Many physical and artificial phenomena can be described by time series. The prediction of such phenomenon could be as complex as interesting. There are many time series forecasting methods, but most of them only look for general rules to predict the whole series. The main problem is that time series usually have local behaviours that don’t allow forecasting the time series by general rules. In this paper, a new method for finding local prediction rules is presented. Those local prediction rules can attain a better general prediction accuracy. The method presented in this paper is based on the evolution of a rule system encoded following a Michigan approach. For testing this method, several time series domains have been used: a widely known artificial one, the Mackey-Glass time series, and two real world ones, the Venice Lagon and the sunspot time series.