Modelos Lee-Carter via SVD e GLM Poisson: um estudo comparativo aplicado à mortalidade no Brasil

Abstract

Mortality forecasting plays a relevant role in actuarial, pension and demographic applications, since it affects the definition of biometric assumptions, the assessment of liabilities and the measurement of longevity risk. In the Brazilian case, this discussion becomes especially important due to the need to work with recent age- and sex-specific series and to assess empirically how methodological choices affect predictive performance. In this context, the predictive performance of two estimation strategies for the Lee-Carter model applied to Brazilian mortality by sex is compared: the classical singular value decomposition approach (LC-SVD) and the generalized linear model formulation with Poisson distribution and exposure offset (LC-Poisson). The analytical database was built for Brazil over the period from 1994 to 2022, covering ages 0 to 90 and the groups male, female and total. The empirical assessment was carried out through backtesting with a fixed split, using 1994 to 2017 for estimation and 2018 to 2022 for testing, with forecasting horizons from 1 to 5 years ahead. Model comparison was based on mean absolute error and root mean squared error, computed on both the original and logarithmic scales, with and without exposure weighting, and complemented by graphical analysis of estimated parameters, observed and predicted trajectories, and the distribution of errors by age and year. The results indicate an advantage for LC-Poisson over shorter horizons, especially one- and two-year-ahead forecasts, whereas LC-SVD becomes relatively more competitive in part of the longer-term horizons. The largest errors were concentrated at older ages and in the most recent years of the testing period, particularly under the impact of the COVID-19 pandemic. It is concluded that the choice of estimation method has a relevant effect on the predictive performance of the Lee-Carter model in the Brazilian case.