Optimal error and GMDH predictors: A comparison with some statistical techniques

This paper presents some results obtained in time series forecasting using two nonstandard approaches and compares them with those obtained by usual statistical techniques. In particular, a new method based on recent results of the General Theory of Optimal Algorithm is considered. This method may be useful when no reliable statistical hypotheses can be made or when a limited number of observations is available. Moreover, a nonlinear modelling technique based on Group Method of Data Handling (GMDH) is also considered to derive forecasts. The well-known Wolf Sunspot Numbers and Annual Canadian Lynx Trappings series are analyzed; the Optimal Error Predictor is also applied to a recently published demographic series on Australian Births. The reported results show that the Optimal Error and GMDH predictors provide accurate one step ahead forecasts with respect to those obtained by some linear and nonlinear statistical models. Furthermore, the Optimal Error Predictor shows very good performances in multistep forecasting.