IDENTIFICATION AND FORECASTING OF SHARP CHANGES IN ECONOMICAL SYSTEMS BY TRACKING OF LOCAL LYAPUNOV EXPONENTS
DOI:
https://doi.org/10.47839/ijc.3.3.317Keywords:
Sharp changes, unpredictability, local Lyapunov exponents, Takens’ theoremAbstract
An approach to detect sharp changes in economical systems was developed in this paper. We will give brief introduction in current methods of prediction of nonlinear and chaotic time-series and give definition of local Lyapunov exponents (LLE). Then author’s approach will be described. Also some numerical results and discussions will be given.References
H. Schuster. Deterministic chaos. Introduction. Moscow, 1988.
P. Chen. A Random-Walk or Color-Chaos on the Stock Market? Time-Frequency Analysis of S&P Indexes, Studies in Nonlinear Dynamics & Econometrics, 1(2) (1996). p. 87-103.
P. Chen. Empirical and Theoretical Evidence of Monetary Chaos. System Dynamics Review, 4 (1988), p. 81-108.
V. I. Oseledec. Multiplicative Ergodic Theorem and Lyapunov Exponents for Dynamical Systems. Trans. of Mosc. Math. Soc., 19 (1968), p. 179-210.
J.-P. Eckmann, D. Ruelle. Ergodic Theory of Chaos and Strange Attractors. Rev. Mod. Phys., 57 (1989), p. 617-656.
H. D. I. Abarbanel, R. Brown, M. B. Kennel. Lyapunov Exponents in Chaotic Systems: Their Importance and Their Evaluation Using Observed Data. Int. J. Mod. Phys., B5 (1991) p. 1347-1375.
F. Takens. Detecting Strange Attractors in Turbulence. Dynamical Systems and Turbulence. Lecture Notes in Mathematics. Ed. by D. A. Rand, L. S. Young. Heidelberg, 1981, p. 366-381.
A. M. Fraser, H. L. Swinney. Independent Coordinates for Strange Attractors from Mutual Information. Phys. Rev. A 33, 1986, p. 1134-1140.
M. B. Kennel, R. Brown, H. D. I. Abarbanel. Determining Embedding Dimension for Phase-Space Reconstruction Using a Geometrical Construction. Phys. Rev. A 45, 1987, p. 3403-3411.
G. Benettin, L. Galgani, J. M. Strelcyn. Kolmogorov Entropy and Numerical Experiments. Phys. Rev. 14, 1976, p. 2338-2345.
V. Golovko, Y. Savitsky, N. Maniakov. Neural Networks for Signal Processing in Measurement Analysis and Industrial Applications: the Case of Chaotic Signal Processing. Chapter in NATO book “Neural Networks for Instrumentation, Measurement and Related Industrial Application”. Amsterdam: IOS Press, 2003, p119-143.
B. A. Bailey, S. Ellner, D. W. Nychka. Chaos with Confidence: Asimptotics and Bifurcations of Local Lyapunov Exponents. Proceeding of the fields. CRM workshop on Nonlinear Dynamics and Time-Series: Building a Bridge between the Natural and Statistical Science 11, 1997, p. 115-133.
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