Fourier Series for Seasonal Traffic Forecasting: An Application to a Real Toll Road Concession in Colombia

Abstract

Toll road concessions are instruments used by governments to transfer risks and finance infrastructure projects needed to sustain economic development. However, these projects are plagued by heavy uncertainties, in part because their free cash flows are affected by unreliable traffic demand forecasts. Accordingly, this study analyses the literature on the field of project evaluation in concessions to extract common practices when forecasting traffic demand. From this information, this research assesses the most common traffic forecasting methods and proposes a new approach that might address flaws in the estimation methods existing in the literature. Thus, the study compares Geometric Brownian Motion (GBM), Mean Reversion (MR), and Fourier series models (FSM). The comparison evaluates the best-fit patterns in traffic demand forecasts given the long-horizon feature of toll road concessions and uncertainty. The models use the historical traffic demand of a real concession initiative within Colombia’s Fourth Generation Roads Concession Program (4G). The results indicate that the Fourier series outperform GBM and MR when forecasting seasonal traffic. Because this finding was obtained from a real toll road with marked seasonality, the study opens a path for further research in traffic forecasting for seasonal behavior.