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

Abstract 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.

[1]  M. Milanese,et al.  Optimal algorithms theory and estimation with unknown but bounded errors , 1982, 1982 21st IEEE Conference on Decision and Control.

[2]  George E. P. Box,et al.  Time Series Analysis: Forecasting and Control , 1977 .

[3]  Charles A. Micchelli,et al.  A Survey of Optimal Recovery , 1977 .

[4]  David M. Allen,et al.  The Relationship Between Variable Selection and Data Agumentation and a Method for Prediction , 1974 .

[5]  Dennis Gabor,et al.  A universal nonlinear filter, predictor and simulator which optimizes itself by a learning process , 1961 .

[6]  M. Waldmeier.  The sunspot-activity in the years 1610-1960 , 1961 .

[7]  H. Tamura,et al.  Heuristics free group method of data handling algorithm of generating optimal partial polynomials with application to air pollution prediction , 1980 .

[8]  Howell Tong,et al.  Some Comments on the Canadian Lynx Data , 1977 .

[9]  M. Milanese,et al.  Robust time series prediction by optimal algorithms theory , 1984, The 23rd IEEE Conference on Decision and Control.

[10]  R. Kashyap,et al.  Dynamic Stochastic Models from Empirical Data. , 1977 .

[11]  Roberto Genesio,et al.  Nonlinear Structure Identification for Multistep Prediction via a Modified GMDH Algorithm , 1985 .

[12]  Saburo Ikeda,et al.  Sequential GMDH Algorithm and Its Application to River Flow Prediction , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[13]  Henryk Wozniakowski,et al.  A general theory of optimal algorithms , 1980, ACM monograph series.

[14]  C. Granger,et al.  An introduction to bilinear time series models , 1979 .

[15]  John McDonald,et al.  Modeling Demographic Relationships: An Analysis of Forecast Functions for Australian Births , 1981 .

[16]  A. M. Walker,et al.  A Survey of statistical work on the Mackenzie River series of annual Canadian lynx trappings for the , 1977 .

[17]  Mahmoud M. Gabr,et al.  THE ESTIMATION AND PREDICTION OF SUBSET BILINEAR TIME SERIES MODELS WITH APPLICATIONS , 1981 .

[18]  H. Akaike.  Fitting autoregressive models for prediction , 1969 .

[19]  R. Tempo,et al.  Optimal algorithms theory for robust estimation and prediction , 1985 .

[20]  Mark A. Franklin,et al.  A Learning Identification Algorithm and Its Application to an Environmental System , 1975, IEEE Transactions on Systems, Man, and Cybernetics.

[21]  H. Tong,et al.  Threshold Autoregression, Limit Cycles and Cyclical Data , 1980 .

[22]  A. Ivakhnenko.  Heuristic self-organization in problems of engineering cybernetics , 1970 .

[23]  E. Parzen.  Some recent advances in time series modeling , 1974 .