al.  Solution of voter model dynamics on annealed small-world networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  R. Meester,et al.  Continuum percolation: Frontmatter , 1996 .

[18]  Jun Wang,et al.  Measuring the correlation complexity between return series by multiscale complex analysis on Potts dynamics , 2017 .

[19]  José Dias Curto,et al.  Modelling heavy tails and asymmetry using ARCH-type models with stable Paretian distributions , 2007 .

[20]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[21]  D. Darling,et al.  A Test of Goodness of Fit , 1954 .

[22]  B. Pompe,et al.  Permutation entropy: a natural complexity measure for time series. , 2002, Physical review letters.

[23]  Hamed Azami,et al.  Dispersion Entropy: A Measure for Time-Series Analysis , 2016, IEEE Signal Processing Letters.

[24]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[25]  Benoit B. Mandelbrot,et al.  Fractals and Scaling in Finance , 1997 .

[26]  Jui-Pin Wang,et al.  Statistical and nonlinear analyses of return volatility dynamics on energy futures , 2019, International Journal of Modern Physics C.

[27]  G. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .

[28]  Wei-Xing Zhou,et al.  The components of empirical multifractality in financial returns , 2009, 0908.1089.

[29]  J. T. Tenreiro Machado.  Complex dynamics of financial indices , 2013 .

[30]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[31]  T. Liggett,et al.  Stochastic Interacting Systems: Contact, Voter and Exclusion Processes , 1999 .

[32]  Elena Napoletano,et al.  Herding as a consensus problem , 2018 .

[33]  José A. R. Vargas,et al.  Robust adaptive synchronization of a hyperchaotic finance system , 2015 .

[34]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[35]  Jun Wang,et al.  Nonlinear continuous fluctuation intensity financial dynamics and complexity behavior. , 2018, Chaos.

[36]  Anil K. Bera,et al.  Efficient tests for normality, homoscedasticity and serial independence of regression residuals , 1980 .

[37]  Jun Wang,et al.  Statistical Properties And Multifractal Behaviors Of Market Returns By Ising Dynamic Systems , 2012 .

[38]  Norden E. Huang,et al.  Ensemble Empirical Mode Decomposition: a Noise-Assisted Data Analysis Method , 2009, Adv. Data Sci. Adapt. Anal..

[39]  V. Plerou,et al.  Econophysics: financial time series from a statistical physics point of view , 2000 .

[40]  Jun Wang,et al.  Volatility clustering and long memory of financial time series and financial price model , 2013, Digit. Signal Process..

[41]  J. T. Tenreiro Machado,et al.  Relative fractional dynamics of stock markets , 2016 .

[42]  Aytaç Altan,et al.  THE EFFECT OF KERNEL VALUES IN SUPPORT VECTOR MACHINE TO FORECASTING PERFORMANCE OF FINANCIAL TIME SERIES , 2019 .

[43]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[44]  N Mariyappa,et al.  Ensemble Empirical Mode Decomposition based methodology for ultrasonic testing of coarse grain austenitic stainless steels. , 2015, Ultrasonics.

[45]  R. Durrett.  Lecture notes on particle systems and percolation , 1988 .

[46]  Haiyang Pan,et al.  Rolling bearing fault detection and diagnosis based on composite multiscale fuzzy entropy and ensemble support vector machines , 2017 .

[47]  Jun Wang,et al.  Interacting price model and fluctuation behavior analysis from Lempel–Ziv complexity and multi-scale weighted-permutation entropy , 2016 .

[48]  J. A. Tenreiro Machado,et al.  Complex dynamics of financial indices , 2013 .

[49]  R. Vilela Mendes.  A fractional calculus interpretation of the fractional volatility model , 2008 .

[50]  David Liu,et al.  Particle-scale modelling of financial price dynamics , 2017, Commun. Nonlinear Sci. Numer. Simul..

[51]  J. S. Armand Eyebe Fouda,et al.  The matching energy: a novel approach for measuring complexity in time series , 2016, Nonlinear Dynamics.

[52]  R. Mantegna,et al.  Scaling behaviour in the dynamics of an economic index , 1995, Nature.

[53]  Di Xiao,et al.  Complexity behaviours of agent-based financial dynamics by hetero-distance contact process , 2020, Nonlinear Dynamics.

[54]  Robert J. Elliott,et al.  Filtering a nonlinear stochastic volatility model , 2012 .

[55]  Andrzej Krawiecki,et al.  Microscopic Spin Model For The Stock Market With Attractor Bubbling And Heterogeneous Agents , 2005 .

[56]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[57]  Jun Wang,et al.  Multiscale behavior of financial time series model from Potts dynamic system , 2014, Nonlinear Dynamics.

[58]  Krzysztof Suchecki,et al.  Voter model dynamics in complex networks: Role of dimensionality, disorder, and degree distribution. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[59]  J. Bouchaud,et al.  HERD BEHAVIOR AND AGGREGATE FLUCTUATIONS IN FINANCIAL MARKETS , 1997, Macroeconomic Dynamics.

[60]  T. Liggett.  Interacting Particle Systems , 1985 .

[61]  Xavier Gabaix,et al.  Economic Fluctuations and Statistical Physics: The Puzzle of Large Fluctuations , 2006 .

[62]  Jiahui Wang,et al.  Modeling Financial Time Series with S-PLUS® , 2003 .

[63]  H. Stanley,et al.  Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series , 2002, physics/0202070.

[64]  Shenzhou Zheng,et al.  Nonlinear Complexity and Chaotic Behaviors on Finite-Range Stochastic Epidemic Financial Dynamics , 2019, Int. J. Bifurc. Chaos.

[65]  Dietrich Stauffer,et al.  Crossover in the Cont–Bouchaud percolation model for market fluctuations , 1998 .

[66]  R. Vilela Mendes,et al.  A fractional calculus interpretation of the fractional volatility model , 2009 .

[67]  Fernando B. M. Duarte,et al.  Dynamics of the Dow Jones and the NASDAQ stock indexes , 2010 .

[68]  Dariusz Grech,et al.  On the multifractal effects generated by monofractal signals , 2013, 1307.2014.

[69]  Denis Boyer,et al.  Interface motion and pinning in small-world networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[70]  R. Mantegna,et al.  An Introduction to Econophysics: Contents , 1999 .

[71]  Wangxin Yu,et al.  Characterization of Surface EMG Signal Based on Fuzzy Entropy , 2007, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[72]  Wei Zhang,et al.  Nonlinear stochastic exclusion financial dynamics modeling and complexity behaviors , 2016, Nonlinear Dynamics.

[73]  D. Foley,et al.  The economy needs agent-based modelling , 2009, Nature.

[74]  Stelios D. Bekiros,et al.  Digital currency forecasting with chaotic meta-heuristic bio-inspired signal processing techniques , 2019, Chaos, Solitons & Fractals.

[75]  J. Tenreiro Machado,et al.  Analysis of financial data series using fractional Fourier transform and multidimensional scaling , 2011 .

[76]  Jun Wang,et al.  Lattice-oriented percolation system applied to volatility behavior of stock market , 2012 .

[77]  R. Cont.  Empirical properties of asset returns: stylized facts and statistical issues , 2001 .

[78]  R. Cont,et al.  Financial Modelling with Jump Processes , 2003 .

[79]  Steven M. Pincus.  Assessing Serial Irregularity and Its Implications for Health , 2001, Annals of the New York Academy of Sciences.