Mortality Models based on the Transform $\log(-\log x)$

TL;DR

This paper introduces a novel stochastic mortality model based on the transform log(-log x)", which captures simple patterns in mortality data and can outperform traditional models like Lee-Carter and Cairns-Blake-Dowd in certain scenarios.

Contribution

It proposes a new mortality modeling approach using the transform log(-log x)", with a representation based on age-constants and stochastic processes, improving forecasting accuracy.

Findings

The new model fits some mortality data better than traditional models.

It provides straightforward mortality projections from the time-processes.

Performance varies depending on data and context.

Abstract

A new stochastic method for describing mortality is proposed and explored. It is based on differences of observed times series of the transform $\log(-\log x)$ of survival probabilities which seem to follow simple patterns over the years. These common structures are gathered by a representation based on age-constants and time-stochastic processes. From the projection of the time-processes the mortality forecasting is straigthforward. Comparisons of the new model with the well-known Lee-Carter and Cairns-Blake-Dowd models employing sex-based mortality data of some countries are provided. Some in-sample and out-of-sample goodness-of-fit criteria show that in some situations the new model performs better than the ones mentioned above. Assessments of the performance of these models using rates of mortality improvement are discussed.