Dynamics of HDI Index: Temporal Dependence Based on D‑vine Copulas Model for Three‑Way Data

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 threeway 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.