Stochastic neural networks with applications to nonlinear time series

we consider a variant of the conventional neural network model, called the stochastic neural network, that can be used to approximate complex nonlinea r stochastic systems. We show how the expectation-maximization algorithm ca n be used to develop efficient estimation schemes that have much lower comp utational complexity than those for conventional neural networks. This enab les us to carry out model selection procedures, such as the Bayesian inform ation criterion, to choose the number of hidden units and the input variabl es for each hidden unit. Stochastic neural networks are shown to have the u niversal approximation property of neural networks. Other important propert ies of the proposed model are given, and model-based multistep-ahead foreca sts are provided. We fit stochastic neural network models to several real a nd simulated time series. Results show that the fitted models improve post- sample forecasts over conventional neural networks and other nonlinear and nonparametric models.