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Recently, Particle Swarm Optimization PSO has evolved as a promising alternative to the standard backpropagation BP algorithm for training Artificial Neural Networks ANNs. PSO is advantageous due to its high search power, fast convergence rate and capability of providing global optimal solution. In this paper, the authors explore the improvements in forecasting accuracies of feedforward as well as recurrent neural networks through training with PSO. Three widely popular versions of the basic PSO algorithm, viz. Trelea-I, Trelea-II and Clerc-Type1 are used to train feedforward ANN FANN and Elman ANN EANN models. A novel nonlinear hybrid architecture is proposed to incorporate the training strengths of all these three PSO algorithms. Experiments are conducted on four real-world time series with the three forecasting models, viz. Box-Jenkins, FANN and EANN. Obtained results clearly demonstrate the superior forecasting performances of all three PSO algorithms over their BP counterpart for both FANN as well as EANN models. Both PSO and BP based neural networks also achieved notably better accuracies than the statistical Box-Jenkins methods. The forecasting performances of the neural network models are further improved through the proposed hybrid PSO framework.