In many practical applications, evaluating the joint impact of combinations of environmental variables is important for risk management and structural design analysis. When such variables are considered simultaneously, non-stationarity can exist within both the marginal distributions and dependence structure, resulting in complex data structures. In the context of extremes, few methods have been proposed for modelling trends in extremal dependence, even though capturing this feature is important for quantifying joint impact. Moreover, most proposed techniques are only applicable to data structures exhibiting asymptotic dependence. Motivated by observed dependence trends of data from the UK Climate Projections, we propose a novel semi-parametric modelling framework for bivariate extremal dependence structures. This framework allows us to capture a wide variety of dependence trends for data exhibiting asymptotic independence. When applied to the climate projection dataset, our model detects significant dependence trends in observations and, in combination with models for marginal non-stationarity, can be used to produce estimates of bivariate risk measures at future time points.

翻译：在许多实际应用中，评估环境变量组合的联合影响对于风险管理与结构设计分析至关重要。当这些变量被同时考虑时，边际分布与依赖结构中均可能存在非平稳性，从而产生复杂的数据结构。在极值分析领域，尽管捕捉极值依赖趋势对量化联合影响具有关键意义，但针对该趋势建模的方法目前仍十分有限。此外，大多数现有技术仅适用于呈现渐近依赖的数据结构。受英国气候预测数据中观测到的依赖趋势启发，我们提出了一种针对双变量极值依赖结构的半参数建模框架。该框架能够捕捉渐近独立数据中广泛存在的依赖趋势。将该模型应用于气候预测数据集时，我们检测到观测数据中存在显著的依赖趋势；结合边际非平稳性模型，该框架可用于预测未来时间点的双变量风险度量估计值。