Skip to main content


We’d like to understand how you use our websites in order to improve them. Register your interest.

Sunspot variability and an attempt to predict solar cycle 23 by adaptive filtering


The series of annual mean relative sunspot numbers (Rz) for 1749–1996 is subjected to the recently developed methodology of Singular Spectrum Analysis (SSA). This technique also enables data-adaptive filtering of the individual spectral components. Low order autoregressive modelling of the components are combined to provide a basis for predicting the solar cycle 23.

The Rz series is largely dominated by a doublet with periods 11.13 and 10.35 yr. close to the nominal solar cycle periodicity, a longer period variation (~110 yr.) which is the envelope of the amplitude maxima and two clusters of periodicities centred around 8 yr. and 5.5 yr. The solar magnetic cycle has no detectable component. The predicted maximum for cycle 23 will have a magnitude of ~130 and the epoch of maximum is expected between late 2000 A.D. and early 2001 A.D.


  1. Attolini, M. R., S. Cechini, M. Galli, and T. Nanni, On the persistence of 22 year solar cycle, Solar Physics, 125, 389–398, 1990.

  2. Brown, G. M., The peak of solar cycle 22: predictions in retrospect, Ann. Geophys., 10, 453–461, 1992.

  3. Cohen, T. J. and P. R. Lintz, Long term periodicities in the sunspot cycle, Nature, 250, 398–400, 1974.

  4. Cole, T. W., Periodicities in solar activity, Solar Physics, 30, 103–110, 1973.

  5. Currie, R. G., Fine structure in the sunspot spectrum 2 to 70 years, Astrophys. Space Sci., 20, 509–518, 1973.

  6. DeMeyer, F., Mathematical modelling of the sunspot number, Solar Physics, 70, 259–272, 1981.

  7. Dettinger, M. D., M. Ghil, C. M. Strong, W. Weibel, and P. Yiou, Software expedites singular spectrum analysis of noisy time series, EOS Trans AGU, 76(2), 12, 14, 21, 1995.

  8. Dicke, R. H., The phase variation of the solar cycle, Solar Physics, 115, 171–181, 1988.

  9. Dodson, H. W. and E. R. Hedeman, Solar Terrestrial Physics/1970 Part I, edited by C. DeJager, pp. 151–172, D. Reidel, Holland, 1972.

  10. Harwood, J. M. and S. R. C. Malin, Sunspot cycle influence on the geomagnetic field, Geophys. J. R. Astr. Soc., 50, 605–619, 1977.

  11. Hathaway, D. H., R. M. Wilson, and E. J. Reichmann, The shape of the sunspot cycle, Solar Physics, 151, 177–190, 1994.

  12. Jinno, K., S. Xu, R. Berndtsson, A. Kawamura, and M. Matsumoto, Prediction of sunspots using reconstructed chaotic system equations, J. Geophys. Res., 100, 14773–14781, 1995.

  13. Kane, R. P. and N. B. Trivedi, Periodicities in sunspot numbers, J. Geomag. Geoelectr., 37, 1071–1085, 1985.

  14. Keppenne, C. L. and M. Ghil, Adaptive filtering and prediction of the southern oscillation index, J. Geophys. Res., 97, 20449–20454, 1992.

  15. Kurths, J. and A. A. Ruzmaikin, On forecasting sunspot numbers, Solar Physics, 126, 407–410, 1990.

  16. MacDonald, G. J., Spectral analysis of time series generated by non linear process, Rev. Geophys. Space Phys., 27, 449–469, 1989.

  17. Marple, S. L., Jr., Digital Spectral Analysis with Applications, pp. 232–236, Prentice Hall, New Jersey, 1987.

  18. McKinnon, J. A., Sunspot numbers 1610–1985 UAG Rep. 95, pp. 112, NOAA Boulder, Colorado, U.S.A., 1987.

  19. Mundt, M. D., W. B. Maguire, II, and R. R. P. Chase, Chaos in the sunspot cycle: Analysis and prediction, J. Geophys. Res., 96, 1705–1716, 1991.

  20. Pasricha, P. K., S. Aggarwal, and B. M. Reddy, Model evaluation of the year-to-year variability in a 11-year sunspot cycle, Ann. Geophys., 9, 696–702, 1991.

  21. Penland, C., M. Ghil, and K. M. Weickmann, Adaptive filtering and maximum entropy spectra with application to changes in atmospheric angular momentum, J. Geophys. Res., 96, 22659–22671, 1991.

  22. Rabin, D., R. M. Wilson, and R. L. Moore, Bimodality of the solar cycle, Geophys. Res. Lett., 13, 352–354, 1986.

  23. Sneyers, R. and P. Cugnon, On the predictability of the Wolfe sunspot number, Ann. Geophys., 4, 81–86, 1986.

  24. Sonett, C. P., Sunspot time series spectrum from square land modulation of the Hale cycle, Geophys. Res. Lett., 9, 1313–1316, 1982.

  25. Ulrych, T. J. and T. N. Bishop, Maximum entropy spectral analysis and autoregressive decomposition, Rev. Geophys. Space Phys., 13, 183–200, 1975.

  26. Vautard, R., P. Yiou, and M. Ghil, Singular spectrum analysis: a toolkit for short, noisy chaotic signal, Physica, D58, 95–126, 1992.

  27. Wilson, R. M., Predicting the maximum amplitude for the sunspot cycle from the rate of rise in sunspot number, Solar Physics, 117, 179–186, 1988.

  28. Wilson, R. M., Predicting the maximum sunspot number: a comparative study between single variate and bivariate precursor techniques, Solar Physics, 125, 143–145, 1990a.

  29. Wilson, R. M., On the average rate of growth in sunspot number and the size of the solar cycle, Solar Physics, 125, 133–141, 1990b.

  30. Wilson, R. M., An early estimate for the size of cycle 23, Solar Physics, 140, 181–193, 1992.

  31. Yule, G. U., On a method for investigating periodicites in disturbed series with special reference to Wolfe’s sunspot number, Phil. Trans. R. Soc. London A, 226, 267–298, 1927.

Download references

Author information



Corresponding author

Correspondence to G. K. Rangarajan.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Rangarajan, G.K. Sunspot variability and an attempt to predict solar cycle 23 by adaptive filtering. Earth Planet Sp 50, 91–100 (1998).

Download citation


  • Solar Activity
  • Solar Cycle
  • Sunspot Number
  • Maximum Entropy Method
  • Solar Physic