We introduce biarchetype analysis for the first time in the context of univariate functional data. This unsupervised methodology extends archetype analysis by simultaneously identifying archetypal structures across both the cases (countries, in our application) and the temporal argument. Both cases and time points are expressed as mixtures of biarchetypes, yielding a concise and highly interpretable representation of complex functional observations. Although biarchetype analysis is not intended as a clustering technique, it offers superior interpretability compared with biclustering approaches, as it is based on extreme, representative patterns rather than average centroids, thereby enhancing human comprehension. We apply the proposed method to 10-year government bond yields of European countries over the period 2001-2025. The results identify three distinct time regimes (the pre-crisis period, the euro-area sovereign debt crisis, and the post-crisis period), and reveal Germany, Greece, and Hungary as country archetypes.

翻译：我们首次在单变量函数数据背景下引入双原型分析。这种无监督方法通过同时识别案例（在本文应用中即国家）和时间维度上的原型结构，扩展了原型分析。案例和时间点均被表示为双原型的混合，从而为复杂函数观测数据提供简洁且高度可解释的表征。尽管双原型分析并非旨在作为一种聚类技术，但它相比双聚类方法具有更优的可解释性，因其基于极端、代表性的模式而非平均质心，从而增强人类理解。我们将所提方法应用于2001-2025年期间欧洲国家十年期政府债券收益率。结果识别出三种不同的时间区间（危机前时期、欧元区主权债务危机时期和危机后时期），并揭示德国、希腊和匈牙利为国家原型。