Change point method for detecting regime shifts in paleoclimatic time series: Application to <i>δ</i>¹⁸O time series of the Plio‐Pleistocene

Abstract

Although different paleoenvironmental time series resolve past climatic change at different time scales, nearly all share one characteristic: they are nonstationary over the length of the record sampled. We describe a recursive dynamic programming change point algorithm that is well suited to identify shifts in the Earth system's variability, as it represents a nonstationary time series as a series of regimes, each of which is homogeneous. The algorithm fits the data by minimizing squared errors not only over the parameters of the models for each subsequence but also over an arbitrary number of boundary points without restrictions on the lengths of regimes. The versatility of the algorithm is illustrated by an application to 5 Ma of Plio‐Pleisotcene δ 18 O variations. We seek to identify either the single dominant “Milankovitch” frequency or linear combinations of frequencies and consistently identify changes ∼780 ka and ∼2.7 Ma, among others, in each analysis done. Our applications also provide support to the recent hypothesis that obliquity‐based Milankovitch terms can account for the circa 100 ka cycle that empirically dominates the most recent 1 million years.