Dynamics Between Atmospheric CO2 Concentration and Global Temperature Anomalies: Evidence of Time-Varying Granger Causality

This study examines whether the predictive relationship between atmospheric CO2 concentration and global surface temperature anomalies remains stable over time. Monthly deseasonalized observations from March 1958 to August 2025 are analyzed with structural-break unit-root tests and forward-expanding, rolling, and recursive-evolving time-varying Granger-causality (TVGC) algorithms within a lag-augmented vector autoregression (LA-VAR). The unit-root evidence classifies temperature anomalies as I(0) and atmospheric CO2 concentration as I(1). With two lags, predictive evidence from CO2 concentration to temperature is weaker and algorithm-dependent, whereas temperature-to-CO2 predictive content is significant across all three algorithms. With 12 lags, the no-Granger-causality null is rejected at the 1% level in both directions and for all algorithms. These results document time variation and lag sensitivity in conditional predictive precedence; they do not establish a bidirectional physical mechanism. The detected changes can support climate-monitoring diagnostics and evidence-informed assessment relevant to Sustainable Development Goals.