Evidence of a random multifractal turbulent structure in the Dow Jones Industrial Average

Abstract This paper uses over 18,000 daily observations on the Dow Jones Industrial Average (DJIA) (from 3 January 1928 to 18 October 2000) and various tests from statistics and dynamical systems theory to support a random multifractal turbulent structure for the US stock market. In particular, this structure is supported by J.C. Vassilicos, A. Demos and F. Tata [Fractals, Chaotic Behavior in Systems, 1994, 249] multifractal structure test and S. Ghashghaie, W. Breymann, J. Peinke, P. Talkner, Y. Dodge [Nature 381 (1996) 767] turbulent behavior test.

[1]  Ioannis Andreadis,et al.  Self-criticality and stochasticity of an S&P 500 index time series , 2000 .

[2]  L. Summers.  Does the Stock Market Rationally Reflect Fundamental Values , 1986 .

[3]  John Christos Vassilicos,et al.  Fractal dimensions and spectra of interfaces with application to turbulence , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[4]  Apostolos Serletis,et al.  On stochasticity and turbulence in the federal funds market , 2001, Int. J. Syst. Sci..

[5]  Corey S. Powell,et al.  Hubble Bags a Great White , 1991 .

[6]  E. Fama.  The Behavior of Stock-Market Prices , 1965 .

[7]  Frederic S. Mishkin,et al.  The economics of money, banking, and financial markets : 1998 readings to accompany Mishkin , 1986 .

[8]  M. Ausloos,et al.  Low q-moment multifractal analysis of Gold price, Dow Jones Industrial Average and BGL-USD exchange rate , 1999 .

[9]  William A. Barnett,et al.  Martingales, Nonlinearity, and Chaos , 2000 .

[10]  E. Fama.  EFFICIENT CAPITAL MARKETS: A REVIEW OF THEORY AND EMPIRICAL WORK* , 1970 .

[11]  P. Bak,et al.  Self-organized criticality , 1991 .

[12]  Rosario N. Mantegna,et al.  Turbulence and financial markets , 1996, Nature.

[13]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[14]  Daniel L. Schacter,et al.  Brain regions associated with retrieval of structurally coherent visual information , 1995, Nature.

[15]  J. Vassilicos,et al.  No Evidence of Chaos But Some Evidence of Multifractals in the Foreign Exchange and the Stock Markets , 1993 .

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