Modeling Long Memory in 67 Million Years of Cyclical Climate Trends: Anticipating Future Cycles

Deep-time climate records contain deterministic orbital signals and persistent stochastic variation, but how these components jointly affect predictability across climate states remains unclear. We analyze the Cenozoic Global Reference benthic foraminifer oxygen and carbon isotope record spanning 67.1 million years. This very long period is divided into seven climate-state segments. For each segment, we estimate deterministic contemporaneous long-run components combining linear trends, eccentricity, obliquity, climatic precession, and identified harmonic frequencies. The remaining variation is modeled with a bivariate vector autoregressive forecasting framework conditioned on astronomical forcing. The selected deterministic and dynamic structures differ substantially across climate states. Obliquity is the most recurrent orbital predictor, whereas squared obliquity, eccentricity, climatic precession, and harmonic components contribute only in particular segments and differ between the two proxies. Forecast accuracy likewise varies across the record, although observed and predicted values agree closely in several segments. A projection for the next 100,000 years provides a baseline implied by natural astronomical forcing and continued Icehouse dynamics. Overall, the results show that orbital responsiveness, proxy interactions, and statistical predictability are state dependent. Deep-time climate variability therefore cannot be represented by a single common combination of deterministic forcing and stochastic dynamics across the complete Cenozoic.