Autocorrelation in Stochastic Models of Dutch Mortality Rates

Abstract

This paper studies different stochastic mortality models with respect to its underlying assumptions. The Lee-Carter model, the rank-p SVD approximation model, the Weighted Least Squares model and the Poisson Bilinear model are discussed and applied to a Dutch data set. In an empirical analysis, it is illustrated how to obtain parameter estimates and how mortality rates can be forecasted. In a second step, the paper examines the model’s underlying assumptions on a residual basis. Several tests are employed testing for normality, homogeneity of variance and autocorrelation. The test results seem to invalidate the models applicability due to failure in the underlying assumptions. In particular the crucial assumption of observational independence does not seem to hold, which may result in prediction intervals that are too narrow. Furthermore, a theoretical explanation for autocorrelation is given and an alternative model (multivariate ARIMA model) is proposed, that does not only rely on a weaker set of assumptions, but also requires less computational effort. Comparing the initial models’ estimates with the estimates of the alternative model, it is concluded that all five stochastic mortality models tend to deliver similar estimates.