This study presents a statistical approach for identifying transitions between climate states, referred to as breakpoints in the econometric literature, using well-established econometric tools for breakpoint detection. We analyze a record of the stable oxygen isotope ratio 𝛿18O, covering 67.1 million years, derived from benthic foraminifera. The dataset is presented in Westerhold et al. (2020) [Science 369, 1383-1387], where the authors use recurrence analysis to identify six climate states: Warmhouse I, Hothouse, Warmhouse II, Coolhouse I, Coolhouse II, and Icehouse, and thus five transitions.

Estimation necessitates a constant observation frequency. We employ mean binning. We explore three model specifications. The first model is a state-dependent mean model, which is equivalent to modeling an abrupt break in the mean of 𝛿18O for each climate state. The second model expands this by including a state-independent autoregressive term, which can be interpreted as making the transitions between states more gradual. The final model expands on the second model by letting the autoregressive term be state-dependent as well, allowing for state-specific autoregressive dynamics. All models incorporate an error term with state-dependent variance.

Fixing the number of breakpoints to five, the resulting breakpoint estimates closely align with those identified by Westerhold et al. (2020) across various binning frequencies and model specifications, demonstrating the robustness of the approach and corroborating the dating of the climate states of Westerhold et al. (2020) with time series analysis. Our approach offers the advantage of constructing confidence intervals for the breakpoints, providing a measure of estimation uncertainty, and it allows testing for the number of breakpoints in the time series.

In conclusion, our study presents a statistically rigorous approach to identifying transitions between climate states as well as their confidence intervals and the number of breakpoints.