A Two-Stage Multi-Agent System to Predict the Unsmoothed Monthly Sunspot Numbers
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.
[1] 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.
[2] 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.
[3] H. Tong, Nonlinear Time Series Analysis: A Dynamical System
Approach. Oxford University Press: Oxford, 1990.
[4] H. Tong, S. Lim, "Threshold autoregressive, limit cycles and cyclical
data," Journal of the Royal Statistical Society B, vol. 42, 1990, pp. 245-
292.
[5] A. Weigend, B. Huberman, and D. Rumelhart, "Predicting the future: a
connectionist approach," International Journal of Neural Systems, vol.
1, 1990, pp. 193-209.
[6] 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.
[7] 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.
[8] 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.
[9] 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.
[10] S. Sell, "Time series forecasting: A multivariate stochastic approach,"
1999. Available: http://arxiv.org/PS_cache/physics/pdf/9901/9901050
v2.pdf.
[11] D. Hathaway, R. Wilson, and E. Reichmann, "A synthesis of solar cycle
prediction techniques," Journal of Geophysical Research, 104, 1999,
pp. 22375-22388.
[12] D. Hathaway, R. Wilson, and E. Reichmann, "Group sunspot numbers:
Sunspot cycle characteristics," Solar Physics, vol. 151, 2002, p. 177.
[13] R. Wilson, and D. Hathaway, "Gauging the nearness and size of cycle
maximum," National Aeronautics and Space Administration, Technical
Publications NASA/TP-2003-212927.
[14] NOAA. Available: ftp://ftp.ngdc.noaa.gov/stp/solar_data/sunspot_
numbers/smoothed.
[15] 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.
[16] D. Nordemann, "Sunspot number time series: Exponential fitting and
solar behavior," Solar Physics, vol. 141, 1992, pp. 199-202.
[17] 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.
[18] 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.
[19] National Geographic Data Center. Available: ftp://ftp.ngdc.noaa.gov/
stp/solar_data/ solar_radio/sunspot_numbers/monthly.
[20] A. Aussem, and F. Murtagh, "Combining neural network forecasts on
wavelet-transformed time series," Connection Science, vol. 9, 1997, pp.
113-121.
[21] M. Kaboudan, "Extended daily exchange rates forecasts using wavelet
temporal resolutions," New Mathematics and Natural Computing, vol.
1, 2005, pp. 79-107.
[22] M. Kaboudan, "Computational forecasting of wavelet-converted
monthly sunspot numbers," Journal of Applied Statistics, vol. 33, 2006,
pp. 925-941.
[23] 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.
[24] 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.
[25] 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.
[26] 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.
[27] S. Eklund, "Time series forecasting using massively parallel genetic
programming," Proceedings, Parallel and Distributed Processing
Symposium 2003, pp. 22-26.
[28] 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.
[29] 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.
[30] 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.
[31] P. Kumar, and E. Foufoula-Georgiou, "Wavelet analysis for geophysical
applications, Reviews of Geophysics, vol. 35, 1997, pp. 385-412.
[32] 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.
[33] H. Lundstedt, L. Liszka, and R. Lundin, "Solar Activity explored with
new wavelet methods," Annales Geophysicae, vol. 23, 2005, pp. 1505-
1511.
[34] J. Koza, Genetic Programming. Cambridge, MA: The MIT Press, 1992.
[35] M. Kaboudan, "Statistical properties of fitted residuals from genetically
evolved models," Journal of Economic Dynamics and Control, vol. 25,
2001, pp. 1719-1749.
[36] M. Kaboudan, "TSGP: A Time Series Genetic Programming Software."
Available: http://Bulldog2.Redlands. edu/fac/mak_kaboudan.
[37] J. Principe, N. Euliano, and C. Lefebvre, Neural and Adaptive Systems:
Fundamentals Through Simulations. New York: John Wiley & Sons,
2003.
[38] NeuroSolutionsTM. The Neural Network Simulation Environment.
Version 4, NeuroDimensions, Inc.: Gainesville, FL, 2002.
[39] 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.
[40] A. Bruce, H. Gao, Applied Wavelet Analysis with S-Plus. New York:
Springer, 1996.
[41] J. Walker, A Primer on Wavelets and Their Scientific Applications.
Boca Raton: Chapman & Hall/CR, 1999.
[42] R. Gençay, F. Selçuk, and B. Whitcher, An Introduction to Wavelets
and Other Filtering Methods in Finance and Economics. San Diego,
CA: Academic Press, 2002.
[43] T. Masters, Neural, Novel and Hybrid Algorithms for Time Series
Prediction. New York: John Wiley & Sons, 1995.
[44] R. Pindyck R, and D. Rubinfeld, Econometric Models and Economic
Forecasting. Boston: Irwin McGraw-Hill, 1998.
[1] 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.
[2] 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.
[3] H. Tong, Nonlinear Time Series Analysis: A Dynamical System
Approach. Oxford University Press: Oxford, 1990.
[4] H. Tong, S. Lim, "Threshold autoregressive, limit cycles and cyclical
data," Journal of the Royal Statistical Society B, vol. 42, 1990, pp. 245-
292.
[5] A. Weigend, B. Huberman, and D. Rumelhart, "Predicting the future: a
connectionist approach," International Journal of Neural Systems, vol.
1, 1990, pp. 193-209.
[6] 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.
[7] 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.
[8] 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.
[9] 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.
[10] S. Sell, "Time series forecasting: A multivariate stochastic approach,"
1999. Available: http://arxiv.org/PS_cache/physics/pdf/9901/9901050
v2.pdf.
[11] D. Hathaway, R. Wilson, and E. Reichmann, "A synthesis of solar cycle
prediction techniques," Journal of Geophysical Research, 104, 1999,
pp. 22375-22388.
[12] D. Hathaway, R. Wilson, and E. Reichmann, "Group sunspot numbers:
Sunspot cycle characteristics," Solar Physics, vol. 151, 2002, p. 177.
[13] R. Wilson, and D. Hathaway, "Gauging the nearness and size of cycle
maximum," National Aeronautics and Space Administration, Technical
Publications NASA/TP-2003-212927.
[14] NOAA. Available: ftp://ftp.ngdc.noaa.gov/stp/solar_data/sunspot_
numbers/smoothed.
[15] 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.
[16] D. Nordemann, "Sunspot number time series: Exponential fitting and
solar behavior," Solar Physics, vol. 141, 1992, pp. 199-202.
[17] 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.
[18] 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.
[19] National Geographic Data Center. Available: ftp://ftp.ngdc.noaa.gov/
stp/solar_data/ solar_radio/sunspot_numbers/monthly.
[20] A. Aussem, and F. Murtagh, "Combining neural network forecasts on
wavelet-transformed time series," Connection Science, vol. 9, 1997, pp.
113-121.
[21] M. Kaboudan, "Extended daily exchange rates forecasts using wavelet
temporal resolutions," New Mathematics and Natural Computing, vol.
1, 2005, pp. 79-107.
[22] M. Kaboudan, "Computational forecasting of wavelet-converted
monthly sunspot numbers," Journal of Applied Statistics, vol. 33, 2006,
pp. 925-941.
[23] 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.
[24] 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.
[25] 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.
[26] 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.
[27] S. Eklund, "Time series forecasting using massively parallel genetic
programming," Proceedings, Parallel and Distributed Processing
Symposium 2003, pp. 22-26.
[28] 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.
[29] 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.
[30] 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.
[31] P. Kumar, and E. Foufoula-Georgiou, "Wavelet analysis for geophysical
applications, Reviews of Geophysics, vol. 35, 1997, pp. 385-412.
[32] 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.
[33] H. Lundstedt, L. Liszka, and R. Lundin, "Solar Activity explored with
new wavelet methods," Annales Geophysicae, vol. 23, 2005, pp. 1505-
1511.
[34] J. Koza, Genetic Programming. Cambridge, MA: The MIT Press, 1992.
[35] M. Kaboudan, "Statistical properties of fitted residuals from genetically
evolved models," Journal of Economic Dynamics and Control, vol. 25,
2001, pp. 1719-1749.
[36] M. Kaboudan, "TSGP: A Time Series Genetic Programming Software."
Available: http://Bulldog2.Redlands. edu/fac/mak_kaboudan.
[37] J. Principe, N. Euliano, and C. Lefebvre, Neural and Adaptive Systems:
Fundamentals Through Simulations. New York: John Wiley & Sons,
2003.
[38] NeuroSolutionsTM. The Neural Network Simulation Environment.
Version 4, NeuroDimensions, Inc.: Gainesville, FL, 2002.
[39] 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.
[40] A. Bruce, H. Gao, Applied Wavelet Analysis with S-Plus. New York:
Springer, 1996.
[41] J. Walker, A Primer on Wavelets and Their Scientific Applications.
Boca Raton: Chapman & Hall/CR, 1999.
[42] R. Gençay, F. Selçuk, and B. Whitcher, An Introduction to Wavelets
and Other Filtering Methods in Finance and Economics. San Diego,
CA: Academic Press, 2002.
[43] T. Masters, Neural, Novel and Hybrid Algorithms for Time Series
Prediction. New York: John Wiley & Sons, 1995.
[44] R. Pindyck R, and D. Rubinfeld, Econometric Models and Economic
Forecasting. Boston: Irwin McGraw-Hill, 1998.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:57051", author = "Mak Kaboudan", title = "A Two-Stage Multi-Agent System to Predict the Unsmoothed Monthly Sunspot Numbers", 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.", keywords = "Computational techniques, discrete wavelet transformations, solar cycle prediction, sunspot numbers.", volume = "3", number = "9", pages = "647-8", }
