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To predict the 100 missing values from a time series of 5000 data points, given for the IJCNN 2004 time series prediction competition, recurrent neural networks (RNNs) are trained with a new learning algorithm. This training algorithm is based on a hybrid of particle swarm optimization (PSO) and evolutionary algorithm (EA). By combining the searching abilities of these two global optimization methods, the evolution of individuals is no longer restricted to be in the same generation, and better performing individuals may produce offspring to replace those with poor performance. Experimental results show that RNNs, trained by the hybrid algorithm, are able to predict the missing values in the time series with minimum error, in comparison with those trained with standard EA and PSO algorithms.