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This paper presents an study about a new Hybrid method -GRASPES - for time series prediction, inspired in F. Takens theorem and based on a multi-start metaheuristic for combinatorial problems - Greedy Randomized Adaptive Search Procedure(GRASP) - and Evolutionary Strategies (ES) concepts. The GRAPES tuning and evolve the Artificial Neural Network parameters configuration, the weights and the minimum number of (and their specific) relevant time lags, searching an optimal or sub-optimal forecasting model for a correct time series representation. An experimental investigation is conducted with the GRASPES with some time series and the results achieved are discussed and compared, according to five well-known performance measures, to other works reported in the literature.