Forecasting noisy time series approximated by neural networks

Abstract

In this work, a proposed methodology for univariate noisy time series prediction approximated by artificial neural networks (ANN) is applied to the problem of forecasting monthly rainfall precipitation in Cuesta El Portezuelo at Catamarca, province of Argentina (- 28°28'11.26";-65°38'14.05") with addition of white noise. The feasibility of the proposed scheme is examined through dynamic modeling of the well-known chaotic time series such as Mackay Glass (MG) and one-dimensional Henon series (HEN). In particular, when the time series is noisy, the underlying dynamical system is nonlinear and temporal dependencies span long time intervals, in which this are also called long memory process. In such cases, the inherent nonlinearity of ANN models and a higher robustness to noise seem to partially explain their better prediction performance. So, in one-step-ahead prediction tasks, the predictive models are required to estimate the next sample value of a noisy time series, without feeding back it to the model’s input regressor. If the user is interested in a longer prediction horizon, a procedure known as long-term prediction, the model’s output should be fed back to the input regressor for a fixed but finite number of time steps. Even though feed-forward networks can be easily adapted to process time series through an input tapped delay line, giving rise to the well-known time tagged feed-forward neural network, respectively. The results show that the new method can improve the predictability of noisy rainfall and chaotic time series with a suitable number of hidden units compared to that of reported in the literature.