The statistical association between temperature and greenhouse gases over glacial cycles is well documented, but causality behind this correlation remains difficult to extract directly from the data. A time lag of CO_2 behind Antarctic temperature—originally thought to hint at a driving role for temperature[2,3]—is absent[4,5] at the last deglaciation, but recently confirmed at the last ice age inception and the end of the earlier termination II (ref. 7). We show that such variable time lags are typical for complex nonlinear systems such as the climate, prohibiting straightforward use of correlation lags to infer causation. However, an insight from dynamical systems theory now allows us to circumvent the classical challenges of unravelling causation from multivariate time series. We build on this insight to demonstrate directly from ice-core data that, over glacial–interglacial timescales, climate dynamics are largely driven by internal Earth system mechanisms, including a marked positive feedback effect from temperature variability on greenhouse-gas concentrations.