Exploring long-term urban cycles with multivariate time-series analysis

European cities underwent long-term socioeconomic transformations resulting in a shift from centralized demographic growth typical of late industrialization to a more recent (and spatially uncoordinated) de-concentration of population and economic activities. While abandoning traditional compact models and moving toward settlement dispersion, population growth in urban areas was assumed to follow a “life cycle” constituted of four developmental stages (urbanization, suburbanization, counter-urbanization, and re-urbanization). We studied anomalies in the City Life Cycle (CLC) of a large metropolitan region (Athens, Greece) with the aim at achieving a less mechanistic interpretation of long-term population growth in complex social contexts. Using population data that cover more than 170 years (1848–2020) and multivariate time-series analysis, a non-linear growth history was delineated, with sequential accelerations and decelerations characteristic of the first CLC stage (urbanization). Considering the classical division in three radio-centric districts (core, ring, and agglomeration), different development stages coexisted since World War II. Heterogeneous suburbanization processes mixed up with late urbanization and weaker impulses of counter-urbanization and re-urbanization. The empirical results of time-series analysis confirm the non-linear expansion of Athens, shedding further light on long-term mechanisms of metropolitan development and informing management policies of urban growth.