Autoregressive integrated moving average (ARIMA) models provide a powerful tool for detecting seasonal patterns in mortality statistics. The strength of ARIMA models lies in their ability to reveal complex structures of temporal interdependence in time series. Moreover, changes in model parameters provide an empirical basis for detecting secular trends and death seasonality patterns. This approach is illustrated by our analysis of changes in the mortality patterns of the population of the town of Es Mercadal on the island of Minorca between 1634 and 1997. These data reveal a transition from an early mortality pattern requiring a complex ARIMA model that accounts for a strong seasonal death pattern and periodic epidemic-related mortality crises to a much simpler 20th-century pattern that can be described by a simple single-parameter ARIMA model. These same data were also analyzed using standard seasonality tests. The results show that the reduction in the number of parameters required to fit the Es Mercadal mortality data coincides with the epidemiological transition in which the predominant causes of morbidly and mortality shift from infectious to degenerative causes.