Frequency-Specific Coupling in Cenozoic Climate Variability

Long paleoclimate time series combine strong persistence, multiple orbital-scale periodicities, and structural changes across climate states. These features complicate the statistical analysis of deep-time proxy records, since common spectral peaks do not necessarily imply stable relationships between variables. We analyze Cenozoic climate variability using the Cenozoic Global Reference benthic isotope record over the last 67.1 million years. The cleaned and interpolated δ18O and δ13C series are studied in a regime-based setting, with segments defined by major Cenozoic climate-state transitions to investigate if a stable coupling occurs between the isotope proxies and Earth’s astronomical variables. The analysis combines long-memory estimation, sequential frequency identification, frequency-adapted unit-root and stationarity testing at zero and harmonic frequencies, and cyclical fractional cointegration. This allows us to distinguish zero-frequency persistence from persistent cyclical behaviour and to test whether shared cyclical frequencies correspond to stable frequency-specific relationships between the proxies and orbital reference variables. The results show that the proxy series are not well described by a simple stationary versus unit-root dichotomy. Instead, they exhibit persistent long-memory dynamics with pronounced cyclical structure. Shared spectral peaks occur across several climate-state segments, yet only selected frequencies support stable fractional cointegration. Thus, isotope proxies and orbital reference variables may overlap spectrally without necessarily forming a stable long memory relationship. A key finding is that the additional split at the Eocene-Oligocene transition reveals a change in the frequency-specific relationship between δ18O and δ13C. Before the transition, stable fractional cointegration is associated with an orbital-scale band, whereas after the transition it shifts toward multi-million-year variability. This points to a substantial reorganisation of the frequency-specific coupling between the oxygen- and carbon-isotope records after the transition.