The functional distance-based approach: An application on long-term Metropolitan Development

Metropolitan development is a complex phenomenon depending on the joint action of multiple socioeconomic and territorial factors, which are generally quantified through indicators interacting across spatial and temporal scales. A comprehensive understanding of metropolitan development requires a detailed examination of the dependence structure within the development trajectories of both urban and suburban areas. Multidimensionality, non-linearity, and evolutionary components at the base of metropolitan development should be jointly considered when investigating the socioeconomic mechanisms underlying the long-term expansion of cities and their surrounding regions. In this multidimensional perspective, the Functional Data Analysis approach enables the simultaneous investigation of the level and evolution over time of multiple socioeconomic processes through summary functional measures, such as the modified hypograph index and the weighted integrated first derivative. Starting from these tools, a functional distance-based approach is proposed to study the relationship between urban and suburban areas from a twofold perspective: focusing on the entire set of metropolitan development indicators, and considering each dimension individually. This approach contributes to overpass the limitations of standard econometric approaches offering a multivariate measure of change in local systems experiencing complex development trajectories. The proposal is illustrated via a simulation study and a real data set.