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.

Time Series: State Space Methods

“…Bijleveld et al (2008) provide further discussions on the latent risk model and show how the general methodology can be effectively used in the assessment of risk. Typical applications for the latent risk model are for studies on insurance claims, credit card purchases, and road safety.…”

Setting Road Safety Targets in Cambodia: A Methodological Demonstration Using the Latent Risk Time Series Model

“…Travel volume data might have been an even better proxy for exposure but these are not available in Cambodia. Different types of models have been used for the extrapolation of time trends in fatality rates, ranging from deterministic models such as classic linear regression models (e.g., [14]), log-linear regression models (e.g., [14,15]), and logistic and exponential models [16] to more advanced stochastic models like ARIMA models (e.g., [17]), the DRAG model [18], and structural time series models (e.g., [19][20][21]). Deterministic models are not well-equipped to handle the dependencies inherently present in time series observations, while stochastic models are.…”

“…This is especially important when it comes to the proper use of statistical tests and to the construction of appropriate confidence limits; see Commandeur et al [22] for details. In order to obtain forecasts of the fatality risk in 2011-2020 in Cambodia it was decided to apply a dedicated structural time series model allowing for the simultaneous analysis of fatalities and motor vehicle data called the latent risk time series model [19].…”

Fitting State Space Models withEViews

“…Section 2 presents the specification of a local level model for data on the annual flow volume from the river Nile in Aswan . Section 3 shows how a "latent risk model" (Bijleveld, Commandeur, Gould, and Koopman 2008) applied to Belgian road accident and exposure data can be developed and estimated in EViews. Section 4 concludes.…”

“…In this section we show how the latent risk model (Bijleveld et al 2008) can be fitted in EViews. Apart from the model specification, an iteration program is presented that can be used to facilitate convergence of the optimization procedure.…”