# Mathias Lindholm: Lexis based mortality forecasting

**Time: **
Wed 2019-03-20 15.15 - 16.15

**Lecturer: **
Mathias Lindholm (Stockholm University)

**Location: ** Room 306, House 6, Kräftriket, Department of Mathematics, Stockholm University ￼

Abstract: A constructive mortality forecasting model is introduced that is based on a data generating process which is defined in terms of continuous-time dynamics of a Lexis diagram. By using counting process arguments the likelihood of the death count data sampled at yearly intervals is shown to be equivalent to that of a certain Poisson likelihood. Based on these observations a Poisson state space model for death counts is introduced where evolution of mortality rates is treated as a latent stochastic process. The latent mortality rate process is driven by a low-dimensional autoregressive process with random drift, where the dimension reduction in a Poisson setting is based on a so-called generalized principal component analysis (GPCA). The full likelihood of the Poisson state space model is not analytically tractable, but it turns out that it is possible to estimate model parameters using the stochastic approximation expectation-maximization (SAEM) algorithm, where sampling is made using particle filter techniques. This circumvents the two-step estimation procedure used for e.g. the Lee-Carter model.

The constructive nature of the introduced model makes it easy to decompose observed variation in terms of population (``Poisson'') variation and variation due to the latent mortality rate process. Moreover, by noting the model's close connection with random effects models, a coefficient of determination-like argument is used to assess to a degree where the model captures adequate variation observed in data.

The modelling approach is illustrated using Swedish and US data, where both in-sample and out-of-sample forecast performance is analyzed. The analysis includes a discussion on choice of starting values and convergence.