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)

• Publisher: Institute of Physics, Polish Academy of Sciences
• 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

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Identifiers

DOI

10.12693/APhysPolA.117.637