Analysis of the dynamic relationship between urban economic growth and energy consumption and environmental quality response from the perspective of an improved VAR model.

To acquire a thorough comprehension of the changing interplay between urban economic expansion and energy usage, the research conducts a dynamic correlation analysis between energy and the economy, integrating heteroskedasticity and differential evolution algorithms to bolster the vector autoregressive model. The experimental results indicated that the improvement strategy enhanced the convergence and solution set distribution of the differential evolutionary algorithm. Granger causality has been identified among urbanization, economic growth, energy consumption, and environmental quality, indicating that timely modifications to economic development and energy strategies can yield positive impacts on urban planning, ecological health, and overall economic progress. While energy consumption and economic growth exhibit a reciprocal influence, it is noteworthy that energy consumption does not serve as a catalyst for sustained long-term economic growth. Consequently, it becomes imperative to incorporate the principles of energy conservation, emission reduction, and environmental protection into the framework of urban economic development planning. Meanwhile, the effect of energy consumption on variables other than urbanization fluctuated greatly, the impact on environmental quality fluctuated from 0.2 to 0.4, and the impact on economic growth continued to rise to 0.4. The methodology suggested by the study accurately mirrors the actual conditions of the economy and energy use. This helps both the government and businesses understand the trends in economic development and make necessary adjustments to their energy strategies.