This article focuses on the synthesis of conditional dependence structure of recursive Bayesian estimation of dynamic state space models with time-varying parameters using a newly modified recursive Bayesian algorithm. The results of empirical applications to climate data from Nigeria reveals that the relationship between energy consumption and carbon dioxide emission in Nigeria reached the lowest peak in the late 1980s and the highest peak in early 2000. For South Africa, the slope trajectory of the model descended to the lowest in the mid-1990s and attained the highest peak in early 2000. These changepoints can be attributed to the economic growth, regime changes, anthropogenic activities, vehicular emissions, population growth and industrial revolution in these countries. These results have implications on climate change prediction and global warming in both countries, and also shows that recursive Bayesian dynamic model with time-varying parameters is suitable for statistical inference in climate change and policy analysis.