A quantitative comparison of the Lee-Carter model under different types of non-Gaussian innovations

Abstract

In the classical Lee-Carter model, the mortality indices that are assumed to be a random walk model with drift are normally distributed. However, for the long-term mortality data, the error terms of the Lee-Carter model and the mortality indices have tails thicker than those of a normal distribution and appear to be skewed. This study therefore adopts five non-Gaussian distributionsStudents t-distribution and its skew extension (i.e., generalised hyperbolic skew Students t-distribution), one finite-activity Lévy model (jump diffusion distribution), and two infinite-activity or pure jump models (variance gamma and normal inverse Gaussian)to model the error terms of the Lee-Carter model. With mortality data from six countries over the period 1900-2007, both in-sample model selection criteria (e.g., Bayesian information criterion, Kolmogorov-Smirnov test, Anderson-Darling test, Cramér-von- Mises test) and out-of-sample projection errors indicate a preference for modelling the Lee-Carter model with non-Gaussian innovations. © 2011 The International Association for the Study of Insurance Economics.