Unifying mortality forecasting model: an investigation of the COM–Poisson distribution in the GAS model for improved projections

Forecasting mortality rates is crucial for evaluating life insurance company solvency, especially amid disruptions caused by phenomena like COVID-19. The Lee–Carter model is commonly employed in mortality modelling; however, extensions that can encompass count data with diverse distributions, such as the Generalized Autoregressive Score (GAS) model utilizing the COM–Poisson distribution, exhibit potential for enhancing time-to-event forecasting accuracy. Using mortality data from 29 countries, this research evaluates various distributions and determines that the COM–Poisson model surpasses the Poisson, binomial, and negative binomial distributions in forecasting mortality rates. The one-step forecasting capability of the GAS model offers distinct advantages, while the COM–Poisson distribution demonstrates enhanced flexibility and versatility by accommodating various distributions, including Poisson and negative binomial. Ultimately, the study determines that the COM–Poisson GAS model is an effective instrument for examining time series data on mortality rates, particularly when facing time-varying parameters and non-conventional data distributions.