In this paper, we propose a retrospective prediction method using econometric regression and ARIMA models combined with the Factor Analysis technique. We have applied it to the reconstruction of the demographic variable births during the eighteenth and nineteenth centuries in the province of Almería. The method is practical when the treatment of a large number of populations (parishes/municipalities) is required and, in relation to other possible prediction methods, the one we present here has the advantage that it only requires as information the previous data of the series itself. Additionally, it provides a statistical indicator of the margin of error that we can tolerate in each forecast. The model presented is useful for medium- and short-term forecasts. Accepting the disadvantage in applications when the time trend does not maintain for many years, the method makes it possible to approximate the forecasts.