Two contradictory approaches—an equilibrium view based on neoclassical economic principles and a structuralist view based on labour needs of core economies—dominate contemporary international migration research. Using a monthly times-series for Essen, Sweden, and France for 1952–1982 of immigration by different nationalities, a specific hypothesis derived from the neoclassical view, relating immigration to economic growth and stagnation, was tested using the Box—Jenkins ARIMA modelling approach. The local labour market of Essen provided the only consistent support for the hypothesis. Most migration flows are described by complex ARIMA models. Immigration legislation had a stronger and more direct effect on the strength and timing of flows than economic trends. Predictions based on univariate and bivariate models are not very useful: immigration trends over the past decade are significantly different from earlier flows.