Skip to main content

Multi-step prediction of Dst index using singular spectrum analysis and locally linear neurofuzzy modeling


Even one-step prediction of natural time series without delay especially in main phase of storm is difficult for many complicated time series such as Dst index. In this study, with a new method based on singular spectrum analysis, we extract the main components of the time series, model each component with a locally linear neurofuzzy network, and utilize the trained networks for multi-step ahead prediction of a validation set of data, and finally combine the predicted patterns for construction of general prediction. Our methods are compared with several previous studies for Dst index prediction. Several solar geomagnetic extreme events are predicted well with our state-of-the-art method; such as extreme events in 14 March 1989 that led to power black-out in Quebec, as well as other extreme storms.


  • Baker, D. N., Statistical analysis in the study of solar wind magnetosphere coupling, in Solar Wind-Magnetosphere Coupling, edited by Y. Kamide and J. A. Slavin, p. 17, Terra Sci., Tokyo, 1986.

    Chapter  Google Scholar 

  • Burton, R. K., R. L. C. T. Russell, An empirical relationship between interplanetary conditions and Dst, J. Geophys. Res., 80, 4204–4214, 1975.

    Article  Google Scholar 

  • Campbell, W., Geomagnetic storms, the Dst ring-current myth and lognormal distributions, J. Aymospheric and Solar Terrestrial Physics, 58(10), 1171–1187, July 1996.

    Article  Google Scholar 

  • Detman, T. R. and D. Vassiliadis, Review of techniques for magnetic storm forecasting, in Magnetic Storms, Geophys. Monogr. Ser., vol. 98, edited by B. T. Tsurutani, W. D. Gonzalez, Y. Kamide, and J. K. Arballo, p. 253, AGU, Washington D.C., 1997.

    Google Scholar 

  • Fenrich, F. R. and J. G. Luhmann, Geomagnetic response to magnetic clouds of different polarity, Geophys. Res. Lett., 25, 2999–3002, 1998.

    Article  Google Scholar 

  • Freeman, J., A. Nagai, P. Reiff, W. Denig, S. Gussenhoven Shea, M. Heinermann, F. Rich, and M. Hairston, The use of neural networks to predict magnetospheric parameters for input to a magnetospheric forecast model, in Artificial Intelligence Applications in Solar Terrestrial Physics, edited by J. Joselyn, H. Lundstedt, and Trollinger, 167, Natl. Oceanic and Atmos. Admin., Boulder, Colorado, 1994.

    Google Scholar 

  • Gleisner, H., H. Lundstedt, and P. Wintoft, Predicting geomagnetic storms from solar-wind data using time-delay neural networks, Ann. Geophys., 14, 679–686, 1996.

    Article  Google Scholar 

  • Gholipour, A., C. M. Shafiee, and B. N. Araabi, Extracting the main patterns of natural time series for long term prediction, J. Aymospheric and Solar Terrestrial Physics, 67(6), 595–603, 2005.

    Article  Google Scholar 

  • Iyemori, T., H. Maeda, and T. Kamei, Impulse response of geomagnetic indices to interplanetary magnetic fields, J. Geomag. Geoelectr., 31(1), 1979.

  • Joselyn, J. A., Geomagnetic activity forecasting: The state of the art, Rev. Geophys., 33, 383, 1995.

    Article  Google Scholar 

  • Kamide, Y., W. Baumjohann, I. A. Daglis, W. D. Gonzalez, M. Grande, J. A. Joselyn, R. L. McPherron, J. L. Phillips, E. G. D. Reeves, G. Rostoker, A. S. Sharma, H. J. Singer, B. T. Tsurutani, and V. M. Vasyliunas, Current understanding of magnetic storms: Storm-substorm relationships, J. Geophys. Res., 103, 17705–17728, 1998.

    Article  Google Scholar 

  • Kugblenu, S., S. Taguchi, and T. Okuzawa, Prediction of the geomagnetic storm associated Dst index using an artificial neural network algorithm, Earth Planets Space, 51, 307–313, 1999.

    Article  Google Scholar 

  • Loskutov, A., I. A. Istomin, K. M. Kuzanyan, and O. L. Kotlyarov, Testing and forecasting the time series of the solar activity by singular spectrum analysis, Nonlin. Phenomena in Complex Syst., 4(1), 47–57, 2001a.

    Google Scholar 

  • Loskutov, A., I. Istomin, O. Kotlyarov, and K. Kuzanyan, A study of the regularities in Solar magnetic activity by singular spectrum analysis, Astronomy Letters, 27(11), 745–753, 2001b.

    Article  Google Scholar 

  • Loskutov, A., I. Istomin, and O. Kotlyarov, Data analysis: generalizations of the local approximation method by singular spectrum analysis,

  • Munsami, V., Determination of the effects of substorms on the storm-time ring current using neural networks, J. Geophys. Res., 105, 27833, 2000.

    Article  Google Scholar 

  • Nagatsuma, T., Geomagnetic Storms, Journal of the Communications Research Laboratory, 49(3), 2002.

  • Nelles, O., Nonlinear System Identification with Local Linear Neuro-Fuzzy Models, PhD Thesis, TU Darmstadt, Shaker Verlag, Aachen, Germany, 1999.

    Google Scholar 

  • Nelles, O., Nonlinear system identification, Springer Verlag, Berlin, 2001.

    Book  Google Scholar 

  • O’Brien, T. P. and R. L. McPherron, An empirical phase space analysis of ring current dynamics: solar wind control of injection and decay, J. Geophys. Res., 105, 7707–7719, 2000a.

    Article  Google Scholar 

  • O’Brien, T. P. and R. L. McPherron, Forecasting the ring current index Dst in real time, J. Atmospheric and Solar-Terrestrial Physics, 62, 1295–1299, 2000b.

    Article  Google Scholar 

  • Temerin, M. and X. Li, A New Model for the Prediction of Dst on the Basis of the Solar Wind, J. Geophs. Res., 107(A12), 1472, doi:10.1029/2001JA007532, 2002.

    Article  Google Scholar 

  • Vassiliadis, D., A. J. Klimas, D. N. Baker, and D. A. Roberts, A description of the solar wind magnetosphere coupling based on nonlinear prediction filters, J. Geophys. Res., 100, 3495, 1995.

    Article  Google Scholar 

  • Vassiliadis, D., A. J. Klimas, and D. N. Baker, Models of Dst Geomagnetic Activity and of its Coupling to Solar Wind Parameters, Phys. Chem. Earth (C), 24(1-3), 107–I12, 1999.

    Google Scholar 

  • Vautard, R., P. Yiou, and M. Ghil, Singular spectrum analysis: A toolkit for short noisy chaotic signals, Physica D, 58, 95–126, 1992.

    Article  Google Scholar 

  • Watanabe, S., E. Sagawa, K. Ohtaka, and H. Shimazu, Prediction of the Dst index from solar wind parameters by a neural network method, J. Communications Research Laboratory, 49(4), 2002.

  • Wintoft, P., Space weather physics—Prediction and classification of solar wind structures and geomagnetic activity using artificial neural networks, PhD Thesis, LUNFD6/(NFAS 1017)/1-86/(1997), 1997.

    Google Scholar 

  • Wintoft, P. and H. Lundstedt, Identification of geoeffective solar wind structures with self-organized maps, AI Applications in Solar-Terrestrial Physics, Lund, Sweden, July 29–31, 1997, edited by I. Sandahl and E. Jonsson, ESA WPP-148, 151–157, 1998.

    Google Scholar 

  • Wu, J.-G., H. Lundstedt, P. Wintoft, and T. R. Detman, Space weather forecasting on the 1997 January halo CME event using neural network models, AI Applications in Solar-Terrestrial Physics, Lund, Sweden, July 29–31, 1997, edited by I. Sandahl and E. Jonsson, ESA WPP-148, 145–150, 1998a.

    Google Scholar 

  • Wu, J.-G., H. Lundstedt, P. Wintoft, and T. R. Detman, Neural network models predicting the magnetospheric response to the 1997 January halo-CME event, Geophys. Res. Lett., 25, 3,031–3,034, 1998b.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Javad Sharifi.

Rights and permissions

Open Access  This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit

Reprints and Permissions

About this article

Cite this article

Sharifi, J., Araabi, B.N. & Lucas, C. Multi-step prediction of Dst index using singular spectrum analysis and locally linear neurofuzzy modeling. Earth Planet Sp 58, 331–341 (2006).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

Key words

  • Singular spectral analysis
  • locally linear neurofuzzy model
  • Dst prediction