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

Abstract

Summary.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.

Road Safety Trends at National Level in Europe: A Review of Time-series Analysis Performed during the Period 2000–12

“…A recent example of stochastic and multivariate approach is the latent risk time series (LRT) modelling (Bijleveld, 2008;Bijleveld, Commandeur, Gould, & Koopman, 2008) which applies to risk in general. In the case of road risk, both the accident risk and the fatality risk may be modelled.…”

Latent risk and trend models for the evolution of annual fatality numbers in 30 European countries

“…So far, it had only been applied to individual countries (e.g., Bijleveld et al, 2008;Van den Bossche et al, 2007;Antoniou and Yannis, 2013). The present study is the first large scale field trial to model road traffic fatalities in terms of fatality risk and exposure to that risk using structural time series methods.…”

“…This specification is identical to the specification of the local linear trend model (see Harvey, 1989;Commandeur and Koopman, 2007;Durbin and Koopman, 2012). 1 We can now provide the complete formulation of the LRT model as it was presented in Bijleveld et al (2008): log(Traffic Volume t ) = level(log(Exposure t )) + ε e t level(log(Exposure t+1 ) = level(log(Exposure t )…”