Title: Extracting causation from millennial-scale climate fluctuations in the last 800 kyr

Abstract: The detection of cause-effect relationships from the analysis of paleoclimatic records is a crucial step to disentangle the main mechanisms at work in the climate system. Here, we show that the approach based on the generalized Fluctuation-Dissipation Relation, complemented by the analysis of the Transfer Entropy, allows the causal links to be identified between temperature, CO2 concentration and astronomical forcing during the glacial cycles of the last 800 kyr based on Antarctic ice core records. When considering the whole spectrum of time scales, the results of the analysis suggest that temperature drives CO2 concentration, or that are both driven by the common astronomical forcing. However, considering only millennial-scale fluctuations, the results reveal the presence of more complex causal links, indicating that CO2 variations contribute to driving the changes of temperature on such time scales. The results also evidence a slow temporal variability in the strength of the millennial-scale causal links between temperature and CO2 concentration.