Data graduation based on statistical time series methods

Abstract

Whittaker's method is one of the most frequently employed techniques to graduate mortality tables. In order for the method to work and produce reasonable results, some subjective input is required from the graduator. In this paper we show that Whittaker' s solution to the graduation problem can be approached from a statistical time series model-based perspective that reduces the subjectivity in its application. It also serves to interpret the graduation problem as a classical estimation problem. In fact, on the basis of some suitable assumptions, we are able to show thatthe Best Linear Unbiased Estimator of the true mortality rates has the form of Whittaker's solution. We also provide some complementary analytical tools aimed at helping the graduator to employ the method in practice and interpret its results from a statistical standpoint. A numerical illustration is shown in detail to exemplify the application of our proposal.