Predicting agent-based financial time series model on lattice fractal with random Legendre neural network

An agent-based financial price model is developed by percolation system on the Sierpinski carpet lattice, in an attempt to reproduce and investigate fluctuation behaviors of price changes in the financial market. The percolation theory is usually used to describe the behaviors of connected clusters in a random graph, and the Sierpinski carpet lattice is an infinitely ramified fractal. We forecast and investigate the stock prices of the financial model by an improved Legendre neural network–Legendre neural network with random time strength function (LeNNRT). To test the LeNNRT and study the fluctuation behaviors of the stock prices on different time lag, the k-day moving average of Shanghai Composite Index and the simulated price series of the proposed model are predicted by the LeNNRT model. We exhibit the predictive results and compare the forecasting accuracies with different values of k for both the real data and the simulated data.

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

[2]  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..

[3]  S. I. Ao,et al.  A hybrid neural network cybernetic system for quantifying cross-market dynamics and business forecasting , 2011, Soft Comput..

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

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

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

[7]  Shouyang Wang,et al.  A multiscale modeling approach incorporating ARIMA and anns for financial market volatility forecasting , 2014, J. Syst. Sci. Complex..

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

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

[10]  J. Bouchaud,et al.  Theory Of Financial Risk And Derivative Pricing , 2000 .

[11]  J. Wang,et al.  Integrating Independent Component Analysis and Principal Component Analysis with Neural Network to Predict Chinese Stock Market , 2011 .

[12]  Masato Shinoda.  Existence of phase transition of percolation on Sierpiński carpet lattices , 2002, Journal of Applied Probability.

[13]  Jun Wang.  SUPERCRITICAL ISING MODEL ON THE LATTICE FRACTAL — THE SIERPINSKI CARPET , 2006 .

[14]  Zoran Miljkovic,et al.  Neural network learning from demonstration and epipolar geometry for visual control of a nonholonomic mobile robot , 2014, Soft Comput..

[15]  Cong Wang,et al.  Special issue on pattern recognition and information processing using neural networks , 2010, Soft Comput..

[16]  Michael G. Madden,et al.  A neural network approach to predicting stock exchange movements using external factors , 2005, Knowl. Based Syst..

[17]  Hong Wang,et al.  Flexible flow shop scheduling: optimum, heuristics and artificial intelligence solutions , 2005, Expert Syst. J. Knowl. Eng..

[18]  Ajith Abraham,et al.  Hybrid Intelligent Systems for Stock Market Analysis , 2001, International Conference on Computational Science.

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

[20]  Kin Keung Lai,et al.  Forecasting China’s Foreign Trade Volume with a Kernel-Based Hybrid Econometric-Ai Ensemble Learning Approach , 2008, J. Syst. Sci. Complex..

[21]  Ganapati Panda,et al.  Efficient prediction of exchange rates with low complexity artificial neural network models , 2009, Expert Syst. Appl..

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

[23]  Masato Shinoda,et al.  Non-existence of phase transition of oriented percolation on Sierpinski carpet lattices , 2003 .

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

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

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

[27]  Baikunth Nath,et al.  A fusion model of HMM, ANN and GA for stock market forecasting , 2007, Expert Syst. Appl..

[28]  Çagdas Hakan Aladag,et al.  A new approach based on artificial neural networks for high order multivariate fuzzy time series , 2009, Expert Syst. Appl..

[29]  Kimon P. Valavanis,et al.  Forecasting stock market short-term trends using a neuro-fuzzy based methodology , 2009, Expert Syst. Appl..

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

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

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

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

[34]  Ying Tan,et al.  A three-layer back-propagation neural network for spam detection using artificial immune concentration , 2009, Soft Comput..

[35]  Refaat El Attar.  Special Functions and Orthogonal Polynomials , 2006 .

[36]  J. Bouchaud,et al.  Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management , 2011 .

[37]  Filippo Castiglione.  Forecasting Price increments using an Artificial Neural Network , 2001, Adv. Complex Syst..

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

[39]  F. Diebold,et al.  The distribution of realized stock return volatility , 2001 .

[40]  H. Stanley,et al.  Linking agent-based models and stochastic models of financial markets , 2012, Proceedings of the National Academy of Sciences.

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

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

[43]  Goutam Chakraborty,et al.  Nonlinear channel equalization for wireless communication systems using Legendre neural networks , 2009, Signal Process..