Self-Organized Criticality and Stock Market Dynamics: an Empirical Study

The stock market is a complex self-interacting system, characterized by intermittent behaviour. Periods of high activity alternate with periods of relative calm. In the present work we investigate empirically the possibility that the market is in a self-organized critical state (SOC). A wavelet transform method is used in order to separate high activity periods, related to the avalanches found in sandpile models, from quiescent. A statistical analysis of the filtered data shows a power law behaviour in the avalanche size, duration and laminar times. The memory process, implied by the power law distribution of the laminar times, is not consistent with classical conservative models for self-organized criticality. We argue that a “near-SOC” state or a time dependence in the driver, which may be chaotic, can explain this behaviour.

[1]  de Carvalho JX,et al.  Self-organized criticality in the olami-feder-christensen model , 1999, Physical review letters.

[2]  M. Farge.  Wavelet Transforms and their Applications to Turbulence , 1992 .

[3]  M. Paczuski,et al.  Price Variations in a Stock Market with Many Agents , 1997 .

[4]  J. Scheinkman,et al.  Aggregate Fluctuations from Independent Sectoral Shocks: Self-Organized Criticality in a Model of Production and Inventory Dynamics , 1992 .

[5]  P. Bak,et al.  Self-organized criticality. , 1988, Physical review. A, General physics.

[6]  Tang,et al.  Self-Organized Criticality: An Explanation of 1/f Noise , 2011 .

[7]  Henrik Jeldtoft Jensen,et al.  Self-Organized Criticality: Emergent Complex Behavior in Physical and Biological Systems , 1998 .

[8]  W. Gosnold.  Heat flow in the Great Plains of the United States , 1990 .

[9]  Kim Christensen,et al.  Variation of the Gutenberg‐Richter b values and nontrivial temporal correlations in a Spring‐Block Model for earthquakes , 1992 .

[10]  M. Farge,et al.  Non-Gaussianity and coherent vortex simulation for two-dimensional turbulence using an adaptive orthogonal wavelet basis , 1999 .

[11]  Anthony W. Thomas,et al.  Symbiosis in the Bak–Sneppen model for biological evolution with economic applications , 2006 .

[12]  K. Nagel,et al.  Deterministic models for traffic jams , 1993, cond-mat/9307064.

[13]  Paczuski,et al.  Emergent traffic jams. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  D. Turcotte,et al.  Fractality and Self-Organized Criticality of Wars , 1998 .

[15]  Vincenzo Carbone,et al.  Wavelet-based filtering of intermittent events from geomagnetic time-series , 2001 .

[16]  Hwa,et al.  Avalanches, hydrodynamics, and discharge events in models of sandpiles. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[17]  Cheng,et al.  Relations of 1/f and 1/f2 power spectra to self-organized criticality. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[18]  M. Freeman,et al.  Power law distributions of burst duration and interburst interval in the solar wind: turbulence or dissipative self-organized criticality? , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  Self-organized criticality driven by deterministic rules , 1997, cond-mat/9702068.

[20]  Vincenzo Carbone,et al.  A note on shell models for MHD turbulence , 1998, chao-dyn/9807032.

[21]  D. Turcotte,et al.  Self-organized criticality , 1999 .

[22]  J. M. McTiernan,et al.  The Waiting-Time Distribution of Solar Flare Hard X-Ray Bursts , 1998 .

[23]  Christensen,et al.  Temporal correlations, universality, and multifractality in a spring-block model of earthquakes. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[24]  E. Lu,et al.  Avalanches and the Distribution of Solar Flares , 1991 .

[25]  M Bartolozzi,et al.  Stochastic cellular automata model for stock market dynamics. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  L. Sorriso-Valvo,et al.  To what extent can dynamical models describe statistical features of turbulent flows , 2002, nlin/0204051.

[27]  Bak,et al.  Punctuated equilibrium and criticality in a simple model of evolution. , 1993, Physical review letters.

[28]  Rosario N. Mantegna,et al.  Book Review: An Introduction to Econophysics, Correlations, and Complexity in Finance, N. Rosario, H. Mantegna, and H. E. Stanley, Cambridge University Press, Cambridge, 2000. , 2000 .

[29]  Takashi Nagatani.  SELF-ORGANIZED CRITICALITY IN 1D TRAFFIC FLOW , 1996 .

[30]  Rosario N. Mantegna,et al.  Stock market dynamics and turbulence: parallel analysis of fluctuation phenomena , 1997 .

[31]  Jörg Baschnagel,et al.  Stochastic Processes: From Physics to Finance , 2000 .

[32]  D. Sornette,et al.  Precursors, aftershocks, criticality and self-organized criticality , 1998 .

[33]  J. Peinke,et al.  Turbulent cascades in foreign exchange markets , 1996, Nature.

[34]  Didier Sornette,et al.  Self-Organized Criticality and Earthquakes , 1989 .

[35]  I. Daubechies.  Orthonormal bases of compactly supported wavelets , 1988 .

[36]  Guido Boffetta,et al.  Power Laws in Solar Flares: Self-Organized Criticality or Turbulence? , 1999, chao-dyn/9904043.

[37]  James M. McTiernan,et al.  Solar flares and avalanches in driven dissipative systems , 1993 .

[38]  T. Nagatani.  Self-organized criticality in 1D traffic flow model with inflow or outflow , 1995 .