Predicting carbon emissions for urban agglomerations by incorporating spatial correlation relationships holds significant importance for formulating regionally coordinated carbon reduction policies. A thorough examination of the spatial correlation in carbon emissions within the Yangtze River Delta urban agglomeration has revealed a significant positive spatial correlation between emissions across different cities. Given the spatial correlation characteristics, non-linear temporal evolution trends and regional variations in carbon emissions, a nonlinear discrete spatiotemporal multivariate grey prediction model (NDSTGM(1,m,N)) is proposed. Firstly, an asymmetric time-varying spatial weight matrix is derived based on the gravity model, and then the spatial correlation effect term is constructed to extract the spatial correlation characteristics. Secondly, the time polynomial term with differentiated order is constructed to capture the nonlinear temporal evolutionary trend of each node. Furthermore, the non-equal order real number domain grey generation operator is introduced to flexibly extract regional difference feature. Meanwhile, the genetic algorithm is designed to realize the collaborative optimization of polynomial order and non-equal order generating operator. Finally, the new model is applied to predict CO2 emissions in the Yangtze River Delta region, and the results show that the model significantly outperforms nine comparative models under different sample sizes, and demonstrates outstanding performance in spatiotemporal feature extraction and prediction accuracy. Moreover, the forecast indicates that the Yangtze River Delta region is expected to achieve the interim goal of reducing carbon emission intensity by more than 20% compared to 2020 by 2025.