Climate observations are predominantly non-stationary time series invalidating the use of standard statistical inference procedures. Econometriccointegration analysis can be used to overcome some of these inferential difficulties. Here I show that a physical two-component energy balance model of global mean climate is equivalent to a cointegrated system that can be mapped to a cointegrated vector autoregression, making it directly testable, and providing a physical basis for the use of econometric methods in climate research. Doing so opens the door to investigating the empirical impacts of shifts from both natural and human sources, assessing simulated climate models by approximating them through cointegrated models, and enables a close linking of data-based macroeconomic models with climate systems. My approach finds statistical support of the model using global mean surface temperatures, 0-700m ocean heat content and radiative forcing (e.g. from greenhouse gases). The model results show that previous empirical estimates of the temperature response to the doubling of CO2 may be misleadingly low due to model mis-specification and the influence of shocks such as volcanic eruptions.