| Summary: | Research on using autoregressive neural networks to forecast nonlinear time series has produced mixed results. While neural networks have been established as universal approximators, large-scale studies comparing neural network forecasts with simpler models have rarely shown better performance for the neural network model. In the best cases, the neural network models prevail only after careful tuning. === We examine the simplest case of an autoregressive neural network, where the current value of Yt is dependent on a function of one lag with one shortcut connection and one hidden unit. We find that even when data are generated from the autoregressive neural network, the location of the series attraction point often leads to data that exhibit little nonlinear behavior. We use these results as a guide in extending traditional theory on nonlinear time series models. Our added theory is used to select parameter values for a simulation and to generate starting values for training a neural network. Performance for different methods of estimating forecasts are compared. We find that even for our relatively simple neural network, where we know the correct number of hidden units, estimating the parameters is a nontrivial task, and forecasts should be approached with caution. === The one-lag, one hidden unit model is then applied to a time series from an experiment in engineering. We find that the methods developed in this paper work well for this data and have promise in applications where measurements are taken often using a computerized setup.
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