Climate persistence, structural change, and heteroscedasticity in CENOGRID: A score-driven fractional

Understanding the persistence of climate shocks and the timing of major climate-state transitions is central to both climate science and climate economics. In this paper, we develop an observable-switching fractionally integrated score-driven model with conditional heteroscedasticity, denoted OS-t-FI[d(st)]-QARBeta-t-EGARCH, that jointly models long-memory dynamics, regime changes, and time-varying volatility. The framework combines score-driven filters with regime-dependent degrees of fractional integration and heavy-tailed conditional distributions, providing a robust and information-theoretically efficient approach for analyzing climate time series. We apply the model to the CENOGRID benthic foraminiferal δ13C and δ18O records covering the last 67.1 million years at 5-kyr resolution. Milankovitch orbital variables (i.e., eccentricity, obliquity, and precession) are incorporated as exogenous controls to account for low-frequency astronomical forcing. Model-comparison results show that the proposed regime-switching fractionally integrated specification outperforms benchmark score-driven and non-switching models according to likelihood-based criteria. The estimated fractional-integration parameters vary across climate regimes, with both regimes exhibiting persistent long-memory dynamics and one regime approaching unit-root behavior. The results provide evidence that Cenozoic climate evolution is characterized by changes in the strength of persistence. The regime dynamics broadly support previously identified climate-state boundaries near 56, 47, 39.7, 34, 13.9, 10, and 3.3 million years ago (Ma), while also suggesting potential additional subdivisions near 58 and 17 Ma. Our findings imply a hierarchical structure of climate evolution in which major climate states contain internally distinct dynamical subperiods. These results matter for long-horizon climate-risk modeling used in energy economics because they indicate that climate persistence and uncertainty vary systematically across climate states.