Time Series Forecasting Using Bayesian Method: Application to Cumulative Rainfall

In this work an algorithm to adjust parameters using a Bayesian method for cumulative rainfall time series forecasting implemented by an ANN-filter is presented. The criterion of adjustment comprises to generate a posterior probability distribution of time series values from forecasted time series, where the structure is changed by considering a Bayesian inference. These are approximated by the ANN based predictor in which a new input is taken in order for changing the structure and parameters of the filter. The proposed technique is based on the prior distribution assumptions. Predictions are obtained by weighting up all possible models and parameter values according to their posterior distribution. Furthermore, if the time series is smooth or rough, the fitting algorithm can be changed to suit, in function of the long or short term stochastic dependence of the time series, an on-line heuristic law to set the training process, modify the NN topology, change the number of patterns and iterations in addition to the Bayesian inference in accordance with Hurst parameter H taking into account that the series forecasted has the same H as the real time series. The performance of the approach is tested over a time series obtained from samples of the Mackey-Glass delay differential equations and cumulative rainfall time series from some geographical points of Cordoba, Argentina.