The Global Carbon Budget, maintained by the Global Carbon Project, summarizes Earth's global carbon cycle through four annual time series beginning in 1959: atmospheric CO$_2$ concentrations, anthropogenic CO$_2$ emissions, and CO$_2$ uptake by land and ocean. We analyze these four time series as a multivariate (cointegrated) system. Statistical tests show that the four time series are cointegrated with rank three and identify anthropogenic CO$_2$ emissions as the single stochastic trend driving the nonstationary dynamics of the system. The three cointegrated relations correspond to the physical relations that the sinks are linearly related to atmospheric concentrations and that the change in concentrations equals emissions minus the combined uptake by land and ocean. Furthermore, likelihood ratio tests show that a parametrically restricted error-correction model that embodies these physical relations and accounts for the El-Ni\~no/Southern Oscillation cannot be rejected on the data. Finally, projections based on this model, using Shared Socioeconomic Pathways scenarios, yield results consistent with established climate science.

翻译：全球碳预算由全球碳项目维护，通过始于1959年的四个年度时间序列总结地球的全球碳循环：大气CO$_2$浓度、人为CO$_2$排放以及陆地和海洋的CO$_2$吸收。我们将这四个时间序列作为一个多元（协整）系统进行分析。统计检验表明，这四个时间序列以秩三协整，并识别出人为CO$_2$排放是驱动系统非平稳动态的唯一随机趋势。三个协整关系对应于以下物理关系：碳汇与大气浓度呈线性相关，以及浓度变化等于排放减去陆地和海洋的总吸收量。此外，似然比检验表明，一个体现这些物理关系并考虑厄尔尼诺/南方涛动的参数限制误差修正模型在数据上无法被拒绝。最后，基于该模型并使用共享社会经济路径情景的预测结果，与既定的气候科学结论一致。