A Non-Parametric Hawkes Process Model of Primary and Secondary Accidents on a UK Smart Motorway. Issue 1 (20th January 2021)

• Record Type: Journal Article
• Authors: Kalair, Kieran; Connaughton, Colm; Alaimo Di Loro, Pierfrancesco
• Is Part Of: Journal of the Royal Statistical Society. Volume 70:Issue 1(2021)
• Page Start: 80
• Page End: 97
• Publication Date: 2021-01-20
• Subjects: Hawkes processes -- non-parametric -- smart motorways -- traffic incidents; Statistics -- Periodicals; 519.5
• DOI: 10.1111/rssc.12450
• Languages: English
• ISSNs: 0035-9254

Abstract

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.