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Model-based Measurement of Latent Risk in Time Series with Applications


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  • Frits Bijleveld

    (SWOV Institute for Road Safety Research, Netherlands)

  • Jacques Commandeur

    (SWOV Institute for Road Safety Research, Netherlands)

  • Phillip Gould

    (Monash University, Melbourne)

  • Siem Jan Koopman

    (Vrije Universiteit Amsterdam)


Risk is at the center of many policy decisions in companies, governments and other institutions. The risk of road fatalities concerns local governments in planning counter- measures, the risk and severity of counterparty default concerns bank risk managers on a daily basis and the risk of infection has actuarial and epidemiological consequences. However, risk can not be observed directly and it usually varies over time. Measuring risk is therefore an important exercise. In this paper we introduce a general multivariate framework for the time series analysis of risk that is modelled as a latent process. The latent risk time series model extends existing approaches by the simultaneous modelling of (i) the exposure to an event, (ii) the risk of that event occurring and (iii) the severity of the event. First, we discuss existing time series approaches for the analysis of risk which have been applied to road safety, actuarial and epidemiological problems. Seco! nd, we present a general model for the analysis of risk and discuss its statistical treatment based on linear state space methods. Third, we apply the methodology to 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.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 05-118/4.

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Date of creation: 19 Dec 2005
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Handle: RePEc:dgr:uvatin:20050118

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Keywords: Actuarial statistics; Dynamic factor analysis; Kalman filter; Maximum likelihood; Road casualties; State space model; Unobserved components;

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  1. Harvey, Andrew, 2001. "Testing in Unobserved Components Models," Journal of Forecasting, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 20(1), pages 1-19, January.
  2. Harvey, A. C., 1986. "The effects of seat belt legislation on British road casualities: A case study in structural modelling : A.C. Harvey and J. Durbing, Journal of the Royal Statistical Society, Series A 149 (1986) (in p," International Journal of Forecasting, Elsevier, Elsevier, vol. 2(4), pages 496-497.
  3. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198523543, October.
  4. B. F. Finkenstädt & B. T. Grenfell, 2000. "Time series modelling of childhood diseases: a dynamical systems approach," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(2), pages 187-205.
  5. Linda Allen & Anthony Saunders, 2003. "A survey of cyclical effects in credit risk measurement model," BIS Working Papers 126, Bank for International Settlements.
  6. Alexander Morton & Bärbel F. Finkenstädt, 2005. "Discrete time modelling of disease incidence time series by using Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 575-594.
  7. 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, American Statistical Association, vol. 99, pages 938-948, December.
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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. 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.


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