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A Two-Stage Multi-Agent System to Predict the Unsmoothed Monthly Sunspot Numbers
Authors: Mak Kaboudan
Abstract:A multi-agent system is developed here to predict monthly details of the upcoming peak of the 24th solar magnetic cycle. While studies typically predict the timing and magnitude of cycle peaks using annual data, this one utilizes the unsmoothed monthly sunspot number instead. Monthly numbers display more pronounced fluctuations during periods of strong solar magnetic activity than the annual sunspot numbers. Because strong magnetic activities may cause significant economic damages, predicting monthly variations should provide different and perhaps helpful information for decision-making purposes. The multi-agent system developed here operates in two stages. In the first, it produces twelve predictions of the monthly numbers. In the second, it uses those predictions to deliver a final forecast. Acting as expert agents, genetic programming and neural networks produce the twelve fits and forecasts as well as the final forecast. According to the results obtained, the next peak is predicted to be 156 and is expected to occur in October 2011- with an average of 136 for that year.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1070013Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 985
 K. Schatten, P. Scherrer, L. Svalgaard, and J. Wilcox, "Using the dynamo theory to predict the sunspot number during solar cycle 21," Geophysics Research Letters, vol. 5, 1978, pp. 411-414.
 M. Gabr, and S. Rao, "The estimation and prediction of subset bilinear time series with applications," Journal of Time Series Analysis, vol. 2, 1981, pp. 155-171.
 H. Tong, Nonlinear Time Series Analysis: A Dynamical System Approach. Oxford University Press: Oxford, 1990.
 H. Tong, S. Lim, "Threshold autoregressive, limit cycles and cyclical data," Journal of the Royal Statistical Society B, vol. 42, 1990, pp. 245- 292.
 A. Weigend, B. Huberman, and D. Rumelhart, "Predicting the future: a connectionist approach," International Journal of Neural Systems, vol. 1, 1990, pp. 193-209.
 A. Dmitriev, Y. Minaeva, Y. Orlov, M. Riazantseva, and I. Veselovsky, "Solar activity forecasting on 1999-2000 by means of artificial neural networks," Reported on EGS XXIV General Assembly, 22 April 1999, The Hague, The Netherlands, http://dbserv.sinp.msu.ru/ RSWI/sun.pdf.
 L. Svalgaard, E. Cliver, and Y. Kamide, "Sunspot cycle 24: Smallest cycle in 100 years?" Geophysical Research Letters, vol. 32, L01104, 2005, pp. 1-4.
 H. Lundstedt, L. Liszka, R. Lundin, and R. Muscheler, "Long-term solar activity explored with wavelet methods," Annales Geophysicae, vol. 24, 2006, pp. 769-778.
 R. Wilson, D. Hathaway, and E. Reichmann, "On the correlation between maximum amplitude and smoothed monthly mean sunspot number during the rise of the cycle (from t=0-48 months past sunspot minimum)," National Aeronautics and Space Administration, Technical Publications NASA/TP-1998-208591.
 S. Sell, "Time series forecasting: A multivariate stochastic approach," 1999. Available: http://arxiv.org/PS_cache/physics/pdf/9901/9901050 v2.pdf.
 D. Hathaway, R. Wilson, and E. Reichmann, "A synthesis of solar cycle prediction techniques," Journal of Geophysical Research, 104, 1999, pp. 22375-22388.
 D. Hathaway, R. Wilson, and E. Reichmann, "Group sunspot numbers: Sunspot cycle characteristics," Solar Physics, vol. 151, 2002, p. 177.
 R. Wilson, and D. Hathaway, "Gauging the nearness and size of cycle maximum," National Aeronautics and Space Administration, Technical Publications NASA/TP-2003-212927.
 NOAA. Available: ftp://ftp.ngdc.noaa.gov/stp/solar_data/sunspot_ numbers/smoothed.
 W. Pesnell, "Predictions of solar cycle 24," NASA, Goddard Space Flight Center, Greenbelt, Maryland. http://www.swpc.noaa.gov/ SolarCycle/SC24/May_24_2007_table.pdf.
 D. Nordemann, "Sunspot number time series: Exponential fitting and solar behavior," Solar Physics, vol. 141, 1992, pp. 199-202.
 T. Lin, and M. Pourahmadi, "Nonparametric and non-linear models and data mining in time series: A case-study on the Canadian lynx data," Applied Statistics, vol. 47, Part 2, 1998, pp. 187-201.
 T. Xu, J. Wu, Z. Wu, and Q. Li, "Long-term sunspot number prediction based on EMD analysis and AR model" Chinese Journal of Astronomy and Astrophysics, vol. 8, 2008, pp.337-342.
 National Geographic Data Center. Available: ftp://ftp.ngdc.noaa.gov/ stp/solar_data/ solar_radio/sunspot_numbers/monthly.
 A. Aussem, and F. Murtagh, "Combining neural network forecasts on wavelet-transformed time series," Connection Science, vol. 9, 1997, pp. 113-121.
 M. Kaboudan, "Extended daily exchange rates forecasts using wavelet temporal resolutions," New Mathematics and Natural Computing, vol. 1, 2005, pp. 79-107.
 M. Kaboudan, "Computational forecasting of wavelet-converted monthly sunspot numbers," Journal of Applied Statistics, vol. 33, 2006, pp. 925-941.
 M. Kaboudan, "Forecasting solar cycles with GP," in Proceedings of Neural, Parallel & Scientific Computations, 2002, ISDA, A. Abraham, N. Baikunth, M. Sambandham, and P. Saratchandran, Atlanta GA.
 A. Orfila, J. Ballester, R. Oliver, A. Alvarez, and J. Tintoré, "Forecasting the solar cycle with genetic algorithms," Astronomy and Astrophysics, vol. 386, 2002, pp. 313-318.
 H. Kwasnicka, and E. Szpunar-Huk, "Genetic programming in data modeling," in Genetic Systems Programming: Theory and Experience, N. Nedjah, and A. Abraham, Springer Berlin / Heidelberg, 2006, pp. 105-130.
 R. Jagielski, "Genetic programming prediction of solar activity, intelligent data engineering and automated learning ÔÇö IDEAL 2000," Data Mining, Financial Engineering, and Intelligent Agents, Lecture Notes in Computer Science, 2008, pp. 191-210.
 S. Eklund, "Time series forecasting using massively parallel genetic programming," Proceedings, Parallel and Distributed Processing Symposium 2003, pp. 22-26.
 X. Li, C. Cheng, W. Wang, and F. Yang, "A study on sunspot number time series prediction using quantum neural networks," Proceedings of the 2008 Second International Conference on Genetic and Evolutionary Computing, 2008, pp. 480-483.
 J. Kyngas, "Forecasting sunspot numbers with neural networks," Report A-1995-1, University of Joensuu, Department of Computer Science, Report Series A. Available: ftp://ftp.cs.joensuu.fi/pub /Reports/A-1995- 1.ps.
 P. Frick, D. Galyagin, D. Hoyt, E. Nesme-Ribes, K. Schatten, D. Sokoloff, and V. Zakharov, "Wavelet analysis of solar activity recorded by sunspot groups," Astronomy and Astrophysics, vol. 328, 1997, pp. 670-681.
 P. Kumar, and E. Foufoula-Georgiou, "Wavelet analysis for geophysical applications, Reviews of Geophysics, vol. 35, 1997, pp. 385-412.
 F. Boberg, H. Lundstedt, J. Hoeksema, P. Scherrer, and W. Lui, "Solar mean magnetic field variability: A wavelet approach to WSO and SOHO/MDI observations," Journal of Geophysical Research, vol. 107, 2002, pp. 15-1 - 15-7.
 H. Lundstedt, L. Liszka, and R. Lundin, "Solar Activity explored with new wavelet methods," Annales Geophysicae, vol. 23, 2005, pp. 1505- 1511.
 J. Koza, Genetic Programming. Cambridge, MA: The MIT Press, 1992.
 M. Kaboudan, "Statistical properties of fitted residuals from genetically evolved models," Journal of Economic Dynamics and Control, vol. 25, 2001, pp. 1719-1749.
 M. Kaboudan, "TSGP: A Time Series Genetic Programming Software." Available: http://Bulldog2.Redlands. edu/fac/mak_kaboudan.
 J. Principe, N. Euliano, and C. Lefebvre, Neural and Adaptive Systems: Fundamentals Through Simulations. New York: John Wiley & Sons, 2003.
 NeuroSolutionsTM. The Neural Network Simulation Environment. Version 4, NeuroDimensions, Inc.: Gainesville, FL, 2002.
 S. Mallat, "A theory for multiresolution signal decomposition: The wavelet representation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, 1989, pp. 674-1989.
 A. Bruce, H. Gao, Applied Wavelet Analysis with S-Plus. New York: Springer, 1996.
 J. Walker, A Primer on Wavelets and Their Scientific Applications. Boca Raton: Chapman & Hall/CR, 1999.
 R. Gen├ºay, F. Sel├ºuk, and B. Whitcher, An Introduction to Wavelets and Other Filtering Methods in Finance and Economics. San Diego, CA: Academic Press, 2002.
 T. Masters, Neural, Novel and Hybrid Algorithms for Time Series Prediction. New York: John Wiley & Sons, 1995.
 R. Pindyck R, and D. Rubinfeld, Econometric Models and Economic Forecasting. Boston: Irwin McGraw-Hill, 1998.