Hierarchical structures in the Gross Domestic Product per capita fluctuation in Latin American countries

A description of relations between the yearly fluctuations of the Gross Domestic Product (GDP) per capita of 19 Latin American (LA) countries is presented using either a linear (PCC) or a nonlinear correlation coefficient (NCC). Various time windows have been examined to measure the weights giving rise to links used to built complex networks for which the countries are nodes. The Average Overlap Index (AOI) for LA countries has been calculated for the two correlation coefficients showing that it is rather systematically higher than for the 25 EU countries.The network structures are thereafter examined through a country elimination scheme based on the removal of the weakest links and raising the AOI threshold level. The PCC and NCC schemes lead to different networks and clusters.A Principal Component Analysis is furthermore made for the two here above defined adjacency matrices resulting from the PCC and NCC methods to represent and analyze the country clustering structure and observe their coherence from such points of view. It is concluded that both PCC and NCC schemes lead to similar clustering though have a different feeling for the sign of correlations. Moreover the 19 LA countries seem to be less tied than the 25 EU.