Bayesian Trend Selection

Motivation. Selecting loss ratio trends is an integral part of NCCI aggregate ratemaking. The trend selection draws on an exponential trend (ET) regression model that is applied, alternatively, to the latest 5, 8, and 15 observations (dubbed 5-point, 8-point, and 15-point ET). Then, using actuarial judgment (which may account for a variety of influences), the three estimates are aggregated into a single forecast. This process of decision making under uncertainty can be formalized using Bayesian model selection.

Method. A Bayesian trend selection (BTS) model is introduced that averages across the three ET models. Using a double-exponential likelihood, this model minimize s the sum of absolute forecast errors for a set of (overlapping) holdout periods. The model selection is accomplished by means of a categorical distribution with a Dirichlet prior. The model is estimated by way of Markov chain Monte Carlo simulation (MCMC).

Results. The BTS is validated on data from past ratemaking seasons. Further, the robustness of the model is examined for past ratemaking data and a long series of injury (and illness) incidence rates for the manufacturing industry. In both cases, the performance of the BTS is compared to the 5-point, 8-point, and 15-point ET, using the random walk as a benchmark. Finally, for the purpose of illustration, the BTS is implemented for an unidentified state.

Availability. The model was implemented in R (cran.r-project .org/), using the sampling platform JAGS (Just Another Gibbs Sampler, www-ice.iarc.fr/~martyn/software/jags/). JAGS was linked to R via the R package rjags (cran.r-project.org/webpackages/rjags/index.html).

Keywords. Model Selection, Model Averaging, Model Robustness, Aggregate Ratemaking, Trend Estimation, Workers Compensation