Abstract
We present algorithms for singular spectrum analysis and local approximation methods used to extrapolate time series. We analyze the advantages and disadvantages of these methods and consider the peculiarities of applying them to various systems. Based on this analysis, we propose a generalization of the local approximation method that makes it suitable for forecasting very noisy time series. We present the results of numerical simulations illustrating the possibilities of the proposed method.
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REFERENCES
G. E. P. Box and G. Jenkins, Time Series Analysis, Forecasting, and Control, Holden-Day, San Francisco, Calif. (1970).
A. S. Monin and L. I. Piterbarg, “Forecasting weather and climate [in Russian], ” in: Limits of Predictability (Yu. A. Kravtsov, ed.), Nauka, Moscow (1992), pp. 28–53; English transl., Springer, Berlin (1993), pp. 7–44.
F. Takens, “Detecting strange attractors in turbulence,” in: Dynamical Systems and Turbulence (Lect. Notes Math., Vol. 898, D. A. Rand and L. S. Young, eds.), Springer, Berlin (1981), pp. 336–381.
J. D. Farmer and J. J. Sidorowich, Phys. Rev. Lett., 59, 845–848 (1987).
R. Vautard, P. Yiou, and M. Ghil, Phys. D, 58, 95–126 (1992).
A. Yu. Loskutov, I. A. Istomin, O. L. Kotlyarov, and K. M. Kuzanyan, Astron. Lett., 27, 745–753 (2001).
M. Ghil et al., Rev. Geophys., 40, No. 3, 1–41 (2002).
D. L. Danilov and A. A. Zhiglyavskii, eds., Basic Ingredients of Time Series: The “Caterpillar” Method [in Russian], St. Petersburg Univ. Publ., St. Petersburg (1997).
I. M. Dremin, O. V. Ivanov, and V. A. Nechitailo, Phys. Usp., 44, 447–478 (2001); A. V. Deshcherevskii, A. A. Lukk, A. Ya. Sidorin, G. V. Vstovsky, and S. F. Timashev, Nat. Hazards and Earth Syst. Sci., 3, No. 2, 159–164 (2003).
D. S. Broomhead and G. P. King, Phys. D, 20, 217–236 (1986).
R. Mañe, “On the dimension of the compact invariant sets of certain nonlinear maps,” in: Dynamical Systems and Turbulence (Lect. Notes Math., Vol. 898, D. A. Rand and L. S. Young, eds.), Springer, Berlin (1981), pp. 230–242.
G. G. Malinetskii and A. B. Potapov, Contemporary Problems of Nonlinear Dynamics [in Russian], URSS, Moscow (2000).
P. Grassberger and I. Procaccia, Phys. Rev. Lett., 50, 346–349 (1983).
P. Grassberger and I. Procaccia, Phys. D, 9, 189–201 (1983).
D. Kahaner, C. Moler, and S. Nash, Numerical Methods and Software, Prentice-Hall, Upper Saddle River, N. J. (1989).
D. Kugiumtzis, O. C. Lingjoerde, and N. Christophersen, Phys. D, 112, 344–360 (1998).
J. D. Farmer and J. J. Sidorowich, “Exploiting chaos to predict the future and reduce noise,” in: Evolution, Learning, and Cognition (Y. C. Lee, ed.), World Scientific, Singapore (1988), pp. 277–330.
K. Judd and M. Small, Phys. D, 136, 31–44 (2000).
A. Yu. Loskutov, I. A. Istomin, O. L. Kotlyarov, and D. I. Zhuravlev, Moscow Univ. Phys. Bull., No. 6, 3–21 (2002).
A. Loskutov, I. A. Istomin, K. M. Kuzanyan, and O. L. Kotlyarov, Nonlinear Phenomena in Complex Systems, 4, No. 1, 47–57 (2001).
A. M. Dubrov, V. S. Mkhitaryan, and L. I. Troshin, Multidimensional Statistical Methods [in Russian], Finansy i Statistika, Moscow (2000).
M. C. Mackey and L. Glass, Science, 197, 287–289 (1977).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 1, pp. 148–159, January, 2005.
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Istomin, I.A., Kotlyarov, O.L. & Loskutov, A.Y. The problem of processing time series: Extending possibilities of the local approximation method using singular spectrum analysis. Theor Math Phys 142, 128–137 (2005). https://doi.org/10.1007/s11232-005-0077-y
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DOI: https://doi.org/10.1007/s11232-005-0077-y