## 1 Introduction

[2] Referring to climate variables that represent various aspects of glacial cycles, *Ruddiman* [2006] quotes Laurent Labeyrie “Everything is correlated to everything.” At first glance, strong collinearity seems an insurmountable obstacle to efforts that use statistical techniques to understand the physical mechanisms that drive glacial cycles.

[3] Strong correlations among trending variables also pose obstacles to a better understanding of economic systems. To surmount this obstacle, economists now use statistical techniques that are based on the idea of cointegration and error correction. These concepts allow economists to evaluate whether correlations among trending variables correspond to statistically meaningful long-run relationships and to trace the dynamics by which variables adjust back to equilibrium after having been pushed away by exogenous shocks. The power of this statistical methodology is the basis for Clive Granger's 2003 Nobel Prize in economics.

[4] Using the ideas of cointegration and equilibrium error correlation, Kaufmann and Juselius (in review) (Herein KJ) use a cointegrated vector autoregressive (CVAR) model to evaluate the role that orbital, seasonal, and spatial variations in solar insolation play in glacial cycles. Results indicate that glacial cycles in temperature, CO_{2}, and ice volume can be simulated accurately using orbital parameters, with lesser contributions from seasonal variations at specific latitudes.

[5] These results are based on a CVAR model whose ability to simulate glacial cycles is determined purely by statistical criteria. This narrow criterion raises the question whether these results reflect the physical and/or biological mechanisms that are hypothesized to generate glacial cycles or whether they are a result of pure statistical curve fitting.

[6] The aim of this paper is, therefore, to go beyond the purely statistical description of the CVAR and test whether the cointegrating relations in the CVAR are consistent with a basic understanding of how the climate system works. This is done by identifying long-run relationships among 10 climate variables and four solar variables and assessing whether the results are consistent with physical and/or biological mechanisms. Identification allows us to discriminate among mechanisms currently described in the literature and quantify the physical and/or biological mechanisms embodied in the CVAR, such as the large (80–100 ppm) changes in atmospheric CO_{2}.

[7] Results indicate that the statistical relations embodied in the CVAR are consistent with the physical and/or biological mechanisms described in the literature. A permanent doubling of CO_{2} generates 11.1°C rise in Antarctic temperature. Large variations in atmospheric CO_{2} over glacial cycles are driven by changes in sea ice and sea surface temperature in southern oceans and marine biological activity, which is represented by a two-step process in which iron dust increases biological activity and the increase in biological activity reduces CO_{2} concentrations. Glacial variations in ice volume, as proxied by δ^{18}O, are driven by changes in global and high latitude solar insolation, latitudinal gradients in solar insolation, and the atmospheric concentration of CO_{2}. Finally, the model is able to quantify the effects of ice volume and ocean temperature on sea level, such that after complete adjustment, sea level rises 14 m per 0.11‰ δ^{18}O and about 17 m/°C of sea surface temperature in southern oceans.

[8] These results, and the methods used to obtain them, are described in four sections and a set of Supporting Information. Section 2 describes the time series that are used to proxy various aspects of the climate and how the CVAR model can be used to test hypotheses about the mechanisms that may drive glacial cycles. Section 3 describes diagnostic statistics that are used to evaluate the identified CVAR model. Section 4 interprets the statistical results relative to hypotheses for the physical mechanisms that are thought to play an important role in glacial cycles. Section 5 concludes by describing the general importance of a multivariate approach, as opposed to the bivariate approach that is used by many analyses.