Background The rising life expectancy at birth marks a significant victory for modern medicine and public health initiatives. Advances in medical technology, improved healthcare services, enhanced nutrition, and greater awareness of health and wellness have all contributed to prolonging the average human lifespan. In recent decades, many countries, particularly in Europe, have seen life expectancy at birth surpass previous historical limits. This increase significantly affects public health, economics, and social structures. As populations age, the demand for healthcare services, long-term care, and pensions increases, adding strain on both public and private sectors. These shifts necessitate modifications in social services, healthcare delivery, and pension plans to accommodate an older demographic. Therefore, accurate forecasts of life expectancy at birth are crucial for governments and organizations to make well-informed decisions and effectively plan for future demographic changes. Forecasting life expectancy at birth has become central to demographic research due to its pivotal role in planning and policy formulation.

Methods Numerous studies have introduced various methods and techniques to predict future life expectancy, utilizing a broad array of statistical tools and models. These methods range from simple linear projections based on historical data to complex models that incorporate multiple variables and sophisticated statistical techniques. Despite the availability of numerous forecasting methods, there is a notable gap in the literature concerning systematic evaluations of these techniques, as most studies focus on creating new forecasting methods or refining existing models to increase predictive accuracy. This study addresses this gap by examining the performance of two principal econometric models, namely the Autoregressive Integrated Moving Average (ARIMA) and the Vector Error Correction (VEC) model, in predicting future life expectancy at birth in Europe. These models represent different approaches to time series forecasting, each with distinct assumptions and capabilities. This research used Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and the Diebold-Mariano (DM) tests to compare the forecast accuracy of the two models.

Results The results from RMSE and MAE showed that the ARIMA model better predicted future life expectancy at birth for half of the European countries in this study, while the VEC model was more accurate for the other half. The DM test indicated statistically significant differences in forecast accuracy between the ARIMA and VEC models in some European countries.

Conclusions This study aimed to determine which model delivers the most accurate and reliable predictions by comparing these models in predicting future life expectancy at birth across several European countries. Such insights are crucial for policymakers, planners, and researchers developing health systems and social policies tailored to an aging European population.