What is the link between temperature, carbon dioxide and methane? : A multivariate Granger causality analysis based on ice core data from Dome C in Antarctica

This paper continues the work of Kang and Larsson Theoretical and Applied Climatology 116:537-548 (2014) What is the link between temperature and carbon dioxide levels? A Granger causality analysis based on ice core data. Theoretical and Applied Climatology 116:537-548, by adding methane to the study of causality between temperature and carbon dioxide. The data used goes 800,000 years back in time which is possible due to it being extracted from ice cores located at Dome C in Antarctica. First we use linear interpolation to make the three data sets equidistant to be able to employ statistical methods. We adjust for a deterministic trend and find the best model fit to be an autoregressive model with lag two and a piecewise quadratic trend. By employing multivariate Granger causality tests we find strong evidence that temperature, carbon dioxide and methane all Granger cause each other in both directions i.e. carbon dioxide Granger causes temperature and temperature Granger causes carbon dioxide, etc. This is in accordance with the findings of Kang and Larsson, with the extension that we can add methane to establish a trivariate feedback system between temperature, carbon dioxide and methane