Multidimensional economic indicators and multivariate functional principal component analysis (MFPCA) in a comparative study of countries' competitiveness

The multivariate pluriformity and complexity of economic-geographic space (e.g., cities or countries) are reflected in their empirical multidimensional data structure with space-time characteristics. The need to reduce the multiple dimensions of an observation space is present in all social (and other) sciences seeking to identify basic patterns or key relations among critical indicators that characterize economic or social features of the phenomena concerned. For this purpose, multivariate statistics has developed an impressive toolbox, in which traditionally a prominent place is taken by the class of principal component analyses (PCA). This technique dates back to the beginning of the last century and is widely employed in empirical research aiming at reducing complexity in observation spaces toward manageable patterns of a smaller dimensionality. In the present study, we develop and present a new methodological contribution to in the PCA field, by shifting from conventional discrete static data to time-series data approximated by a continuous intertemporal curve reflecting the evolution of the socioeconomic data concerned. In this paper, the statistical foundation of this new approach, called multivariate functional principal component analysis (MFPCA), will be outlined and tested for a multivariate long-range data set on statistical indicators for several countries. The practical validity of the MFPCA method will be demonstrated by means of an application to the evolution of socioeconomic competitiveness (in this paper, we use the WEF definition of competitiveness, which is: "Competitiveness is the set of institutions, policies, and factors that determine the level of productivity of a country" WEF 2015) in different countries of the world, based on official World Economic Forum (WEF) data spanning the period 2008-2015. Our analysis brings to light interesting findings and differences compared to the initial, officially published WEF information.