Enhancing on-line multivariate flow forecasts for road traffic networks Osvaldo Anacleto * Department of Mathematics and Statistics, The Open University Catriona Queen Department of Mathematics and Statistics, The Open University Casper Albers Department of Psychometrics and Statistics, University of Groningen Abstract Traffic flow data are routinely collected for many networks worldwide. These in- variably very large data sets can be used as part of a traffic management system, for which good short-term traffic flow forecasting models are crucial. The linear multi- regression dynamic model (LMDM) has been shown to be promising for forecasting flows, accommodating high-dimensional, 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 — namely occupancy, headway and speed — each of which has a non-linear relationship with flow. This paper investigates how cubic splines can be used to in- corporate these extra variables into the LMDM in order to enhance flow forecasts. Cubic splines are also introduced into the LMDM for accommodating the daily cycle exhibited by traffic flows. The paper focuses on flow forecasts at a busy motorway intersection near Manchester, UK. Keywords: linear multiregression dynamic model, dynamic linear model, cubic splines, oc- cupancy, headway, speed. * Corresponding author (o.anacleto-junior@open.ac.uk). The authors thank the Highways Agency for providing the data used in this paper and also Les Lyman from Mott MacDonald for valuable discussions on preliminary data analyses. 1