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Model-based measurement of latent risk in time series with applications


  • Frits Bijleveld
  • Jacques Commandeur
  • Phillip Gould
  • Siem Jan Koopman


Risk is at the centre of many policy decisions in companies, governments and other institutions. The risk of road fatalities concerns local governments in planning countermeasures, the risk and severity of counterparty default concerns bank risk managers daily and the risk of infection has actuarial and epidemiological consequences. However, risk cannot be observed directly and it usually varies over time. We introduce a general multivariate time series model for the analysis of risk based on latent processes for the exposure to an event, the risk of that event occurring and the severity of the event. Linear state space methods can be used for the statistical treatment of the model. The new framework is illustrated for time series of insurance claims, credit card purchases and road safety. It is shown that the general methodology can be effectively used in the assessment of risk. Copyright 2008 Royal Statistical Society.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:jorssa:v:171:y:2008:i:1:p:265-277

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    References listed on IDEAS

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    2. De Jong, Piet & Boyle, Phelim P., 1983. "Monitoring mortality : A state-space approach," Journal of Econometrics, Elsevier, vol. 23(1), pages 131-146, September.
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    4. Linda Allen & Anthony Saunders, 2003. "A survey of cyclical effects in credit risk measurement model," BIS Working Papers 126, Bank for International Settlements.
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    6. Gaudry, M., 1984. "Drag, un Modele de la Demande Routiere, des Accidents et de Leur Gravite, Applique au Quebec de 1956 a 1982," Cahiers de recherche 8432, Universite de Montreal, Departement de sciences economiques.
    7. Lel Li & Karl Kim, 2000. "Estimating driver crash risks based on the extended Bradley-Terry model: an induced exposure method," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 163(2), pages 227-240.
    8. Francesca Dominici & Aidan M.C. Dermott & Trevor J. Hastie, 2004. "Improved Semiparametric Time Series Models of Air Pollution and Mortality," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 938-948, December.
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    Cited by:

    1. 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.
    2. Weijermars, Wendy & Wesemann, Paul, 2013. "Road safety forecasting and ex-ante evaluation of policy in the Netherlands," Transportation Research Part A: Policy and Practice, Elsevier, vol. 52(C), pages 64-72.
    3. 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.

    More about this item

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation


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