DOI: https://doi.org/10.15588/1607-3274-2014-2-18

COMPARATIVE ANALYSIS OF THE COMPLEXITY OF CHAOTIC AND STOCHASTIC TIME SERIES

L. O. Kirichenko, Yu. A. Kobitskaya, A. Yu. Habacheva

Abstract


The new approach to the recognition mechanism of the time series generating process based on the results of the entropy and the recurrent analysis is proposed. The comparative analysis of the realizations properties of chaotic and stochastic processes with different correlation structure was carried out. It is shown that the derived set of information characteristics allows to distinguish the realizations of deterministic chaotic and fractal random processes. Depending on complexity measures of time series of process parameters were obtained. The information characteristics dependencies from the process parameters were obtained. The results of bioelectric signals and financial time series study are presented.


Keywords


time series, measures of complexity, approximate entropy, recurrence plot, pseudo-phase space, embedding dimension.

References


Mun F. Chaotic Vibrations / F. Mun. – New York : Wiley, 1987. – 309 р. 2. Peitgen H. Chaos and Fractals. New Frontiers of Science / H.-O. Peitgen, H. Jorgens, D. Saupe. – New York : Springer, 2004. – 895 p. 3. Shuster H. G. Deterministic Chaos: An Introduction, second revised edition / H. G. Shuster. – New York : VCH Publishers, 1988. – 248 p. 4. Takens F. Detecting strange attractors in turbulence / F. Takens, D. A. Rand, L.-S. Young // Dynamical Systems and Turbulence. – New York : Springer-Verlag, 1981. – Vol. 898. – Р. 366–381. 5. Ширяев А. Н. Основы стохастической финансовой математики. Том 1: Факты. Модели / А. Н. Ширяев. – М. : Фазис, 1998. – 512 с. 6. Dabi-Prashad O. Investigation of Time Series of Original Values of Currency Rates Measured on Small Time Frames on FOREX Using Methods of Chaos Theory / O. Dabi-Prashad, L. Kirichenko // Radioelectronics & Informatics. – 2009. – No. 4. – P. 18–24. 7. Pincus S. M. Approximate entropy as a measure of system complexity / S. M. Pincus // Proceedings of the National Academy of Sciences. – 1991. – Vol. 88. – Р. 2297–2301. 8. Eckmann J. P. Recurrence Plots of Dynamical Systems / J. P. Eckmann, S. O. Kamphorst, D. Ruelle // Europhysics Letters. – 1987. – No. 4. – Р. 973–977. 9. March T. K. Recurrence plot statistics and the effect of embedding / T. K. March, S. C. Chapman, R. O. Dendy // Physica D: Nonlinear Phenomena. – Netherlands : Elsevier, 2005. – P. 171–184.


GOST Style Citations








Copyright (c) 2015 L. O. Kirichenko, Yu. A. Kobitskaya, A. Yu. Habacheva

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Address of the journal editorial office:
Editorial office of the journal «Radio Electronics, Computer Science, Control»,
National University "Zaporizhzhia Polytechnic", 
Zhukovskogo street, 64, Zaporizhzhia, 69063, Ukraine. 
Telephone: +38-061-769-82-96 – the Editing and Publishing Department.
E-mail: rvv@zntu.edu.ua

The reference to the journal is obligatory in the cases of complete or partial use of its materials.