- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 612738, 12 pages
Nonlinear Analysis of Return Time Series Model by Oriented Percolation Dynamic System
Institute of Financial Mathematics and Financial Engineering, School of Science, Beijing Jiaotong University, Beijing 100044, China
Received 13 June 2013; Revised 18 September 2013; Accepted 18 September 2013
Academic Editor: Luca Guerrini
Copyright © 2013 Anqi Pei and Jun Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- F. Black, “Studies of stock price volatility changes,” in Proceedings of the Meetings of the American Statistical Association, Business and Economical Statistics Section, pp. 177–181, 1976.
- J. P. Bouchaud, A. Matacz, and M. Potters, “Leverage effect in financial markets: the retarded volatility model,” Physical Review Letters, vol. 87, no. 22, Article ID 228701, 4 pages, 2001.
- J. P. Bouchaud and M. Potters, Theory of Financial Risks: From Statistical Physics to Risk Management, Cambridge University Press, 2000.
- J. Y. Campbell and L. Hentschel, “No news is good news: an asymmetric model of changing volatility in stock returns,” Journal of Financial Economics, vol. 31, no. 3, pp. 281–318, 1992.
- J. Y. Campbell, A. W. Lo, and A. C. McKinley, The Econometrics of Financial Markets, Princeton University Press, Princeton, NJ, USA, 1997.
- R. Cont and J.-P. Bouchaud, “Herd behavior and aggregate fluctuations in financial markets,” Macroeconomic Dynamics, vol. 4, no. 2, pp. 170–196, 2000.
- Z. Ding, C. W. J. Granger, and R. F. Engle, “A long memory property of stock market returns and a new model,” Journal of Empirical Finance, vol. 1, no. 1, pp. 83–106, 1993.
- P. Grau-Carles, “Long-range power-law correlations in stock returns,” Physica A, vol. 299, no. 3-4, pp. 521–527, 2001.
- Y. L. Guo and J. Wang, “Simulation and statistical analysis of market return fluctuation by Zipf method,” Mathematical Problems in Engineering, vol. 2011, Article ID 253523, 14 pages, 2011.
- R. A. Haugen, E. Talmor, and W. N. Torous, “The effect of volatility changes on the level of stock prices and expected future returns,” The Journal of Finance, vol. 46, no. 3, pp. 985–1007, 1991.
- Z. Liao and J. Wang, “Forecasting model of global stock index by stochastic time effective neural network,” Expert Systems with Applications, vol. 37, no. 1, pp. 834–841, 2010.
- L. Sabatelli, S. Keating, J. Dudley, and P. Richmond, “Waiting time distributions in financial markets,” The European Physical Journal B, vol. 27, no. 2, pp. 273–275, 2002.
- H. E. Stanley, J. S. Andrade Jr., S. Havlin, H. A. Makse, and B. Suki, “Percolation phenomena: a broad-brush introduction with some recent applications to porous media, liquid water, and city growth,” Physica A, vol. 266, no. 1–4, pp. 5–16, 1999.
- D. Stauffer and A. Aharony, Introduction to Percolation Theory, Taylor & Francis, London, UK, 2001.
- D. Stauffer and T. J. P. Penna, “Crossover in the Cont-Bouchaud percolation model for market fluctuations,” Physica A, vol. 256, no. 1-2, pp. 284–290, 1998.
- F. Wang and J. Wang, “Statistical analysis and forecasting of return interval for SSE and model by lattice percolation system and neural network,” Computers & Industrial Engineering, vol. 62, no. 1, pp. 198–205, 2012.
- J. Wang, Q. Y. Wang, and J. G. Shao, “Fluctuations of stock price model by statistical physics systems,” Mathematical and Computer Modelling, vol. 51, no. 5-6, pp. 431–440, 2010.
- T. S. Wang, J. Wang, and B. Fan, “Statistical analysis by statistical physics model for the stock markets,” International Journal of Modern Physics C, vol. 20, no. 10, pp. 1547–1562, 2009.
- X. Wang and J. Wang, “Statistical behavior of a financial model by lattice fractal Sierpinski carpet percolation,” Journal of Applied Mathematics, vol. 2012, Article ID 735068, 12 pages, 2012.
- D. Xiao and J. Wang, “Modelling stock price dynamics by continuum percolation system and relevant complex systems analysis,” Physica A, vol. 391, no. 20, pp. 4827–4838, 2012.
- Y. Yu and J. Wang, “Lattice-oriented percolation system applied to volatility behavior of stock market,” Journal of Applied Statistics, vol. 39, no. 4, pp. 785–797, 2012.
- J. H. Zhang, J. Wang, and J. Shao, “Finite-range contact process on the market return intervals distributions,” Advances in Complex Systems, vol. 13, no. 5, pp. 643–657, 2010.
- R. Gaylord and P. Wellin, Computer Simulations with Mathematica: Explorations in the Physical, Biological and Social Science, Springer, New York, NY, USA, 1995.
- K. Ilinski, Physics of Finance: Gauge Modeling in Non-Equilibrium Pricing, John Wiley, New York, NY, USA, 2001.
- R. N. Mantegna and H. E. Stanley, An Introduction to Econophysics, Cambridge University Press, Cambridge, UK, 1999.
- R. Durrett, Lecture Notes on Particle Systems and Percolation, Wadsworth & Brooks, California, Calif, USA, 1988.
- R. Durrett, “Oriented percolation in two dimensions,” The Annals of Probability, vol. 12, no. 4, pp. 999–1040, 1984.
- G. Grimmett, Percolation, Springer, Berlin, Germany, 2nd edition, 1999.
- T. M. Liggett, Stochastic Interacting Systems: Contact, Voter and Exclusion Processes, Springer, New York, NY, USA, 1999.
- J. Wang, J. G. Shao, and B. T. Wang, “Analysis of two-layered random interfaces for two dimensional Widom-Rowlinson's model,” Abstract and Applied Analysis, vol. 2011, Article ID 858725, 21 pages, 2011.
- F. Wang, K. Yamasaki, S. Havlin, and H. E. Stanley, “Scaling and memory of intraday volatility return intervals in stock markets,” Physical Review E, vol. 73, no. 2, Article ID 026117, 8 pages, 2006.
- D. Lamberton and B. Lapeyre, Introduction to Stochastic Calculus Applied to Finance, Chapman and Hall/CRC, London, UK, 2000.
- S. M. Ross, An Introduction to Mathematical Finance, Cambridge University Press, Cambridge, UK, 1999.