The forecasting power of different methods is tested utilizing crime data for 1120 inland municipalities in Colombia. Using data from 2003 to 2018, five different forecasting methods are used: ETS, ARIMA, STAR, a classical beta convergence based model, and a spatial beta convergence model. First, it is shown that overall municipal crime disparities are steadily decreasing over time. This indicates that convergence and spatial effects are pivotal for the study of the dynamics of crime in Colombian municipalities. Time series cross-validation for 4-year ahead forecasts is implemented to assess the accuracy of all models. It is found that the STAR and the beta models have the lowest root mean squared errors. Therefore, as time goes by, space appears to play a more important role in the evolution of homicide rates. The paper concludes with some policy implications in terms of spatial effects and the mitigation of crime.