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.

Modelling Route Choice Decisions of Car Travellers Using Combined GPS and Diary Data

“…traffic safety, reliability of travel times (Papinski et al, 2009)), and situational variables (e.g. weather conditions (Cools et al, 2010a, Cools et al, 2010c, holiday effects (Cools et al, 2009, Cools et al, 2010b and traffic information (Zhang and Levinson, 2008)). Moreover, future research should extent to other transport modes such as walking, bicycle use, public transport and carpooling.…”

The use of time series forecasting in zone order picking systems to predict order pickers’ workload

“…A spectral analysis is a statistical method to detect regular cyclical patterns. The reader is referred to Cools, Moons, and Wets (2009) for a more extensive description of a spectral analysis. By looking at the results of the spectral analysis presented in figure 2, both a semi-weekly and weekly recurring cycle can be identified in the data as indicated by respectively the global maximum at period 2.5 and the local maximum at period 5.…”

“…This model is known as an autoregressive integrated moving average (ARIMA) forecasting model. The forecasting value is calculated by the sum of last observation and a forecast shift compared to last period (Athanasopoulos et al 2011;Chase Jr 2013;Cools, Moons, and Wets 2009). While the ARIMA model is able to eliminate trends, the full SARIMA model, as represented by equation 1, is able to additionally take seasonal cycles into account.…”

“…By seasonal differencing, both trend and seasonal patterns can be eliminated at once. Therefore, the resulting time series may become stationary and require no further differencing (Athanasopoulos et al 2011;Chase Jr 2013;Cools, Moons, and Wets 2009).…”

“…Those dummy variables represent the first four working days of the week (i.e., Monday, Tuesday, Wednesday, and Thursday). Friday is used as reference day to prevent multicollinearity (Cools, Moons, and Wets 2009).…”