Trends, time-varying and nonlinear time series models for NGRIP and VOSTOK paleoclimate data

Abstract

In order to gain further insights into stochastic behaviour of paleoclimate data, including timescales at and below Milankovitch forcing, three specific questions are discussed using δ18O NGRIP and Vostok Deuterium content data. A comparison of ordinary and time-varying coefficients autoregressive (AR) models shows that both data sets are distinguishable from data generated by suitable low-order AR processes in contrast to earlier conclusions. A harmonic regression analysis clearly distinguishing between discrete and continuous spectra detects cycles corresponding to variations of eccentricity, obliquity and precession. Contribution of eccentricity to the total variance in the last 422,766-year Vostok data is close to, while the variance reduction delivered jointly by obliquity and precession is substantially smaller than a previous recent finding. A harmonic regression analysis with time-varying frequencies and amplitudes is also performed. This approach delivers a gain over the constant frequency model at any reasonable significance level. It is demonstrated that variations of frequencies are at least partly due to real variations and not merely to timescale uncertainties. In order to consider nonlinearity in paleoclimate data, threshold autoregressive (TAR) models are applied to time series examined. A bivariate TAR model describing simultaneous NGRIP and Vostok data exhibits three fix points and one limit cycle related to a part of Dansgaard–Oeschger events. The model selected suggests that Greenland has a primary role in the Greenland–Antarctica climate variation relationship.