Traffic flow data are routinely collected for many networks worldwide. These invariably large data sets can be used as part of a traffic management system, for which good traffic flow forecasting models are crucial. The linear multiregression dynamic model (LMDM) has been shown to be promising for forecasting flows, accommodating multivariate flow time series, while being a computationally simple model to use. While statistical flow forecasting models usually base their forecasts on flow data alone, data for other traffic variables are also routinely collected. This paper shows how cubic splines can be used to incorporate extra variables into the LMDM in order to enhance flow forecasts. Cubic splines are also introduced into the LMDM to parsimoniously accommodate the daily cycle exhibited by traffic flows.
The proposed methodology allows the LMDM to provide more accurate forecasts when forecasting flows in a real high-dimensional traffic data set. The resulting extended LMDM can deal with some important traffic modelling issues not usually considered in flow forecasting models. Additionally, the model can be implemented in a real-time environment, a crucial requirement for traffic management systems designed to support decisions and actions to alleviate congestion and keep traffic flowing.