Abstract

In this work a feed-forward neural networks (NN) based nonlinear autoregressive filter (NAR) approach for forecasting cumulative monthly rainfall time series is presented. The filter parameter adjustment is performed in accordance with time series roughness. This method has concordance with the long or short term stochastic dependence of the time series and the proposal is 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 2000-2010, 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. The results of the forecasting shows a good performance of the predictor system applied to time series from several benchmark of MG equations and monthly cumulative rainfall time series owing to similar roughness between the original and the stochastic forecasted time series, evaluated by Hand H_e, respectively. These have a promising scope for a sort of rough time series, like rainfall time series and serve to be applied to meteorological variables as soil moisture, humidity.

Key words: Neural networks, rainfall, time series forecast, Hurst’s parameter, Mackey-Glass.