Nonlinear analysis of volatility duration financial series model by stochastic interacting dynamic system

A stochastic financial price model is introduced by the contact dynamic system to simulate the behaviors of real asset markets. The contact system is a model for epidemic spreading that mimics the interplay of local infections and recovery of individuals. We also develop an analysis method to detect the duration and intensity relationship in volatility series, this research shows an analysis approach to the time series analysis. In the empirical research of volatility duration series of returns, the Zipf behaviors of Shanghai Stock Exchange Composite Index and the simulative data derived from the proposed financial model are analyzed by comparison. Furthermore, we study the cross-correlation behaviors of pair normalized volatility duration series for the simulation data and the real markets data.

[1]  Mu-Fa Chen,et al.  From Markov Chains to Non-Equilibrium Particle Systems , 1992 .

[2]  Bernard Lapeyre,et al.  Introduction to Stochastic Calculus Applied to Finance , 2007 .

[3]  Dietrich Stauffer,et al.  Sharp peaks in the percolation model for stock markets , 2000 .

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

[5]  Paul R. Wellin,et al.  Computer simulations with Mathematica - explorations in complex physical and biological systems , 1995 .

[6]  Jun Wang,et al.  Dependence phenomenon analysis of the stock market , 2013 .

[7]  George Kingsley Zipf,et al.  Human behavior and the principle of least effort , 1949 .

[8]  Jun Wang,et al.  Finite-Range Contact Process on the Market Return Intervals Distributions , 2010, Adv. Complex Syst..

[9]  Kazuko Yamasaki,et al.  Scaling and memory of intraday volatility return intervals in stock markets. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[11]  Thomas Lux,et al.  Financial power laws: Empirical evidence, models, and mechanism , 2016 .

[12]  Jun Wang,et al.  Fluctuation prediction of stock market index by Legendre neural network with random time strength function , 2012, Neurocomputing.

[13]  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 .

[14]  G. Zipf.  The Psycho-Biology Of Language: AN INTRODUCTION TO DYNAMIC PHILOLOGY , 1999 .

[15]  Jun Wang,et al.  Simulation and Statistical Analysis of Market Return Fluctuationby Zipf Method , 2011 .

[16]  E. Michael Azoff,et al.  Neural Network Time Series: Forecasting of Financial Markets , 1994 .

[17]  Jun Wang,et al.  Statistical analysis and forecasting of return interval for SSE and model by lattice percolation system and neural network , 2012, Comput. Ind. Eng..

[18]  Jun Wang,et al.  Voter interacting systems applied to Chinese stock markets , 2011, Math. Comput. Simul..

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

[20]  A. Whitehead.  An Introduction to Mathematics , 1949, Nature.

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

[22]  H. Stanley,et al.  Cross-correlations between volume change and price change , 2009, Proceedings of the National Academy of Sciences.

[23]  Kazuko Yamasaki,et al.  Scaling and memory in volatility return intervals in financial markets. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[24]  Jun Wang,et al.  Modeling stock price dynamics by continuum percolation system and relevant complex systems analysis , 2012 .

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

[26]  Jun Wang,et al.  Forecasting model of global stock index by stochastic time effective neural network , 2008, Expert Syst. Appl..

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

[28]  H. Stanley,et al.  Detrended cross-correlation analysis: a new method for analyzing two nonstationary time series. , 2007, Physical review letters.

[29]  Kirill Ilinski,et al.  Physics of Finance: Gauge Modelling in Non-Equilibrium Pricing , 2001 .

[30]  Jun Wang,et al.  Fluctuations of stock price model by statistical physics systems , 2010, Math. Comput. Model..

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

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

[33]  Jose Alvarez-Ramirez,et al.  Symmetry/anti-symmetry phase transitions in crude oil markets , 2003 .

[34]  Wen Shi,et al.  Multifractal detrended cross-correlation analysis for power markets , 2013, Nonlinear Dynamics.

[35]  H. Stanley,et al.  Quantifying cross-correlations using local and global detrending approaches , 2009 .

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

[37]  David S. Stoffer,et al.  Time series analysis and its applications , 2000 .

[38]  Laurent E. Calvet,et al.  Multifractal Volatility: Theory, Forecasting, and Pricing , 2008 .

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

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

[41]  Jun Wang,et al.  Modeling and simulation of the market fluctuations by the finite range contact systems , 2010, Simul. Model. Pract. Theory.

[42]  V. T. Chow.  Handbook of applied hydrology , 2017 .

[43]  Jun Wang,et al.  Statistical Analysis By Statistical Physics Model For The Stock Markets , 2009 .

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

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

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

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

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

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