Fourier Analysis of an Expanded Gravity Model for Spatio-Temporal Interactions

Fourier analysis and cross-correlation function are successfully applied to improving the conventional gravity model of interaction between cities by introducing a time variable to the attraction measures (e.g., city sizes). The traditional model assumes spatial interaction as instantaneous, while the new model considers the interaction as a temporal process and measures it as an aggregation over a period of time. By doing so, the new model not only is more theoretically sound, but also enables us to integrate the analysis of temporal process into spatial interaction modeling. Based on cross-correlation function, the developed model is calibrated by Fourier analysis techniques, and the computation process is demonstrated in four steps. The paper uses a simple case study to illustrate the approach to modeling the interurban interaction, and highlight the relationship between the new model and the conventional gravity model.