Does Sunspot Numbers Cause Global Temperatures? A Reconsideration Using a Non-Parametric Causality Test

This paper applies several causality tests to analyze whether sunspot numbers (used as an approximate proxy for the solar activity) cause global temperatures, using monthly data covering the time period 1880:1-2013:9. Both parametric and non-parametric causality tests are performed, which concludes standard time domain Granger causality test, the frequency domain causality test and the Singular Spectrum Analysis (SSA)-based causality test. Standard time domain Granger causality test fails to reject the null hypothesis that sunspot numbers does 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 to 2.6 months) and long (10.3 months and above) cycle lengths respectively. Our results highlight the importance of analyzing 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. We also performed SSA-based causality test on both the monthly data of the time period 1936:3-1986:11 and 1986:12-2013:9. Significant causality relationships are detected for the time period 1936:3-1986:11 and the time range of 1986:12-2013:9. What is more, we also confirm causality relationship between global temperatures and sunspot numbers in the first subsample. SSA-based causality test shows powerful sensitiveness of detecting causality relationship that previous methods could not detect. Generally speaking, the non-parametric SSA-based causality test outperformed both time domain and frequency domain causality tests. Further, given the wide-spread discussion in the literature, that 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, SSA-based causality test provides the most accurate results for each subsample and it can also show clear support of predictability on forecasting between tested variables.