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Solar Physics

, Volume 257, Issue 2, pp 371–381 | Cite as

Time Series Modeling of Sunspot Numbers Using Long-Range Cyclical Dependence

  • Luis A. Gil-Alana
Article

Abstract

This paper deals with the analysis of the sunspot number time series using a new technique based on cyclical long-range dependence. The results show that sunspot numbers have a periodicity of 130 months but, more importantly, that the series is highly persistent, with an order of cyclical fractional integration slightly above 0.30. That means that the series displays long memory, with a large degree of dependence between the observations that tends to disappear very slowly in time.

Keywords

Fractional integration Long-range dependence Sunspot cycles Sunspot numbers 

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References

  1. Aguirre, L.A., Letellier, C., Maquet, J.: 2008, Solar Phys. 249, 103. CrossRefADSGoogle Scholar
  2. Andel, J.: 1986, Kybernetika 22, 105. zbMATHMathSciNetGoogle Scholar
  3. Ballester, J.L., Oliver, R.: 1999, Astrophys. J. 522, 153. CrossRefADSGoogle Scholar
  4. Bloomfield, P.: 1992, Clim. Change 21, 275. CrossRefGoogle Scholar
  5. Box, G.E.P., Pierce, D.A.: 1970, J. Am. Stat. Assoc. 65, 1509. zbMATHCrossRefMathSciNetGoogle Scholar
  6. Chung, C.-F.: 1996a, J. Time Ser. Anal. 17, 111. zbMATHCrossRefMathSciNetGoogle Scholar
  7. Chung, C.-F.: 1996b, J. Econom. 73, 237. zbMATHCrossRefGoogle Scholar
  8. Dalla, V., Hidalgo, J.: 2005, J. Econom. 129, 219. CrossRefMathSciNetGoogle Scholar
  9. Ferrara, L., Guegan, D.: 2001, J. Forecast. 20, 581. CrossRefGoogle Scholar
  10. Gholipour, A., Lucas, C., Babak, N.A., Shafiee, M.: 2005, J. Atmos. Solar-Terr. Phys. 67, 595. CrossRefADSGoogle Scholar
  11. Gil-Alana, L.A.: 2003, Int. J. Clim. 23, 1699. CrossRefGoogle Scholar
  12. Gil-Alana, L.A.: 2005, J. Clim. 18, 5357. CrossRefADSGoogle Scholar
  13. Gil-Alana, L.A.: 2007, Ann. Econ. Finance 1, 1. Google Scholar
  14. Gil-Alana, L.A.: 2009, J. Stat. Comput. Simul. doi: 10.1080/00949650802322111. Google Scholar
  15. Granger, C.W.J.: 1980, J. Econom. 14, 227. zbMATHCrossRefMathSciNetGoogle Scholar
  16. Gray, H.L., Zhang, N., Woodward, W.A.: 1989, J. Time Ser. Anal. 10, 233. zbMATHCrossRefMathSciNetGoogle Scholar
  17. Gray, H.L., Zhang, N., Woodward, W.A.: 1994, J. Time Ser. Anal. 15, 561. zbMATHCrossRefMathSciNetGoogle Scholar
  18. Hathaway, D.H., Wilson, R.M., Reichmann, E.J.J.: 1999, J. Geophys. Res. 104, 22375. CrossRefADSGoogle Scholar
  19. Hsu, N.-J., Tsai, H.: 2009, J. Stat. Plan. Inf. 139, 1992. zbMATHCrossRefGoogle Scholar
  20. Koscielny-Bunde, E., Bunde, A., Havlin, S., Roman, H.E., Goldreich, Schellnhuber, H.J.: 1998, Phys. Rev. Lett. 81, 729. CrossRefADSGoogle Scholar
  21. Lewis, P.A.W., Ray, B.K.: 1997, J. Am. Stat. Assoc. 92, 881. zbMATHCrossRefGoogle Scholar
  22. Lindström, J., Kokko, H., Ranta, E.: 1996, Oikos 77, 565. CrossRefGoogle Scholar
  23. Ljung, G.M., Box, G.E.P.: 1978, Biometrika 65, 297–303. zbMATHCrossRefGoogle Scholar
  24. Magnus, W., Oberhettinger, F., Soni, R.P.: 1966, Formulas and Theorems for the Special Functions of Mathematical Physics, Springer, Berlin, 254. zbMATHGoogle Scholar
  25. Maraun, D., Rust, H.W., Timmer, H.: 2004, Nonlinear Process. Geophys. 11, 495. ADSGoogle Scholar
  26. McLeod, A.I., Hipel, K.W.: 1978, Water Resour. Res. 14, 491. CrossRefADSGoogle Scholar
  27. Morris, M.J.: 1977, J. Roy. Stat. Soc. Ser. A 140, 437. CrossRefGoogle Scholar
  28. Pelletier, J., Turcotte, D.: 1999, Adv. Geophys. 40, 91. Google Scholar
  29. Percival, D.B., Overland, J.E., Mofjeld, H.O.: 2004, In: Brillinger, D.R., Robinson, E.A., Schoenberg, F.P. (eds.) Time Series Analysis and Applications to Geophysical Systems. Springer, Berlin, 151. Google Scholar
  30. Pethkar, J.S., Selvam, A.M.: 1997, In: Goswani, P. (ed.) Proc. TROPMET-97 Symp. Indian Meteorological Society, New Delhi, http://xxx.1an1.gov/html/physics/0104056. Google Scholar
  31. Rainville, E.D.: 1960, Special Functions, MacMillan, New York, 365. zbMATHGoogle Scholar
  32. Robinson, P.M.: 1978, Scand. J. Stat. 5, 163. Google Scholar
  33. Robinson, P.M.: 1994, J. Am. Stat. Assoc. 89, 1420. zbMATHCrossRefGoogle Scholar
  34. Sadek, N., Khotanzad, A.: 2004, Comput. Commun. 2, 963. Google Scholar
  35. Schatten, K.H.: 1998, In: Donahue, R.A., Bookbinder, J.A. (eds.) The Tenth Cambridge Workshop on Cool Stars, Stellar Systems and the Sun CS-154, Astron. Soc. Pac., San Francisco, 1315. Google Scholar
  36. Schuster, A.: 1906, Philos. Trans. Roy. Soc. 206, 69. CrossRefADSGoogle Scholar
  37. Schwabe, S.H.: 1843, Astron. Nachr. 20, 234. CrossRefGoogle Scholar
  38. Smith, R.L.: 1993, In: Barnett, V., Turkman, K.F. (eds.) Long-Range Dependence and Global Warming, Statistics for the Environment. Wiley, New York, 141. Google Scholar
  39. Waldmeier, M.: 1961, The Sunspot Activity in the Years 1610 – 1960. Swiss Federal Observatory, Zurich. Google Scholar
  40. Xu, T., Wu, J., Wu, Z.-S., Li, Q.: 2007, Chin. J. Astron. Astrophys. 3, 337. Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Faculty of EconomicsUniversity of NavarraPamplonaSpain

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