Heterogeneous predictive association of CO2 with global warming

Global warming is a non-uniform process across space and time. This opens the door to a heterogeneous relationship between ${\text{CO}}_2$ and temperature that needs to be explored going beyond the standard analysis based on mean temperature. We revisit this topic through the lens of a new class of factor models for high-dimensional panel data, called quantile factor models. This technique extracts quantile-dependent factors from the distributions of temperature across a wide range of stable weather stations in the northern and southern hemispheres over 1959–2018. In particular, we test whether the (detrended) growth rate of ${\text{CO}}_2$ concentrations helps to predict the underlying factors of the different quantiles of the distribution of (detrended) temperatures in the time dimension. We document that predictive association is greater at the lower and medium quantiles than at the upper quantiles of temperature in all stations, and provide some conjectures about what could be behind this non-uniformity. These findings complement recent results in the literature documenting steeper trends in lower temperature levels than in other parts of the spatial distribution.