Biarchetype analysis for univariate functional data. An application to macroeconomic financial time series

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.

A multi-criteria decision support system to evaluate the effectiveness of training courses on citizens' employability

This study examines the impact of lifelong learning on the professional lives of employed and unemployed individuals. Lifelong learning is a crucial factor in securing employment or enhancing one's existing career prospects. To achieve this objective, this study proposes the implementation of a multi-criteria decision support system for the evaluation of training courses in accordance with their capacity to enhance the employability of the students. The methodology is delineated in four stages. Firstly, a `working life curve' was defined to provide a quantitative description of an individual's working life. Secondly, an analysis based on K-medoids clustering defined a control group for each individual for comparison. Thirdly, the performance of a course according to each of the four predefined criteria was calculated using a t-test to determine the mean performance value of those who took the course. Ultimately, the unweighted TOPSIS method was used to evaluate the efficacy of the various training courses in relation to the four criteria. This approach effectively addresses the challenge of using extensive datasets within a system while facilitating the application of a multi-criteria unweighted TOPSIS method. The results of the multi-criteria TOPSIS method indicated that training courses related to the professional fields of administration and management, hostel and tourism and community and sociocultural services have positive impact on employability and improving the working conditions of citizens. However, courses that demonstrate the greatest effectiveness in ranking are the least demanded by citizens. The results will help policymakers evaluate the effectiveness of each training course offered by the regional government.