Local multifractality in urban systems—the case study of housing prices in the greater Paris region

Abstract

Even though the study of fractal and multifractal properties has now become an established approach for statistical urban data analysis, the accurate multifractal characterisation of smaller, district-scale spatial units is still a somewhat challenging task. The latter issue is key for understanding complex spatial correlations within urban regions while the methodological challenge can be mainly attributed to inhomogeneous data availability over their territories. We demonstrate how the approach proposed here for the multifractal analysis of irregular marked point processes is able to estimate local self-similarity and intermittency exponents in a satisfactory manner via combining methods from classical multifractal and geographical analysis. With the aim of emphasizing general applicability, we first introduce the procedure on synthetic data using a multifractal random field as mark superposed on two distinct spatial distributions. We go on to illustrate the methodology on the example of home prices in the greater Paris region, France. In the context of complex urban systems, our findings proclaim the need for separately tackling processes on the geolocation (support) and any attached value (mark, e.g. home prices) of geospatial data points in an attempt to fully describe the phenomenon under observation. In particular, the results are indicators of the strength of global and local spatial dependency in the housing price structure and how these build distinct layered patterns within and outside of the municipal boundary. The derived properties are of potential urban policy and strategic planning relevance for the timely identification of local vulnerabilities while they are also intended to be combinable with existing price indices in the regional economics context.