Fractional Langevin model of memory in financial time series

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 65, Issue 3, 2002, Pages

  West, Bruce J ^a,b   Picozzi, Sergio ^a  

^a DUKE UNIVERSITY   (United States)

^b U S ARMY RESEARCH OFFICE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FINANCIAL TIME SERIES; FRACTIONAL LANGEVIN MODEL; PRICE INDEX FLUCTUATIONS; STATISTICAL PHYSICS;

CORRELATION METHODS; DIFFERENTIATION (CALCULUS); FINANCE; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; ORDINARY DIFFERENTIAL EQUATIONS; PROBABILITY DENSITY FUNCTION; TIME SERIES ANALYSIS;

STATISTICAL TESTS;

EID: 41349117569     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.65.037106     Document Type: Article

References (25)

1. P. Grigolini, A. Rocco, and B. J. West, Phys. Rev. E 59, 2603 (1999).
2. L. Bachelier, Ann. Sci. Ec. Normale Super, Suppl. No. 1017 (1900).
3. P. Cootners, The Random Character of Stock Market Prices (MIT, Cambridge, MA, 1964).
4. B. B. Mandelbrot, Fractals and Scaling in Finance: Discontinuity, Concentration, Risk (Springer-Verlag, New York, 1997).
5. P. Gopikrishnan, V. Pleron, Y. Liu, L. A. N. Amaral, X. Gabaix, and H. E. Stanley, Physica A 287, 362 (2000).
6. D. Sornette and C. Vanneste, Phys. Rev. Lett. 68, 612 (1992).
7. D. L. Turcotte, Fractals and Chaos in Geology and Geophysics (Cambridge University Press, Cambridge, 1992).
8. U. Frisch, Turbulence, the Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, 1995).
9. B. J. West, Physiology, Promiscuity and Prophecy at the Millennium: A Tale of Tails, Studies of Nonlinear Phenomena in the Life Sciences Vol. 7 (World Scientific, Singapore, 1999).
10. P. Gopikrishnan, V. Plerou, L. A. Nunes Amaral, M. Meyer, and H. E. Stanley, Phys. Rev. E 60, 5305 (1999).
11. Y. Liu, P. Gopikrishnan, P. Cizeau, M. Meyer, C-K. Peng, and H. E. Stanley, Phys. Rev. E 60, 1390 (1999).
12. P. Gopikrishnan, V. Plerou, X. Gavaiz, and H. E. Stanley, Phys. Rev. E 62, R4493 (2000).
13. V. Plerou, P. Gopikrishnan, L. A. Nunes Amaral, M. Meyer, and H. E. Stanley, Phys. Rev. E 60, 6519 (1999).
14. E. W. Montroll and W. W. Badger, Introduction to the Quantitative Aspects of Social Phenomena (Gordon and Breach, New York, 1974).
15. A. Rocco and B. J. West, Physica A 265, 535 (1999).
16. E. E. Peters, Fractal Market Analysis (Wiley, New York, 1994).
17. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations (Wiley, New York, 1993).
18. K. Lindenberg and B. J. West, The Nonequilibrium Statistical Mechanics of Open and Closed Systems (VCH, New York, 1990).
19. B. J. West, M. Bologna, and P. Grigolini, Physics of Fractal Operators(Springer-Verlag, New York, 2002).
20. W. G. Glöckle and T. F. Nonnenmacher, J. Stat. Phys. 71, 741 (1993);
21. W. G. GlöckleT. F. NonnenmacherRheol. Acta 33, 337 (1994).
22. V. Kobelev and E. Romanov (unpublished).
23. R. N. Mantegna and H. E. Stanley, An Introduction to Econophysics (Cambridge University Press, Cambridge, 2000).
24. E. F. Fama, J. Financ. 25, 383 (1971);
25. J. Financ.E. F. Fama46, 1575 (1991).