A Feed-Forward Neural Networks-Based Nonlinear Autoregressive Model for Forecasting Time Series

Abstract

Abstract. In this work a feed-forward NN based NAR model for forecasting time series is presented. The learning rule used to adjust the NN weights is based on the Levenberg-Marquardt method. In function of the long or short term stochastic dependence of the time series, we propose an on-line heuristic law to set the training process and to modify the NN topology. The approach is tested over five time series obtained from samples of the Mackey-Glass delay differential equations and from monthly cumulative rainfall. Three sets of parameters for MG solution were used, whereas the monthly cumulative rainfall belongs to two different sites and times period, La Perla 1962-1971 and Santa Francisca 200-2010, both located at Córdoba, Argentina. The approach performance presented is shown by forecasting the 18 future values from each time series simulated by a Monte Carlo of 500 trials with fractional Gaussian noise to specify the variance.