Classic Granger causality may not be appropriate for diagnosing CO2-temperature and other noisy relationships

The Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR4) suggests with evidence that increased emissions of carbon dioxide (CO2), especially from human sources, leads to global warming. However, our ability to confirm this suggestion purely from statistical methods based on global-average time series of observations is still unclear. Granger causality has been used by previous researchers to test this hypothesis in a statistically principled way; however, the results have been mixed. In this work the classic Granger causality is implemented through a partial F-tests to radiative forcing (RF, a transformation of CO2) and global land surface temperature anomalies (GT), followed by a series of statistical checks. The results seem to indicate a feedback relationship between the two variables, with Granger causality mostly going from RF to GT. We check the validity of our test results by evaluating the evolving correlation structure between the two variables and the El Niņo/Southern Oscillation (ENSO) indices, and by conducting numerous Granger causal simulations with GT and RF, GT and ENSO, and GT and spatially-averaged North Atlantic sea surface temperature (SST). Our simulations suggest that Granger casuality in this form is not appropriate for studying the dependence structure of GT and RF, but can be appropriate for other relationships, including GT and SST as well as GT and ENSO. The reliability of this form of Granger causality seems to depend on many data characteristics, including but not limited to order of integration/co-integration, normality condition, noise type and level, number of samples, and whether data arises from a stochastic or deterministic process. Given that this form of Granger causality is currently used in many disciplines, our results may be useful to understand the reliability of such tests. In the future, a form of Granger causality which is more robust to these factors may need to be investigated. Without a robust Granger test, we must be cautious and thorough in testing for Granger casuality as well as in any conclusions we derive from such tests.