Placement of climate state–dependent variance in state-space models

Determine whether climate state–dependent variance differentiation should be modeled in the measurement equation (observation noise) or in the transition equation (latent state evolution) within continuous-time unobserved-components state-space models for the δ18O and δ13C time series from benthic foraminifera, where climate regimes (Warmhouse/Hothouse/Coolhouse/Icehouse) induce variance shifts across periods.

Background

The paper models the δ18O and δ13C paleoclimate proxy series using continuous-time unobserved-components state-space models that naturally handle irregular sampling, multiple observations per timestamp, and nonstationary behavior. Measurement noise is represented in the measurement equation, while the underlying climate signal evolves via the transition equation.

Westerhold et al. (2020) identify six distinct climate states across the Cenozoic. The authors incorporate this by allowing variances to differ across climate states. A modeling choice arises: whether to attribute climate state–dependent variance changes to observation noise (measurement equation) or to the evolution of the latent climate signal (transition equation).

The authors select the transition equation for practical and interpretational reasons (they already model paper-specific measurement variances, and they want the latent component to represent a climate state variable). However, they explicitly acknowledge uncertainty about which placement is appropriate, leaving the question unresolved.