Spatiotemporal information fusion for urban-agglomeration carbon-emission forecasting: a grey multivariate model with composite city proximity

Purpose Accurate multi-city carbon emission forecasts are essential for climate policy. Currently, rapid urbanisation has woven cities into coupled economic and infrastructural networks. Thus, this study aims to model evolving inter-city spillovers to enhance spatiotemporal carbon emission predictions for urban agglomeration. Design/methodology/approach This work develops a spatiotemporal discrete grey multivariate model, denoted as STDGM (1, N, M), in which a composite spatiotemporal-proximity coefficient dynamically fuses geographic distance with time-varying economic distance. Consequently, the proposed mode can track inter-city spillover effects through geographic and economic proximity. Additionally, a particle-swarm algorithm is applied to calibrate the weights between the two distances' parameters. Findings Empirically, the model is tested on annual data for thirteen Jiangsu cities (2010–2022) and outperforms the classical grey models, neural networks and statistical benchmarks, achieving an average mean absolute percentage error of 1.97% and maintaining the narrowest error range under extensive Monte Carlo robustness checks. Research limitations/implications The findings show that embedding adaptive spatiotemporal interactions in a grey prediction model lifts forecast accuracy and yields interpretable results, providing planners with a reliable tool for designing collaborative and region-specific mitigation pathways. Originality/value This work initially embeds adaptive geographic–economic proximity within a grey multivariate model. It combines small-sample efficiency, dynamic spatial realism and interpretability in a unified framework, offering researchers and policymakers a novel tool for coordinated urban-agglomeration decarbonisation.