A New Approach for Time Series Forecasting: Bayesian Enhanced by Fractional Brownian Motion with Application to Rainfall Series

A new predictor algorithm based on Bayesian enhanced approach (BEA) for long-term chaotic time series using artificial neural networks (ANN) is presented. The technique based on stochastic models uses Bayesian inference by means of Fractional Brownian Motion as model data and Beta model as prior information. However, the need of experimental data for specifying and estimating causal models has not changed. Indeed, Bayes method provides another way to incorporate prior knowledge in forecasting models; the simplest representations of prior knowledge in forecasting models are hard to beat in many forecasting situations, either because prior knowledge is insufficient to improve on models or because prior knowledge leads to the conclusion that the situation is stable. This work contributes with long-term time series prediction, to give forecast horizons up to 18 steps ahead. Thus, the forecasted values and validation data are presented by solutions of benchmark chaotic series such as Mackey-Glass, Lorenz, Henon, Logistic, Rössler, Ikeda, Quadratic one-dimensional map series and monthly cumulative rainfall collected from Despeñaderos, Cordoba, Argentina. The computational results are evaluated against several non-linear ANN predictors proposed before on high roughness series that shows a better performance of Bayesian Enhanced approach in long-term forecasting. Keywords—long-term prediction; neural networks; Bayesian inference; Fractional Brownian Motion; Hurst parameter