Motivation: Estimating the trend of the severity, frequency, and loss ratio rates of growth is an integral part of NCCI ratemaking. The time series from which such trend estimation has to be derived are typically short and volatile, comprising only 19 observations or, equivalently, 18 rates of growth. Thus, separating signal (i.e., trend) from (white) noise is particularly challenging.
Method: NCCI has developed a Bayesian Statistical Trend model that is geared toward extracting the trend in short and high-volatility time series. This model has been optimized by minimizing the root mean squared prediction error across NCCI states using three-year hold-out periods (as the applicable forecasting horizon is typically around three years).
Results: We present trend estimates for severity, frequency, and loss ratio rates of growth for an unidentified state. The model is robust to outliers and delivers stable, yet time-varying trend estimates.
Conclusions: The statistical properties of the model are conducive to rate stability and, at the same time, allow the practicing actuary to recognize changes in trend.
Availability: The model runs in WinBUGS 1.4.3 (https://www.mrc-bsu.cam.ac.uk/?s=WinBUGS) within the R (https://www.r-project.org/) package R2WinBUGS (http://cran.r-project.org). WinBUGS is administered by the MRC Biostatistics Unit, University of Cambridge, UK; R is administered by the Technical University of Vienna, Austria. WinBUGS and R are GNU projects of the Free Software Foundation and hence available free of charge.
Keywords: Trend and loss development; Bayesian methods; time series; Workers Compensation.
