Forecasting CO2 emissions in BRICS countries using the grey breakpoint prediction models

In this paper, three novel grey breakpoint prediction models are proposed based on calculating the development coefficient and grey action of grey prediction models after fuzzy breakpoints, unifying the calculation methods for parameter estimation and the relevant time-response equations, and using the particle swarm optimisation algorithm to optimise the two-stage background values. Finally, the novel grey breakpoint prediction models are used to simulate and forecast the CO2 emissions in BRICS countries. We can see that by setting time breakpoints and fuzzy breakpoint intervals, the novel methods successfully detect abrupt changes in the system and achieve accurate predictions, thus improving the accuracy and applicability of the grey model. The new grey breakpoint prediction models demonstrate better estimation in all cases in CO2 emissions forecasting. The projections show that between 2022 and 2025, CO2 emissions in Brazil and South Africa will decrease each year, while CO2 emissions in China, Russia and India will increase each year, but the upwards trend in India shows signs of slowing.