Fractals, Log-Periodicity and Financial Crashes

• Authors: P. Oświęcimka , S. Drożdż , J. Kwapień , A. Górski
• Languages of publication: EN

Abstracts

EN

Presence of self-similar patterns in the financial dynamics is by now well established and even convincingly quantified within the multifractal formalism. Here we focus attention on one particular aspect of this self-similarity which potentially is related to the discrete-scale invariance underlying the system composition and manifests itself by the log-periodic oscillations cascading self-similarly through various time scales. Such oscillations accumulate at the turning (critical) points that in the financial dynamics are often identified as crashes. This property thus allows us to develop a methodology that may be useful also for prediction. A model Weierstrass-type function is used to illustrate the relevant effects and several examples demonstrating that such effects in the real financial markets take place indeed, are reviewed.

Keywords

EN

52.35.Mw; 05.45.Df; 05.70.Jk

Discipline

• 05.45.Df: Fractals(see also 47.53.+n Fractals in fluid dynamics; 61.43.Hv Fractals; macroscopic aggregates in structure of solids)
• 52.35.Mw: Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
• 05.70.Jk: Critical point phenomena(for quantum critical phenomena in superconductivity, see 74.40.Kb)

• Journal: Acta Physica Polonica A
• Year: 2010
• Volume: 117
• Issue: 4
• Pages: 637-639

Dates

published

2010-04

Contributors

author

P. Oświęcimka

• Institute of Nuclear Physics, Polish Academy of Sciences, E. Radzikowskiego 152, PL-31-342 Kraków, Poland

author

S. Drożdż

• Institute of Nuclear Physics, Polish Academy of Sciences, E. Radzikowskiego 152, PL-31-342 Kraków, Poland
• Faculty of Mathematics and Natural Sciences, University of Rzeszów, PL-35-310, Rzeszów, Poland

author

J. Kwapień

• Institute of Nuclear Physics, Polish Academy of Sciences, E. Radzikowskiego 152, PL-31-342 Kraków, Poland

author

A. Górski

• Institute of Nuclear Physics, Polish Academy of Sciences, E. Radzikowskiego 152, PL-31-342 Kraków, Poland

References

• 1. B.B. Mandelbrot, Science 155, 638 (1967)
• 2. B.B. Mandelbrot, The fractal geometry of Nature, W.H. Freeman, San Francisco 1982
• 3. M.V. Berry, Z.V. Lewis, Proc. R. Soc. Lond. A 370, 459 (1980)
• 4. S. Gluzman, D. Sornette, Phys. Rev. E 65, 036142 (2002)
• 5. D. Sornette, Why Stock Markets Crash: Critical Events in Complex Financial Systems, Princeton University Press, Princeton 2003
• 6. S. Drożdż, F. Ruf, J. Speth, M. Wójcik, Eur. Phys. J. B 10, 589 (1999)
• 7. S. Drożdż, F. Grümmer, F. Ruf, J. Speth, Physica A 324, 174 (2003)
• 8. M. Bartolozzi, S. Drożdż, D.B. Leinweber, J. Speth, A.W. Thomas, Int. J. Mod. Phys. C 16, 1347 (2005)
• 9. S. Drożdż, J. Kwapień, P. Oświęcimka, J. Speth, Acta Phys. Pol. A 114, 539 (2008)
• 10. S. Drożdż, J. Kwapień, P. Oświęcimka, Acta Phys. Pol. A 114, 699 (2008)

Identifiers

DOI

10.12693/APhysPolA.117.637