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Multivariate non-linear time series modelling of exposure and risk in road safety research


  • Frits Bijleveld
  • Jacques Commandeur
  • Siem Jan Koopman
  • Kees van Montfort


A multivariate non-linear time series model for road safety data is presented. The model is applied in a case-study into the development of a yearly time series of numbers of fatal accidents (inside and outside urban areas) and numbers of kilometres driven by motor vehicles in the Netherlands between 1961 and 2000. The model accounts for missing entries in the disaggregated numbers of kilometres driven although the aggregated numbers are observed throughout. We consider a multivariate non-linear time series model for the analysis of these data. The model consists of dynamic unobserved factors for exposure and risk that are related in a non-linear way to the number of fatal accidents. The multivariate dimension of the model is due to its inclusion of multiple time series for inside and outside urban areas. Approximate maximum likelihood methods based on the extended Kalman filter are utilized for the estimation of unknown parameters. The latent factors are estimated by extended smoothing methods. It is concluded that the salient features of the observed time series are captured by the model in a satisfactory way. Copyright (c) 2010 Royal Statistical Society.

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  • Frits Bijleveld & Jacques Commandeur & Siem Jan Koopman & Kees van Montfort, 2010. "Multivariate non-linear time series modelling of exposure and risk in road safety research," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(1), pages 145-161.
  • Handle: RePEc:bla:jorssc:v:59:y:2010:i:1:p:145-161

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    References listed on IDEAS

    1. Frits Bijleveld & Jacques Commandeur & Phillip Gould & Siem Jan Koopman, 2008. "Model-based measurement of latent risk in time series with applications," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(1), pages 265-277.
    2. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
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    Cited by:

    1. Dadashova, Bahar & Ramírez Arenas, Blanca & McWilliams Mira, José & Izquierdo Aparicio, Francisco, 2014. "Explanatory and prediction power of two macro models. An application to van-involved accidents in Spain," Transport Policy, Elsevier, vol. 32(C), pages 203-217.
    2. Ahn, Kwang Woo & Chan, Kung-Sik, 2014. "Approximate conditional least squares estimation of a nonlinear state-space model via an unscented Kalman filter," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 243-254.
    3. repec:bla:jorssa:v:180:y:2017:i:1:p:119-139 is not listed on IDEAS

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