Investigating the Variability in Daily Traffic Counts through use of ARIMAX and SARIMAX Models

Abstract

In this paper, daily traffic counts are explained and forecast by different modeling philosophies: an approach using autoregressive integrated moving average (ARIMA) models with explanatory variables (i.e., the ARIMAX model) and approaches using a seasonal autoregressive integrated moving average (SARIMA) model as well as a SARIMA model with explanatory variables (i.e., the SARIMAX model). Special emphasis is placed on the investigation of seasonality in daily traffic data and on the identification and comparison of holiday effects at different sites. To get insight into prior cyclic patterns in the daily traffic counts, spectral analysis provides the required framework to highlight periodicities in the data. The analyses use data from single inductive loop detectors, which were collected in 2003, 2004, and 2005. Four traffic count locations are investigated in this study: an upstream and a downstream traffic count site on a highway used extensively by commuters, and an upstream and a downstream traffic count site on a highway typically used for leisure travel. The different modeling techniques show that weekly cycles appear to determine the variation in daily traffic counts. The comparison between seasonal and holiday effects at different site locations reveals that both the ARIMAX and the SARIMAX modeling approaches are valid frameworks for identifying and quantifying possible influencing effects. The techniques yield the insight that holidays have a noticeable impact on highways extensively used by commuters, while having a more ambiguous impact on highways typically used for leisure travel. Future research challenges are the modeling of daily traffic counts on secondary roads and the simultaneous modeling of underlying reasons for travel and revealed traffic patterns.