Artificial neural networks (NNs) are widely used in modeling and forecasting time series. Since most practical time series are non-stationary, NN forecasters are often implemented using recurrent/delayed connections to handle the temporal component of the time varying sequence. These recurrent/delayed connections increase the number of weights required to be optimized during training of the NN. Particle swarm optimization (PSO) is now an established method for training NNs, and was shown in several studies to outperform the classical backpropagation training algorithm. The original PSO was, however, designed for static environments. In dealing with non-stationary data, modified versions of PSOs for optimization in dynamic environments are used. These dynamic PSOs have been successfully used to train NNs on classification problems under non-stationary environments. This paper formulates training of a NN forecaster as dynamic optimization problem to investigate if recurrent/delayed connections are necessary in a NN time series forecaster when a dynamic PSO is used as the training algorithm. Experiments were carried out on eight forecasting problems. For each problem, a feedforward NN (FNN) is trained with a dynamic PSO algorithm and the performance is compared to that obtained from four different types of recurrent NNs (RNN) each trained using gradient descent, a standard PSO for static environments and the dynamic PSO algorithm. The RNNs employed were an Elman NN, a Jordan NN, a multirecurrent NN and a time delay NN. The performance of these forecasting models were evaluated under three different dynamic environmental scenarios. The results show that the FNNs trained with the dynamic PSO significantly outperformed all the RNNs trained using any of the other algorithms considered. These findings highlight that recurrent/delayed connections are not necessary in NNs used for time series forecasting (for the time series considered in this study) as long as a dynamic PSO algorithm is used as the training method.