Abstract
The sunspot record of solar magnetic activity is studied as a nonstationary time series by means of a previously developed algorithm for treating perturbed dynamical systems. This approach incorporates secular changes into the modeling process through an external driving parameter, whose temporal behavior is shown to correspond in this case to the long-term trend of the sunspot record. Our method is able to reduce by approximately 13% the prediction error of this series when compared to the standard stationary approach. Such a reduction is remarkable in view of the benchmark status of the sunspot record in the statistical literature and, moreover, the fact that this gain is obtained over the performance of an already very competitive modeling technique based on ensembles of artificial neural networks.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Calvo, R. A., Piacentini, R. D., and Ceccatto, H. A.: 1995, Astrophys. J. 444, 916.
Choudhuri, A. R.: 1992, Astron. Astrophys. 253, 277.
Christensen-Dalsgaard, J., Dappen, W., Ajukov, S. V., Anderson, E. R., Antia, H. M., Basu, S., Baturin, V. A., Berthomieu, G., Chaboyer, B., Chitre, S. M., Cox, A. N., Demarque, P., Donatowicz, J., Dziembowski, W. A., Gabriel, M., Gough, D. O., Guenther, A. G., Guzik, J. A., Harvey, J. W., Hill, F., Houdek, G., Iglesias, C. A., Kosovichev, E. J., Leibacher, J. W., Morel, P., Proffitt, C. R., Provost, J., Reiter, J., Rhodes, E. J., Rogers, F. J., Roxburgh, I. W., Thompson, M. J., and Ulrich, R. K.: 1996, Science 272, 1286.
García, A. and Mouradian, Z.: 1998, Solar Phys. 180, 495.
Gleissberg, W.: 1971, Solar Phys. 21, 240.
Granitto, P. M., Verdes, P. F., Navone, H. D., and Ceccatto, H. A.: 2001, Int. J. Neur. Sys. 11, 305.
Hoyt, D. V. and Schatten, K. H.: 1998, Solar Phys. 181, 491.
Knobloch, E. and Landsberg, A. S.: 1996, Monthly Notices Royal Astron. Soc. 278, 294.
Lockwood, M., Stamper, R., and Wild, M. N.: 1999, Nature (London) 399, 437.
Maunder, E. W.: 1922, Brit. Astron. Assoc. J. 32, 140.
Mininni, P. D., Gómez, D. O., and Mindlin, G. B.: 2000, Phys. Rev. Lett. 85, 5476.
Mininni, P. D., Gómez, D. O., and Mindlin, G. B.: 2002, Phys. Rev. Lett. 89, 061101.
Naftaly, U., Intrator, N., and Horn, D.: 1997, Network: Comput. Neur. Systems 8, 283.
Pi, H. and Peterson, C.: 1994, Neur. Comput. 6, 509.
Priest, E. R.: 1984, Solar Magnetohydrodynamics, D. Reidel Publ. Co. Dordrecht, Holland.
Schwabe, H.: 1843, Astron. Nachr. 20, 495.
Sharkey, A. J. C. (ed.): 1999, Combining Artificial Neural Nets: Ensemble and Modular Multi-Net Systems, Perspectives in Neural Computing, Springer-Verlag, Berlin.
Solanki, S. K., Schüssler, M., and Fligge, M.: 2000, Nature (London) 408, 445.
Solanki, S. K., Schüssler, M., and Fligge, M.: 2002, Astron. Astrophys. 383, 706.
Usoskin, I. G. and Mursula, K.: 2003, Solar Phys. 218, 319.
Usoskin, I. G., Solanki, S. K., Schüssler, M., Mursula, K., and Alanko, K.: 2003, Phys. Rev. Lett. 91, 211101.
Verdes, P. F., Granitto, P. M., Navone, H. D., and Ceccatto, H. A.: 2001, Phys. Rev. Lett. 87, 124101.
Weigend, A. and Gershenfeld, N. A. (eds.): 1994, ‘Time Series Prediction: Forecasting the Future and Understanding the Past’, Vol. XV of Santa Fe Institute Studies in the Science of Complexity, Addison-Wesley, New York.
Wolf, R.: 1852, Acad. Sci. Compt. Rend. 35, 704.
Yule, G. U.: 1927, Phil. Trans. R. Soc. London A226, 267.
Zeldovich, Y. B. and Ruzmaikin, A. A.: 1990, Magnetic Fields in Astrophysics, Gordon and Breach, New York
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Verdes, P., Granitto, P. & Ceccatto, H. Secular Behavior of Solar Magnetic Activity: Nonstationary Time-Series Analysis of the Sunspot Record. Solar Physics 221, 167–177 (2004). https://doi.org/10.1023/B:SOLA.0000033361.20655.ed
Issue Date:
DOI: https://doi.org/10.1023/B:SOLA.0000033361.20655.ed