Modelling the Interactions in Paleoclimate Data from Ice Cores

This paper considers methods for testing directions of causation in the paleoclimate series for temperature and CO2 concentration derived from Antarctic ice cores from 800,000 years BP. These series are well-known to move together in the transitions between glacial and interglacial periods, but the dynamic relationship between the series is open to dispute. Bivariate models are constructed, in the context of which we perform tests for Granger causality, or in other words for asymmetry in the pattern of dynamic interactions. An important question is the stationarity of the series, because di¤erent statistical techniques are called for in stationary and integrated models. Previous work with climate data has focused on a cointegration approach appropriate to integrated series, but a range of tests show no evidence of integrated behaviour in these seres. A second important question is linearity, whether the dynamics in mean can be adequately represented by a high-order vector autoregressive process. This modelling approach is compared with a nonlinear Markov switching mechanism, in which the glacial/interglacial switches are controlled by a common hidden discrete process with …xed conditional probabilities of changes of state. A further characteristic of the data that comes to light is pronounced conditional heteroscedasticity, with much larger disturbances in evidence around the glacial/interglacial transitions.This data feature is e¤ectively accounted for by …tting a GARCH component.