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Iterative Algorithms for detecting mortality trends in the family of Lee Carter Models

In the current literature, there are several papers which have considered the modelling and forecasting of population mortality using the Lee-Carter framework. According to Booth (2006), the Lee-Carter-based approach is widely considered because it produces fairly realistic life expectancy forecasts, which are used as reference values for other modelling methods. In recent years, there have been several extensions of the standard LC method, retaining some of its basic properties, but adding additional statistical features too. In 2006, Renshaw and Haberman developed a special adaptation of the LC method. They transformed the basic LC model into a more general framework in order to analyse the relationship between age and time and their joint impact on the mortality rates. This transformation gave birth to the so-called age-period-cohort (APC) log-bilinear generalized linear models (GLM) with Poisson error structures. In this paper, we take into consideration a family of generalised log-linear models of the LC type structure with Poisson errors that includes the basic LC model too. In this framework, we implement a specialised iterative regression methodology based on Poisson likelihood maximization process. In particular, we make use of the approach proposed and illustrated in Renshaw and Haberman (2006), which generalises the basic LC modelling framework to develop a tailored iterative process for updating the parameter estimates. In order to assess the goodness of fit of the regression, we provide a range of residual analyses with corresponding target fitted values. Diagnostic plots are provided to show the results.