There are essentially two approaches to climate modelling. Over the past decades, efforts to understand climate dynamics have been dominated by computationally-intensive modelling aiming to include all possible processes, essentially by integrating the equations for the relevant physics. This is the bottom-up approach. However, even the largest models include many approximations and the cumulative effect of these approximations make it impossible to predict the evolution of climate over several tens of thousands of years. For this reason a more phenomenological approach is also useful. It consists in identifying coherent spatio-temporal structures in the climate time-series in order to understand how they interact. Theoretically, the two approaches focus on different levels of information and they should be complementary. In practice, they are generally perceived to be in philosophical opposition and there is no unifying methodological framework. Our ambition is to provide this methodological framework with a focus on climate dynamics at the scale of the Pleistocene (last 2 million years). We pursue a triple objective (1) the framework must be rigorous but flexible enough to test competing theories of ice ages (2) it must avoid circular reasonings associated with ``tuning'' (3) it must provide a credible basis to unify our knowledge of climate dynamics and provide a state-of-the-art ``prediction horizon''. To this end we propose a methodology spanning different but complementary disciplines: physical climatology, empirical palaeoclimatology, dynamical system analysis and applied Bayesian statistics. It is intended to have a wide applicability in climate science where there is an interest in using reduced-order representations of the climate system.