Bayesian enhanced ensemble approach (BEEA) for time series forecasting

We propose a new ensemble forecasting method, Bayesian enhanced ensemble approach (BEEA), to model neural networks for time series forecasting. Motivated by looking to get better prediction algorithms, our proposed algorithm can effectively integrate the data from different methods modified by Bayesian learning. A dataset of univariate time series (seasonal and non-seasonal) is used to forecast short-long prediction horizons, mainly 3 and 18 out-of-sample. Comparative simulations of our method with ten existing linear and nonlinear forecasting approaches, namely, Energy associated to series (EAS), Energy associated to series modify by Renyis's entropy (EASmod), Bayesian approach (BA), Bayesian enhanced (BEA), Bayesian enhanced modified by Renyi's entropy (BEMA), Bayesian enhanced modified by relative entropy (BEAmod.) is presented. Relative advantages and limitations of the ensemble approach in contrast with some reported in the literature illustrates the effectiveness of the Bayesian enhanced ensemble approach (BEEA) through different forecasting horizons in both, the learning process and the validation test using the MASE, SMAPE and RMSE forecast error metrics to highlight the performance and limitations of the BEEA approach.