Many authors use feedforward neural networks for modeling and forecasting time series. Most of these applications are mainly experimental, and it is often difficult to extract a general methodology from the published studies. In particular, the choice of architecture is a tricky problem. We try to combine the statistical techniques of linear and nonlinear time series with the connectionist approach. The asymptotical properties of the estimators lead us to propose a systematic methodology to determine which weights are nonsignificant and to eliminate them to simplify the architecture. This method (SSM or statistical stepwise method) is compared to other pruning techniques and is applied to some artificial series, to the famous Sunspots benchmark, and to daily electrical consumption data.

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