  We analyze and model the stochastic behavior of paleoclimate time series and
assess the implications for the coupling of climate variables during the
Pleistocene glacial cycles. We examine 800 kyr of carbon dioxide, methane,
nitrous oxide, and temperature proxy data from the EPICA Dome-C ice core, which
are characterized by 100~kyr glacial cycles overlain by fluctuations across a
wide range of time scales. We quantify this behavior through multifractal
time-weighted detrended fluctuation analysis, which distinguishes near
red-noise and white-noise behavior below and above the 100~kyr glacial cycle
respectively in all records. This allows us to model each time series as a
one-dimensional periodic non-autonomous stochastic dynamical system, and assess
the stability of physical processes and the fidelity of model-simulated time
series. We extend this approach to a four-variable model with linear coupling
terms, which we interpret in terms of the interrelationships between the time
series. Methane and nitrous oxide are found to have significant destabilizing
influences, while carbon dioxide and temperature have smaller stabilizing
influences. We draw conclusions about causal relationships in glacial
transitions and the climate processes that may have facilitated these
couplings, and highlight opportunities to further develop stochastic modeling
approaches.
