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.