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To predict the 100 missing values from the time series consisting of 5000 data given for the IJCNN 2004 time series prediction competition, we applied an architecture which automates the design of recurrent neural networks using a new evolutionary learning algorithm. This new evolutionary learning 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 performed individuals may produce offspring to replace those with poor performance. The novel algorithm is then applied to the recurrent neural network for the time series prediction. The experimental results show that our approach gives good performance in predicting the missing values from the time series.