The HDI (Human Development Index) is a widely used index based on the average of measures of health, education, and income. It assesses the progress of countries worldwide. The publicly available data set associated with the HDI can be seen as a table with 3 dimensions (three-way table): countries, indexes regarding progress, and years (from 2010 to 2018). Thus, modeling the serial dependence structure of this type of intricate three-way tables is a challenge. D-vine copulas are a special class of multivariate copulas that are particularly suited for modeling serial dependence. This work aims to assess the evolution of the dependence relationship between the indexes of the HDI data set over time through D-vine copulas, which has not been fully used before in the area, as far as we are concerned. We tested our approach to European and African countries and compare their results.

HDI（人类发展指数）是基于健康，教育和收入指标的平均值而被广泛使用的指数。它评估了世界各国的进展。与人类发展指数相关的公开可用数据集可以看成是一个具有3个维度的表格（3个维度的表格）：国家，有关进展的指数和年份（2010年至2018年）。因此，对这种复杂的三向表的串行依赖性结构进行建模是一个挑战。D-vine copulas是一类特殊的多元copulas，特别适合于建模序列依赖性。这项工作旨在通过D-vine copulas评估HDI数据集的索引之间的依存关系随时间的变化，就我们而言，该区域以前尚未得到充分利用。