This study investigates how alternative ARIMA model specifications can be used to infer the underlying trend structure—deterministic or stochastic—of the life expectancy at birth time series for the Italian population over the period 1974–2024. By comparing two ARIMA(1,d,0) models and two ARIMA(1,d,1) models, each estimated with and without a deterministic trend component, we aim to assess not only forecast accuracy but also the capacity of each model to capture the structural dynamics of the series, particularly in the presence of exogenous shocks. The COVID-19 outbreak in 2020 is treated as a structural shock and serves as a testing ground for evaluating model adaptability and long-run behavior. Our analysis employs stationarity tests, residual diagnostics, impulse response functions (IRFs), model fit statistics, and forecast error measures. Results indicate that while trend-based ARIMA models tend to provide better in-sample statistical fit, they often fail to capture the persistent deviations induced by structural breaks. In contrast, the ARIMA(1,d,1) model without a deterministic trend offers greater flexibility and superior post-shock forecasting performance. The paper concludes by proposing a structured approach to model selection under structural uncertainty, highlighting how comparative model analysis can inform our understanding of time series behavior over a given historical period.