Analysis of a Gaussian process and feed-forward neural networks based filter for forecasting short rainfall time series

Abstract

In this paper, an analysis of kernel (GP) and feedforward neural networks (FFNN) based filter to forecast short rainfall time series is presented. For the FFNN, the learning rule used to adjust the filter weights is based on the Levenberg-Marquardt method and Bayesian approach by the assumption of the prior distributions. In addition, a heuristic law is used to relate the time series roughness with the tuning process. The input patterns for both NN-based and kernel models are the values of rainfall time series after applying a time-delay operator. Hence, the NN's outputs will tend to approximate the current value of the time series. The time lagged inputs of the GP and their covariance functions are both determined via a multicriteria genetic algorithm, called NSGA-II. The optimization criteria are the quantity of inputs and the filter's performance on the known data which leads to Pareto optimal solutions. Both filters - FFNN and GP Kernel - are tested over a rainfall time series obtained from La Sevillana establishment. This work proposed a comparison of well-known filter referenced in early work where the contribution resides in the analysis of the best horizon of the forecasted rainfall time series proposed by Bayesian adjustment. The performance attained is shown by the forecast of the next 15 months values of rainfall time series from La Sevillana establishment located in (-31° 1'22.46S, 62°40'9.57O) Balnearia, Cordoba, Argentina.