Rapid design of neural networks for time series prediction

Abstract

The article explores the possibility of rapidly designing an appropriate neural net (NN) for time series prediction based on information obtained from stochastic modeling. Such an analysis could provide some initial knowledge regarding the choice of an NN architecture and parameters, as well as regarding an appropriate data sampling rate. Stochastic analysis provides a complementary approach to previously proposed dynamical system analysis for NN design. Based on E. Takens's theorem (1981), an estimate of the dimension m of the manifold from which the time series originated can be used to construct an NN model using 2m+1 external inputs. This design is further extended by M.A.S. Potts and D.S. Broomhead (1991) who first embed the state space of a discrete time dynamical system in a manifold of dimension n>>2m+1, which is further projected to its 2m+1 principal components used as external inputs in a radial basis function NN model for time series prediction. Our approach is to perform an initial stochastic analysis of the data and to choose an appropriate NN architecture, and possibly initial values for the NN parameters, according to the most adequate linear model.