This paper develops a copula-based time-series framework for modelling sovereign credit rating activity and its dependence dynamics, with extensions incorporating climate risk. We introduce a mixed-difference transformation that maps discrete annual counts of sovereign rating actions into a continuous domain, enabling flexible copula modelling. Building on a MAG(1) copula process, we extend the framework to a MAGMAR(1,1) specification combining moving-aggregate and autoregressive dependence, and establish consistency and asymptotic normality of the associated maximum likelihood estimators. The empirical analysis uses a multi-agency panel of sovereign ratings and country-level carbon intensity, aggregated to an annual measure of global rating activity. Results reveal strong nonlinear dependence and pronounced clustering of high-activity years, with the Gumbel MAGMAR(1,1) specification delivering the strongest empirical performance among the models considered, while standard Markov copulas and Poisson count models perform substantially worse. Climate covariates improve marginal models but do not materially enhance dependence dynamics, suggesting limited incremental explanatory power of the chosen aggregate climate proxy. The results highlight the value of parsimonious copula-based models for sovereign migration risk and stress testing.

翻译：本文开发了基于Copula的时间序列框架，用于建模主权信用评级活动及其依赖动态，并扩展纳入气候风险。我们引入混合差分变换，将离散的主权评级动作年度计数映射至连续域，从而实现灵活的Copula建模。基于MAG(1) Copula过程，我们将框架扩展至结合移动聚合与自回归依赖的MAGMAR(1,1)规范，并建立相关最大似然估计量的一致性和渐近正态性。实证分析采用多机构主权评级面板数据与国别碳强度指标，聚合为全球评级活动的年度度量。结果显示强非线性依赖及高活动年份的显著聚类现象，其中Gumbel MAGMAR(1,1)规范在考量模型中表现最优，而标准马尔可夫Copula与泊松计数模型表现显著逊色。气候协变量可改进边际模型但未实质增强依赖动态，表明所选聚合气候代理的增量解释力有限。研究结果凸显了简约型Copula模型在主权迁移风险与压力测试中的价值。