Forecasting Actuarial Time Series: A Practical Study of the Effect of Statistical Pre-Adjustments

One of the most important risks in the actuarial industry is the longevity risk. The accurate prediction of mortality rates plays a crucial role in the management of the aforementioned risk. Such predictions are performed by modelling the mortality rates using mortality models. Aiming at possible improvements in such forecasts, in this work we examine the effect of data transformation and “linearization” on the quality of time series forecasts of mortality rate data. By the term time series “linearization” is meant the treatment of causes that disrupt the underlying stochastic process measured by a time series. The dataset consists of the time series of the period indices uncovering the mortality trend for England-Wales according to published mortality models. Results indicate a clear improvement in interval forecasts. However, the result on point forecasts is not as clear as is the case of interval forecasts. The documented improvement in interval forecasts can significantly affect the Solvency Capital Requirement, and subsequently the Solvency Ratio for a pension fund. Such an improvement might put some pension providers at a competitive advantage as they have less capital locked in their liabilities. In addition, it was confirmed that the transformed-linearized time series of mortality rates satisfy to a higher extent the need for normality as compared to the original series.