My PhD project was focused on applied and theoretical developments of statistical models which use graphs to represent high-dimensional time series observed on networks.
To test these methods, I used traffic data from an intersection of the motorways M60, M602 and M62 in Manchester, UK.
The Manchester network (from Google Maps)
Road traffic data are very often collected minute-by-minute over long periods of time by using loop detectors. This process generates huge datasets of high-dimensional time series, which can be used as part of an on-line traffic management system to monitor and control traffic flows in order to reduce or prevent congestion. As an example, the Highways Agency in England usually imposes variable speed limits to keep the traffic flowing.
Despite the extensive literature on traffic modelling, very few models take into account the multivariate nature of the data or use all the information available the loop detectors. Also, the majority of these models cannot provide real-time forecasts, which are crucial when immediate actions for alleviating congestion are needed.
Dynamic graphical models represent any conditional independence relationships related to causality across a time series by a graph such as a directed acyclic graph (DAG). This DAG is then used to break the multivariate model into simpler univariate components, and each of which can be modelled by a (conditionally) univariate dynamic model.
This model has already been shown to be promising for real-time multivariate traffic flow forecasting and also in other applications. Additionally, I also developed during my PhD the dynamic chain graph model, which accommodates possible symmetries that may be present in any network. This new model can provide better forecasts when compared to dynamic graphical models based on DAGs.