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Global temperatures and sunspot numbers. Are they related?

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  • Gil-Alana, Luis A.
  • Yaya, OlaOluwa S.
  • Shittu, Olanrewaju I.

Abstract

This paper deals with the analysis of global temperatures and sunspot numbers and the relationship between the two. We use techniques based on the concept of long range dependence. For the temperatures, the best specification seems to be a fractionally integrated or I(d) model with an order of integration d of about 0.46 and an estimated time trend coefficient that suggests that temperatures have increased by about 0.57 °C over the last one hundred years. However, for the sunspot numbers, a cyclical fractional model seems to be more appropriate, with a periodicity of 11 years per cycle and an order of integration of about 0.40. Thus, the two series display long memory and fractional integration. However, the fact that both series display poles in the spectrum at different frequencies implies that we fail to reject the null hypothesis of no relationship between the two variables in the long run. Moreover, assuming that the sunspots are exogenous, the results show no statistical significance of this variable on the global temperatures, which is one of the main contributions of the present work.

Suggested Citation

  • Gil-Alana, Luis A. & Yaya, OlaOluwa S. & Shittu, Olanrewaju I., 2014. "Global temperatures and sunspot numbers. Are they related?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 396(C), pages 42-50.
    • Handle: RePEc:eee:phsmap:v:396:y:2014:i:c:p:42-50
    DOI: 10.1016/j.physa.2013.10.043
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    References listed on IDEAS

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    1. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
    2. L. A. Gil‐Alana, 2001. "Testing Stochastic Cycles in Macroeconomic Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(4), pages 411-430, July.
    3. Violetta Dalla & Javier Hidalgo, 2005. "A Parametric Bootstrap Test for Cycles," STICERD - Econometrics Paper Series 486, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    4. Granger, Clive W. J. & Hyung, Namwon, 2004. "Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 399-421, June.
    5. Dalla, Violetta & Hidalgo, Javier, 2005. "A parametric bootstrap test for cycles," LSE Research Online Documents on Economics 6829, London School of Economics and Political Science, LSE Library.
    6. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    7. Dalla, Violetta & Hidalgo, Javier, 2005. "A parametric bootstrap test for cycles," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 219-261.
    8. Chung, Ching-Fan, 1996. "Estimating a generalized long memory process," Journal of Econometrics, Elsevier, vol. 73(1), pages 237-259, July.
    9. Luis A. Gil-Alana, 2009. "Time series modelling of sunspot numbers using long range cyclical dependence," Faculty Working Papers 06/09, School of Economics and Business Administration, University of Navarra.
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    Cited by:

    1. Rangan Gupta & Luis A. Gil-Alana & Olaoluwa S. Yaya, 2015. "Do sunspot numbers cause global temperatures? Evidence from a frequency domain causality test," Applied Economics, Taylor & Francis Journals, vol. 47(8), pages 798-808, February.
    2. Hassani, Hossein & Huang, Xu & Gupta, Rangan & Ghodsi, Mansi, 2016. "Does sunspot numbers cause global temperatures? A reconsideration using non-parametric causality tests," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 54-65.
    3. Kristoufek, Ladislav, 2017. "Has global warming modified the relationship between sunspot numbers and global temperatures?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 351-358.
    4. Baker, Robert G.V., 2017. "The Sun–Earth connect 2: Modelling patterns of a fractal Sun in time and space using the fine structure constant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 508-531.
    5. Baker, Robert G.V., 2016. "The Sun–Earth connect 1: A fractional d-matrix of solar emissions compared to spectral analysis evidence of solar measurements and climate proxies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 235-258.

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