The main cause of global warming is carbon dioxide ( \(\hbox {CO}_2\) ) emissions, acting as a significant greenhouse gas. These emissions stem from various sources and significantly contribute to climate change. Fortunately, we have countermeasures like carbon taxes to curb \(\hbox {CO}_2\) output. Carbon taxes incentivise a reduction in \(\hbox {CO}_2\) production and a shift towards cleaner energy sources by placing a cost on emissions. This paper investigates the interplay between carbon tax policy, carbon emissions, economic output (GDP) and renewable energy consumption. A system of differential equations is constructed to model these relationships based on a comprehensive literature review. Parameter estimation based on real-world data yielded successful fits for the variables. However, the fit for the carbon tax equation is less conclusive, suggesting a more complex relationship with carbon emissions. Stability analysis and the boundedness of the system are carried out. Auto-regressive integrated moving average (ARIMA) forecasting is employed to predict future trends. The results suggest a projected increase in GDP and renewable energy consumption over the next ten years, indicating a potential for a cleaner energy transition. Furthermore, the forecasts anticipate a rise in carbon tax implementation. This analysis emphasises how important carbon taxes are for cutting emissions and advancing renewable energy. Results indicate that carbon taxes can promote decarbonisation and economic growth, despite the complicated link between them and \(\hbox {CO}_2\) emissions. Both GDP growth and the use of renewable energy are anticipated to increase. However, policies must be improved to combat climate change effectively. Future studies should improve parameters and investigate other relevant elements to promote a low-carbon future.
