Nonlinear Structure Identification for Multistep Prediction via a Modified GMDH Algorithm

Abstract A revised version of the Group Method of Data Handling (GMDH) specifically oriented to nonlinear modelling and forecasting of time series is presented. Particular attention is devoted to the problems of partial models optimal structure determination and selection of intermediate variables, both affecting the final choice of the model. In particular, the selection of intermediate variables is performed on the basis of a criterion which is different from the one used to choose partial model structures. The proposed criterion, which is based on multistep prediction errors, allows the optimization of the final model structure according to the range of prediction lead times of interest. Results referring to the application of the proposed modified GMDH to two classical time series are reported and compared with some of the results available in the literature.