Do sunspot numbers cause global temperatures? Evidence from a frequency domain causality test

Abstract

This article applies the causality test in the frequency domain, developed by Breitung and Candelon (2006), to analyse whether sunspot numbers (used as a partial approximation to solar irradiance) cause global temperatures, using monthly data covering the time period 1880:1–2013:9. While standard time domain Granger causality test fails to reject the null hypothesis that sunspot numbers do not cause global temperatures for both full and sub-samples (identified based on tests of structural breaks), the frequency domain causality test detects predictability for both the full-sample and the last sub-sample at short (2–2.6 months) and long (10.3 months and above) cycle lengths, respectively. Our results highlight the importance of analysing causality using the frequency domain test, which, unlike the time domain Granger causality test, allows us to decompose causality by different time horizons, and hence, could detect predictability at certain cycle lengths even when the time domain causality test might fail to pick up any causality. Further, given the widespread discussion in the literature, those results for the full-sample causality, irrespective of whether it is in time or frequency domains, cannot be relied upon when there are structural breaks present, and one needs to draw inference regarding causality from the sub-samples, we can conclude that there has been an emergence of causality running from sunspot numbers to global temperatures only recently at cycle length of 10.3 months and above.

Keywords:

• causality
• frequency domain
• global temperatures predictability
• sunspot numbers

JEL Classification:

• C32
• Q54

Acknowledgement

We would like to thank an anonymous referee for many helpful comments. Any remaining errors are, however, solely ours.

Notes

¹ The null hypothesis that global temperatures cause sunspot numbers is overwhelmingly rejected based on both the time domain and frequency domain causality tests. These results are available upon request from the authors.

² As mentioned earlier, we could alternatively to the sunspot numbers used solar irradiance. Note that the number of sunspots correlates with it over the period (since 1973) when satellite measurements of absolute radiation flux were available. Studies conducted by Vaquero et al. (2006) and Preminger and Walton (2005) reconstruct total solar irradiance from sunspot areas. See also Ambelu et al. (2011) and Scafetta and Willson (2009, 2014) to remark the differences between the sunspot number records and the total solar irradiance records.

³ We also carried out impulse response analysis for the full-sample on a VAR(4), with the shocks being identified by the standard Choleski decomposition, whereby SS was, understandably, ordered first. The results revealed that though a shock to SS leads to an increase in GT, the effect is only significant for the 3-month-ahead horizon.

⁴ The details of these tests are available upon request from the authors.

⁵ Recall that the frequency (ω) on the horizontal axis can be translated into a cycle or periodicity of T months by T = (2π/ω), where T is the period.