Modeling Long Memory Cyclical Trends in the Cenozoic

Long paleoclimate time series combine strong persistence, multiple orbital cycles, and regime shifts, which complicates the analysis of dynamical coupling and predictability. We analyze Cenozoic variability using the Cenozoic global reference benthic foraminiferal carbon and oxygen isotope dataset, in a regime based time series framework that integrates deterministic decomposition, cyclical fractional cointegration, and regime aware forecasting. We divide the record into segments in line with the major Cenozoic climate states. Within each segment, deterministic components are estimated and removed, including linear trends, orbital forcing variables, and harmonic cycles identified via a GARMA based filtering procedure. We then apply cyclical fractional cointegration tests at shared orbital frequencies to assess whether common spectral peaks reflect a stable frequency specific linkage (cointegration) between the proxies and orbital variables. The results reveal pronounced regime dependence. The long eccentricity cycle (405 kyr) shows recurrent evidence of cointegration with both proxies across different climate states. For obliquity, an indication of frequency specific linkage is primarily found after the middle Miocene Climate Transition. Finally, we fit regime specific VAR(2) models to the residuals and report in-sample forecasts, and we generate a 100 kyr out-of-sample projection based on the Icehouse specific dynamics. Forecast behaviour varies across climate states, highlighting that non-stationarity and regime specific dynamics place strong constraints on predictability in long paleoclimate records.