Fractals, Log Periodicity and Financial Crashes

P. Oświęcimkaa, S. Drożdża, b, J. Kwapieńa, and A.Z. Górskia a Institute of Nuclear Physics, Polish Academy of Sciences, E. Radzikowskiego 152, PL-31-342 Kraków, Poland b Faculty of Mathematics and Natural Sciences, University of Rzeszów, PL-35-310, Rzeszów, Poland

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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.

DOI: 10.12693/APhysPolA.117.637 PACS numbers: 52.35.Mw, 05.45.Df, 05.70.Jk