Forecasting the time series of sunspot numbers

Solar Physics

Volumn 249, Issue 1, 2008, Pages 103-120

  Aguirre, L A ^a   Letellier, C ^b   Maquet, J ^b  

^a FEDERAL UNIVERSITY OF MINAS GERAIS   (Brazil)

^b UNIVERSITÉ ET INSA DE ROUEN   (France)

Author keywords

Forecasting solar activity; Nonlinear models; Prediction; Sunspot numbers

Indexed keywords

EID: 42449104286     PISSN: 00380938     EISSN: 1573093X     Source Type: Journal    
DOI: 10.1007/s11207-008-9160-5     Document Type: Article

References (53)

1. Aguirre, L.A.: 1995, A nonlinear correlation function for selecting the delay time in dynamical reconstructions. Phys. Lett. A 203(2∈-∈3), 88∈-∈94.
2. Aguirre, L.A., Billings, S.A.: 1995, Retrieving dynamical invariants from chaotic data using NARMAX models. Int. J. Bifurc. Chaos 5(2), 449∈-∈474.
3. Aguirre, L.A., Letellier, C.: 2005, Observability of multivariable differential embeddings. J. Phys. A: Math. Gen. 38, 6311∈-∈6326.
4. Aguirre, L.A., Mendes, E.M.A.M.: 1996, Nonlinear polynomial models: structure, term clusters and fixed points. Int. J. Bifurc. Chaos 6(2), 279∈-∈294.
5. Aguirre, L.A., Rodrigues, G.G., Mendes, E.M.A.M.: 1997, Nonlinear identification and cluster analysis of chaotic attractors from a real implementation of Chua's circuit. Int. J. Bifurc. Chaos 7(6), 1411∈-∈1423.
6. Aguirre, L.A., Barros, V.C., Souza, A.V.P.: 1999, Nonlinear multivariable modeling and analysis of sleep apnea time series. Comput. Biol. Med. 29(3), 207∈-∈228.
7. Aguirre, L.A., Furtado, E.C., Tôrres, L.A.B.: 2006, Evaluation of dynamical models: Dissipative synchronization and other techniques. Phys. Rev. E 74, 019612.
8. Aguirre, L.A., Rodrigues, D.D., Lima, S.T., Martinez, C.B.: 2008, Dynamical prediction and pattern mapping in short term load-forecasting. Electr. Power Energy Syst. 30, 73∈-∈82.
9. Attia, A.F., Abdel-Hamid, R., Quassim, M.: 2005, Prediction of solar activity based on neuro-fuzzy modeling. Solar Phys. 227, 177∈-∈191.
10. Barkhatov, N.A., Korolev, A.V., Ponomarev, S.M., Sakharov, S.Y.: 2001, Long-term forecasting of solar activity indices using neural networks. Radiophys. Quantum Electron. 44(9), 742∈-∈749.
11. Billings, S.A., Chen, S., Korenberg, M.J.: 1989, Identification of MIMO nonlinear systems using a forward-regression orthogonal estimator. Int. J. Control 49(6), 2157∈-∈2189.
12. Bracewell, R.N.: 1953, The sunspot number series. Nature 171, 649∈-∈650.
13. Buchler, J.R., Kolláth, Z., Cadmus, R.R., Jr.: 2004, Evidence for low-dimensional chaos in semiregular variable stars. Astrophys. J. 613, 532∈-∈547.
14. Cameron, R., Schüssler, M.: 2007, Solar cycle prediction using precursors and flux transport models. Astrophys. J. 659, 801∈-∈811.
15. Carbonell, M., Oliver, R., Ballester, J.L.: 1994, A search for chaotic behavior in solar activity. Astron. Astrophys. 290(3), 983∈-∈994.
16. Chen, S., Billings, S.A., Luo, W.: 1989, Orthogonal least squares methods and their application to nonlinear system identification. Int. J. Control 50(5), 1873∈-∈1896.
17. Choudhuri, A.R., Chatterjee, P., Jiang, J.: 2007, Predicting solar cycle 24 with a solar dynamo model. Phys. Rev. Lett. 98(5), 131103.
18. De Meyer, F.: 2003, A transfer function model for the sunspot cycle. Solar Phys. 217, 349∈-∈366.
19. Duhau, S.: 2003, An early prediction of maximum sunspot number in solar cycle 24. Solar Phys. 213, 203∈-∈212.
20. Eddy, J.A.: 1976, The Maunder minimum. Science 192, 1189∈- ∈1202.
21. Gholipour, A., Lucas, C., Araabi, B.N., Shafiee, M.: 2005, Solar activity forecast: Spectral analysis and neurofuzzy prediction. J. Atmos. Solar-Terr. Phys. 67, 595∈-∈603.
22. Gilmore, R., Lefranc, M.: 2002, The Topology of Chaos, Wiley Interscience, New York.
23. Gilmore, R., Letellier, C.: 2007, The Symmetry of Chaos, Oxford University Press, New York.
24. Hathaway, D.H., Wilson, R.M., Reichmann, E.J.: 1994, The shape of the sunspot cycle. Solar Phys. 151, 177∈-∈190.
25. Hoyt, D.V., Schatten, K.H.: 1998, Group sunspot numbers: a new solar activity reconstruction. Solar Phys. 179, 189∈-∈219.
26. Kremliovsky, M.N.: 1994, Can we understand time scales of solar activity? Solar Phys. 151, 351∈-∈370.
27. Kremliovsky, M.N.: 1995, Limits of predictability of solar activity. Solar Phys. 159, 371∈-∈380.
28. Lainscsek, C.S.M., Schürrer, F., Kadtke, J.: 1998, A general form for global dynamical data models for three-dimensional systems. Int. J. Bifurc. Chaos 8(5), 899∈-∈914.
29. Letellier, C., Gilmore, R.: 2001, Covering dynamical systems: Two-fold covers. Phys. Rev. E 63, 016206.
30. Letellier, C., Malasoma, J.M.: 2001, Unimodal order in the image of the simplest equivariant jerk system. Phys. Rev. E 64, 067202.
31. Letellier, C., Dutertre, P., Maheu, B.: 1995, Unstable periodic orbits and templates of the Rössler system: Toward a systematic topological characterization. Chaos 5(1), 271∈-∈282.
32. Letellier, C., Le Sceller, L., Dutertre, P., Gouesbet, G., Fei, Z., Hudson, J.L.: 1995, Topological characterization and global vector field reconstruction from an experimental electrochemical system. J. Phys. Chem. A 99, 7016∈-∈7027.
33. Letellier, C., Dutertre, P., Reizner, J., Gouesbet, G.: 1996, Evolution of multimodal map induced by an equivariant vector field. J. Phys. A 29, 5359∈-∈5373.
34. Letellier, C., Maquet, J., Labro, H., Le Sceller, L., Gouesbet, G., Arnéodo, A.: 1998, Analyzing chaotic behaviour in a belousov-zhabotinskii reaction by using a global vector field reconstruction. J. Phys. Chem. A 102, 10265∈-∈10273.
35. Letellier, C., Aguirre, L.A., Maquet, J., Gilmore, R.: 2006, Evidence for low dimensional chaos in sunspot cycles. Astron. Astrophys. 449, 379∈-∈387.
36. Li, K.J.: 1999, The shape of the sunspot cycle described by sunspot areas. Astron. Astrophys. 345, 1006∈-∈1010.
37. Li, Q.X., Li, K.J.: 2007, Low dimensional chaos from the group sunspot numbers. Chin. J. Astron. Astrophys. 7(3), 435∈-∈440.
38. Li, K.J., Yun, H.S., Gu, X.M.: 2001, On long-term predictions of the maximum sunspot numbers of solar cycles 21 to 23. Astron. Astrophys. 368, 285∈-∈291.
39. Makarenko, N.G., Karimova, L.M., Novak, M.M.: 2007, Investigation of global solar magnetic field by computational topology methods. Physica A 380, 98∈-∈108.
40. Mindlin, G.B., Gilmore, R.: 1992, Topological analysis and synthesis of chaotic time series. Physica D 58, 229∈-∈242.
41. Mininni, P.D., Gómez, D.O., Mindlin, G.B.: 2000, Stochastic relaxation oscillator model for the solar cycle. Phys. Rev. Lett. 85(25), 5476∈-∈5479.
42. Moroz, I., Letellier, C., Gilmore, R.: 2007, When are projections also embeddings? Phys. Rev. E 75, 046201.
43. Nikonova, M.V., Klochek, N.V., Smolkov, G.Y.: 2000, Forecasting the solar activity using the nonlinear spectral model. Adv. Space Res. 26(1), 183∈-∈186.
44. Ogurtsov, M.G.: 2005, On the possibility of forecasting the sun's activity using radiocarbon solar proxy. Solar Phys. 231, 167∈-∈176.
45. Orfila, A., Ballester, J.L., Oliver, R., Alvarez, A., Tintoré, J.: 2002, Evidence for low dimensional chaos in sunspot cycles. Astron. Astrophys. 386, 313∈-∈318.
46. Qin, Z.: 1998, The transitional time scale from stochastic to chaotic behavior for solar activity. Solar Phys. 178, 423∈-∈431.
47. Schatten, K.: 2003, Long-range solar activity predictions: a reprieve from cycle #∈24's activity. In: Flight Mechanics Symposium. NASA Goddard Space Flight Center, Greenbelt, 1∈-∈11.
48. Sello, S.: 2001, Solar cycle forecasting: A nonlinear dynamics approach. Astron. Astrophys. 377, 312∈-∈320.
49. Sello, S.: 2003, Solar cycle activity: A preliminary prediction for cycle #24. Astron. Astrophys. 410, 691∈-∈693.
50. Svalgaard, L., Cliver, E.W., Kamide, Y.: 2005, Sunspot cycle 24: Smallest cycle in 100 years? Geophys. Res. Lett. 32, L01104.
51. Tsirulnik, L.B., Kuznetsova, T.V., Oraevsky, V.N.: 1997, Forecasting the 23rd and 24th solar cycles on the basis of MGM spectrum. Adv. Space Res. 20(12), 2369∈-∈2372.
52. Tufillaro, N.B., Wyckoff, P., Brown, R., Schreiber, T., Molteno, T.: 1995, Topological time-series analysis of a string experiment and its synchronized model. Phys. Rev. E 51(1), 164∈-∈174.
53. Wolf, R.: 1852, Sunspot epochs since A.D. 1610: The periodic return of sunspot minima. Acad. Sci. C. R. 35, 704∈-∈705.