This paper presents a new method to forecast short rainfall time-series. The new framework is by means of Bayesian enhanced modified combined approach (BEMCA) using permutation and relative entropy with Bayesian inference. The aim at the proposed filter is focused on short datasets consisting of at least 36 samples. The structure of the artificial neural networks (ANNs) change according to data model selected, such as the Bayesian approach can be combined with the entropic information of the series. Then computational results are assessed on time series competition and rainfall series, afterwards they are compared with ANN nonlinear approaches proposed in recent work and naïve linear technique such us ARMA. To show a better performance of BEMCA filter, results are analyzed in their forecast horizons by SMAPE and RMSE indices. BEMCA filter shows an increase of accuracy in 3-6 prediction horizon analyzing the dynamic behavior of chaotic series for short series predictions.