The problem of processing time series: Extending possibilities of the local approximation method using singular spectrum analysis
Teoretičeskaâ i matematičeskaâ fizika, Tome 142 (2005) no. 1, pp. 148-159 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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.
Keywords: time series, forecast, local approximation.
Mots-clés : chaos
@article{TMF_2005_142_1_a12,
     author = {I. A. Istomin and O. L. Kotlyarov and A. Yu. Loskutov},
     title = {The problem of processing time series: {Extending} possibilities of the local approximation method using singular spectrum analysis},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {148--159},
     year = {2005},
     volume = {142},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2005_142_1_a12/}
}
TY  - JOUR
AU  - I. A. Istomin
AU  - O. L. Kotlyarov
AU  - A. Yu. Loskutov
TI  - The problem of processing time series: Extending possibilities of the local approximation method using singular spectrum analysis
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2005
SP  - 148
EP  - 159
VL  - 142
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2005_142_1_a12/
LA  - ru
ID  - TMF_2005_142_1_a12
ER  - 
%0 Journal Article
%A I. A. Istomin
%A O. L. Kotlyarov
%A A. Yu. Loskutov
%T The problem of processing time series: Extending possibilities of the local approximation method using singular spectrum analysis
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2005
%P 148-159
%V 142
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2005_142_1_a12/
%G ru
%F TMF_2005_142_1_a12
I. A. Istomin; O. L. Kotlyarov; A. Yu. Loskutov. The problem of processing time series: Extending possibilities of the local approximation method using singular spectrum analysis. Teoretičeskaâ i matematičeskaâ fizika, Tome 142 (2005) no. 1, pp. 148-159. http://geodesic.mathdoc.fr/item/TMF_2005_142_1_a12/

[1] Dzh. Boks, G. Dzhenkins, Analiz vremennýkh ryadov. Prognoz i upravlenie, Mir, M., 1974

[2] A. S. Monin, L. I. Piterbarg, “Predskazuemost pogody i klimata”, Predely predskazuemosti, ed. Yu. A. Kravtsov, Nauka, M., 1992, 28–53

[3] F. Takens, “Detecting strange attractors in turbulence”, Dynamical Systems and Turbulence, Lect. Notes in Math., 898, eds. D. A. Rand, L. S. Young, Springer, Berlin, 1981, 336–381 | MR

[4] J. D. Farmer, J. J. Sidorowich, Phys. Rev. Lett., 59 (1987), 845–848 | DOI | MR

[5] R. Vautard, P. Yiou, M. Ghil, Physica D, 58 (1992), 95–126 | DOI

[6] A. Yu. Loskutov, I. A. Istomin, O. L. Kotlyarov, K. M. Kuzanyan, Pisma v Astron. zhurn., 27:11 (2001), 867–876

[7] M. Ghil, M. R. Allen, M. D. Dettinger et al., Rev. Geophys., 40(3) (2002), 1–41 | DOI | MR

[8] D. L. Danilov, A. A. Zhiglyavskii (red.), Glavnye komponenty vremennykh ryadov: metod “Gusenitsa”, Izd-vo SPb GU, SPb., 1997

[9] I. M. Dremin, O. V. Ivanov, V. A. Nechitailo, UFN, 171:5 (2001), 465–501 ; A. V. Descherevsky, A. A. Lukk, A. Sidorin, G. V. Vstovsky, S. F. Timashev, Nat. Hazards and Earth Syst. Sci., 3:2 (2003), 159–164 | DOI | DOI

[10] D. S. Broomhead, G. P. King, Physica D, 20 (1986), 217–236 | DOI | MR | Zbl

[11] R. Mañe, “On the dimension of the compact invariant sets of certain nonlinear maps”, Dynamical Systems and Turbulence, Lect. Notes in Math., 898, eds. D. A. Rand, L. S. Young, Springer, Berlin, 1981, 230–242 | DOI | MR

[12] G. G. Malinetskii, A. B. Potapov, Sovremennye problemy nelineinoi dinamiki, URSS, M., 2000

[13] P. Grassberger, I. Procaccia, Phys. Rev. Lett., 50 (1983), 346–349 | DOI | MR

[14] P. Grassberger, I. Procaccia, Physica D, 9:1–2 (1983), 189–201 | DOI | MR

[15] D. Kakhaner, K. Mouler, S. Nesh, Chislennye metody i programmnoe obespechenie, Mir, M., 1998

[16] D. Kugiumtzis, O. C. Lingjoerde, N. Christophersen, Physica D, 112 (1998), 344–360 | DOI | MR | Zbl

[17] J. D. Farmer, J. J. Sidorowich, “Exploting chaos to predict the future and reduce noise”, Evolution, Learning, and Cognition, ed. Y. C. Lee, World Scientific, Singapore, 1988, 277–330 | MR

[18] K. Judd, M. Small, Physica D, 136 (2000), 31–44 | DOI | MR | Zbl

[19] A. Yu. Loskutov, O. L. Kotlyarov, I. A. Istomin, D. I. Zhuravlev, Vestn. MGU. Fizika, Astronomiya, 2002, no. 6, 3–21 | MR

[20] A. Loskutov, I. A. Istomin, K. M. Kuzanyan, O. L. Kotlyarov, Nonlin. Phenomena in Complex Syst., 4:1 (2001), 47–57 | MR

[21] A. M. Dubrov, V. S. Mkhitaryan, L. I. Troshin, Mnogomernye statisticheskie metody, Finansy i statistika, M., 2000

[22] M. C. Mackey, L. Glass, Science, 197 (1977), 287–289 | DOI