Well chosen inputs such as a window of time-delayed inputs, or intelligently preprocessed inputs, are more important than recurrence.
Neural networks do well on moderately noisy and chaotic time series' such as sunspot data.
A single neural network or genetic program generalizes poorly on weekly stock market indices due to the low signal to noise ratio. When the responses of a number of networks are averaged, the resulting forecast shows substantial profits on historical data. Feedforward and recurrent neural networks and genetic programs for stock market and time series forecasting. Master's thesis, Brown University, June 1993. Doc 862 Introduction to the Theory of Neural Computation - John, Krogh et al.