Stochastic neural networks and their applications to regression analysis and time series forecasting.

摘要

Neural networks recently attracted a lot of attention from a variety of disciplines including engineering, finance, computer science, applied mathematics and statistics. Although the methodology has been claimed to be successful in different areas, the commonly-used estimation algorithm "back-propagation" is still difficult to apply, especially when the number of parameters is large.; In order to ease the estimation difficulty, we propose a new model, namely, the stochastic neural network (SNN). SNN shares the universal approximation property with the neural networks and provides a parallel estimation procedure which is an application of the EM algorithm (Dempster, Laird and Rubin (1977)). Besides, we provide a stepwise model selection procedure for SNN to avoid overfitting. Both estimation and model selection procedures are shown to be successful in simulated and real examples.; Another popular application of neural networks is time series forecasting. An easy-to-check condition for the geometric ergodicity of SNN is given. SNN gives reliable non-linear forecasts for various simulated and real time series.