Time series modeling of paleoclimate data

Abstract

This paper applies time series modeling methods to paleoclimate series for temperature, ice volume, and atmospheric concentrations of CO2 and CH4. These series, inferred from Antarctic ice and ocean cores, are well known to move together in the transitions between glacial and interglacial periods, but the dynamic relationship between the series is open to question. A further unresolved issue is the role of Milankovitch theory, in which the glacial/interglacial cycles are correlated with orbital variations. We perform tests for Granger causality in the context of a vector autoregression model. Previous work with climate series has assumed nonstationarity and adopted a cointegration approach, but in a range of tests, we find no evidence of integrated behavior. We use conventional autoregressive methodology while allowing for conditional heteroscedasticity in the residuals, associated with the transitional periods. Copyright © 2015 John Wiley & Sons, Ltd.

Testing Cointegrating Relationships Using Irregular and Non‐Contemporaneous Series with an Application to Paleoclimate Data

“…Using linear interpolation with no lagged differences, we reject both nulls with the trace statistics, suggesting that the series are cointegrated by any linear combination – i.e., that they do not have stochastic trends in the first place. This finding is not consistent with that of Kaufmann and Juselius (), but it is consistent with that of the univariate unit root tests of Davidson et al (). In spite of the under‐rejection of no cointegration by in the simulations, both residual‐based tests support cointegration.…”

“…Taking into account the size distortions, the empirical evidence generally supports the cointegration of CO 2 concentrations and temperature found by Kaufmann and Juselius () in the sense that the null of no cointegration is rejected. However, an additional rejection of the cointegration null against the stationary alternative either supports the stationarity finding of Davidson et al (), who also use linear interpolation, or else suggests the possibility that the size distortion is not completely eliminated or that level shifts apparent in the data may be contributing additional distortion.…”

“…The problems of irregularity and non‐contemporaneity are salient in the paleoclimate literature. In the context of unit root and cointegration testing, they have been bridged by linear interpolation (Davidson et al , ; Kaufmann and Juselius, ). The present analysis reveals size distortion in standard cointegration tests using linear interpolation, echoing and expanding on the findings of Ghysels and Miller () of size distortion of such tests when linear interpolation is used in the related context of mixed‐frequency time series.…”

“…Or, it could be caused by a modeling deficiency of the individual series. For example, although trending behavior appears in the data, Davidson et al () do not find statistical evidence of unit root‐type trends.…”

The poly‐log Weibull model applied to space‐time interpolation of temperature

“…Studies to detect those trends could be realized through the analysis of historical time series (Brillinger & Finney, 2014;Davidson, Stephenson, & Turasie, 2016;Guttorp & Xu, 2011) of atmospheric variables from a network of weather stations, using some adjusted predictive statistical model for the spatial interpolation (Krähenmann, Bissolli, Rapp, & Ahrens, 2011). However, every model is prone to have erroneous temperature values due to the vast distances involved and the sparsity of stations within the state.…”