Advertisement

Automation and Remote Control

, Volume 62, Issue 4, pp 607–616 | Cite as

Multifractality and Self-Adjustment of the Attraction Channel of Stock Market

  • V. G. Kleparskii
Article

Abstract

For different evolutionary stages of the stock market, the fractal dimensionality of the attraction zone was estimated for the short-term and medium-term dynamic structures using by way of example the cost of the futures contract by the Standard and Poors 500 stock index. Adaptation of the stock market to a new environment was shown to be realized through reducing the fractal dimensionality, that is, chaoticity of motion, of the short-term dynamic structures. Minimization of the fractal dimensionality with the increase of the efficient existence of the dynamic component substructures was shown to be the prerequisite for stability of the multifractal dynamic system of the stock market.

Keywords

Dynamic System Mechanical Engineer System Theory Stock Market Evolutionary Stage 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    Soros, G., The Alchemy of Finance: Reading the Mind of the Market, New York: Wiley, 1994. Translated under the title Alkhimiya finansov, Moscow: INFRA-M, 1999.Google Scholar
  2. 2.
    Frish, U., Turbulence, in Nasledie A.N. Kolmogorova (A.N. Kolmogorov's Heritage), Moscow: Fazis, 1998.Google Scholar
  3. 3.
    Nelkin, M., Universality and Scaling in Fully Developed Turbulence, Adv. Phys., 1994, vol. 43, no. 3, pp. 143–181.Google Scholar
  4. 4.
    Karmatskii, N.I. and Kleparskii, V.G., Dynamic Structurization and Fractality of the Information and Investment Flows, Avtom. Telemekh., 1999, no. 9, pp. 115–121.Google Scholar
  5. 5.
    Kleparskii, V.G., Evaluation of the Fractal Dimensionality of the Attractor of the Stock Market Structure, in Teoriya aktivnykh struktur. (Theory of Active Structures), Burkov, V.N. et al., Eds., Moscow: IPU, 1999, pp. 214–215.Google Scholar
  6. 6.
    Zaslavskii, G.M. and Sagdeev, R.Z., Vvedenie v nelinei'nuyu fiziku: ot mayatnika do turbulentnosti i khaosa (Introduction to the Nonlinear Physics: From Pendulum to Turbulence and Chaos), Moscow: Nauka, 1988.Google Scholar
  7. 7.
    Cross, M.C. and Hohenberg, P.S., Pattern Formation Outside of Equilibrium, Rev. Mod. Phys., 1993, vol. 65, no. 3, part. II, pp. 851–1112.Google Scholar
  8. 8.
    Feder, J., Fractals, New York: Plenum, 1988.Google Scholar
  9. 9.
    Oboukhov, A.M., Some Specific Features of Atmospheric Turbulence, J. Fluid Mech., 1962, vol. 13, pp. 77–81.Google Scholar
  10. 10.
    Kolmogorov, A.N., A Refinement of Previous Hypotheses Concerning the Local Structure of Turbulence in a Viscous Incompressible Fluid at High Reynolds Number, J. Fluid Mech., 1962, vol. 13, pp. 82–85.Google Scholar
  11. 11.
    Ghashghaie, S., Breymann, W., Peinke, J., et al., Turbulent Cascades in Foreign Exchange Markets, Nature, 1996, vol. 381, pp. 767–770.Google Scholar
  12. 12.
    Mantegna, R.N. and Stanley, H.E., Turbulence and Financial Markets, Nature, 1996, vol. 383, pp. 587–588.Google Scholar

Copyright information

© MAIK “Nauka/Interperiodica” 2001

Authors and Affiliations

  • V. G. Kleparskii
    • 1
  1. 1.Trapeznikov Institute of Control SciencesRussian Academy of SciencesMoscowRussia

Personalised recommendations