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The relationship between GHG emissions and global warming is studied through multi-level rolling analysis to assess whether or not there are increasing rates in global climate change as a result of higher levels of anthropogenic emissions, as we move forward in time. Furthermore, in order to assess whether we observe tail dependence, representing simultaneous occurrence of extreme events, we employ copula methods. Our main findings suggest a constant effect of emissions on temperature anomalies especially in the last decades. On the other hand we observe positive upper tail dependence in our copula analyses. This implies a comparably high probability of joint extreme large values (i.e., high temperatures and emission concentrations). As a guide to policy, it suggests to keep down extreme events in emissions to prevent possibilities of extreme warmings.