Comparison of iterative and direct approaches for multi-steps ahead time series forecasting using adaptive Hybrid-RBF neural network

Most available forecasters were designed in non-adaptive approach whereby the forecasters´ parameters were updated during training phase. Slightly different, this paper introduces an adaptive forecaster built from the Hybrid Radial Basis Function neural network, in which its parameters were updated continuously in real time using new data. To achieve this, two learning algorithms: Adaptive Fuzzy C-Means Clustering and Exponential Weighted Recursive Least Square were used to train the Hybrid Radial Basis Function in adaptive mode. The multi-steps ahead forecasting were achieved by using two approaches: iterative and direct. The performance of each approach is measured by the Root Mean Square Error and R² test of the actual and forecasted output on two time series data: Mackey-Glass and Data Series A from Santa-Fe Competition. Simulation results show that the adaptive forecaster is able to produce accurate forecasting output for several steps ahead depending on the complexity of data. Simulation results also reveal that the direct approach overcomes iterative approach in long distance forecasting.