ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Loskutov A. J., Kozlov A. A., Hahanov J. M. Entropy and forecasting of time series in the theory of dynamical systems. Izvestiya VUZ. Applied Nonlinear Dynamics, 2009, vol. 17, iss. 4, pp. 98-113. DOI: 10.18500/0869-6632-2009-17-4-98-113

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 859)
Article type: 

Entropy and forecasting of time series in the theory of dynamical systems

Loskutov Aleksandr Jurevich, Lomonosov Moscow State University
Kozlov Aleksandr Aleksandrovich, Lomonosov Moscow State University
Hahanov Jurij Mihajlovich, Lomonosov Moscow State University

A contemporary consideration of such concepts as dimension and entropy of dynamical systems is given. Description of these characteristics includes into the analysis the other notions and properties related to complicated behavior of nonlinear systems as embedding dimension, prediction horizon etc., which are used in the paper. A question concerning the application of these ideas to real observables of the economical origin, i.e. market prices of the companies Schlumberger, Deutsche Bank, Honda, Toyota, Starbucks, BP is studied. By means of the method of singular spectrum analysis the forecasting of the market prices of these companies in different phases of the economical cycle – just before crisis and during the crisis – is given. Main advantages and demerits of the method used are found.

  1. Loskutov AYu, Mikhailov AS. Fundamentals of the theory of complex systems. Moscow-Izhevsk: Institute of Computer Sciences, ICR; 2007. 620 p. (In Russian).
  2. Kronover RM. Fractals and chaos in dynamic systems. Fundamentals of theory. Moscow: Postmarket; 2000. 352 p. (In Russian).
  3. Kuznetsov SP. Dynamic chaos. Moscow: Fizmatlit; 2001. 296 p. (In Russian).
  4. Schuster GG. Deterministic chaos. Moscow: Mir; 1988. 240 p. (In Russian).
  5. Malinetsky GG, Potapov AB. Modern problems of nonlinear dynamics. Moscow: URSS; 2002. 358 p. (In Russian).
  6. Peters E. Chaos and order in capital markets. A new analytical view of cycles, prices and market variability. Moscow: Mir; 2000. 333 p. (In Russian).
  7. Pu T. Nonlinear economic dynamics. Moscow: URSS; 2002. 198 p. (In Russian).
  8. Kantz H., Schreiber T. Nonlinear time series analysis. Cambridge: Cambridge University Press; 1997. 304 p.
  9. Abarbanel HDI, Brown R, Sidorowich JJ, Tsimring LS. The analysis of observed chaotic data in physical systems. Rev. Mod. Phys. 1993;65(4):1331–1392. DOI: 10.1103/REVMODPHYS.65.1331.
  10. Mandelbrot B. The Fractal Geometry of Nature. New York: W.H. Freeman and Company; 1983. 468 p.
  11. The main components of the time series are the “Caterpillar” method. Ed. Danilov DL, Zhiglyavsky AA. St. Petersburg: St. Petersburg University Press; 1997. 308 p. (In Russian).
  12. Loskutov AYu, Zhuravlev DI, Kotlyarov OL. Applications Of A Local Approximation Technique For Forecasting Of Economic Indicators. Voprosi analyza i upravleniya riskom. 2003;1(1):21–31.
  13. Istomin IA, Kotlyarov OL, Loskutov AYu. The problem of processing time series: Extending possibilities of the local approximation method using singular spectrum analysis. Theoret. and Math. Phys. 2005;142(1):128–137. DOI: 10.4213/tmf1771.
  14. Packard NH, Crutchfield JP, Farmer JD, Shaw RS. Geometry from a time series. Phys. Rev. Lett. 1980;45:712–716.
  15. Takens F. Dynamical systems and turbulence. Lect. Notes in Math. Berlin: Springer; 1981. No 898. 336–381 p.
  16. Grassberger P, Procaccia I. Characterization of strange attractors. Phys. Rev. Lett. 1983;50(5):346–349. DOI: 10.1103/PHYSREVLETT.50.346.
  17. Grassberger P, Procaccia I. Measuring the strangeness of strange attractors. Physica D. 1983;9(1-2):189–208. DOI: 10.1016/0167-2789(83)90298-1.
  18. Grassberger P, Procaccia I. Estimation of the Kolmogorov Entropy from a chaotic signal. Phys. Rev. A. 1983;28(4):2591–2593. DOI: 10.1103/PHYSREVA.28.2591.
  19. Illarionov A. Early recession. Smart Money. 2008;46(136).
  20. Romanovsky MYu, Romanovsky YuM. Introduction to Economophysics. Statistical and dynamic models. Moscow-Izhevsk: Institute of Computer Sciences; 2007. 340 p. (In Russian).
Short text (in English):
(downloads: 124)