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A non‐parametric Hawkes process model of primary and secondary accidents on a UK smart motorway

Kieran Kalair, Colm Connaughton and Pierfrancesco Alaimo Di Loro

Journal of the Royal Statistical Society Series C, 2021, vol. 70, issue 1, 80-97

Abstract: A self‐exciting spatiotemporal point process is fitted to incident data from the UK National Traffic Information Service to model the rates of primary and secondary accidents on the M25 motorway in a 12‐month period during 2017–2018. This process uses a background component to represent primary accidents, and a self‐exciting component to represent secondary accidents. The background consists of periodic daily and weekly components, a spatial component and a long‐term trend. The self‐exciting components are decaying, unidirectional functions of space and time. These components are determined via kernel smoothing and likelihood estimation. Temporally, the background is stable across seasons with a daily double peak structure reflecting commuting patterns. Spatially, there are two peaks in intensity, one of which becomes more pronounced during the study period. Self‐excitation accounts for 6–7% of the data with associated time and length scales around 100 min and 1 km, respectively. In‐sample and out‐of‐sample validation are performed to assess the model fit. When we restrict the data to incidents that resulted in large speed drops on the network, the results remain coherent.

Date: 2021
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