Inductive Modeling Method (GMDH) in Problems of Intellectual Data Analysis and Forecasting

Abstract

This chapter is devoted to the investigation and application of fuzzy inductive modeling method known as Group Method of Data Handling (GMDH) in problems of intellectual data analysis (Data Mining), in particularly its application in the forecasting problem in macroeconomy and financial sphere. The problem consists in forecasting models construction and finding unknown functional dependence between given set of macroeconomic indices and forecasted variable using experimental data. The advantage of inductive modeling method GMDH is a possibility of constructing adequate model directly in the process of algorithm run. The specificity of fuzzy GMDH is getting the interval estimates for forecasting variables. In this chapter the review of main results concerning GMDH and fuzzy GMDH is presented, analysis of application of various membership functions (MF) and perspectives of fuzzy GMDH application for forecasting in macroeconomy and financial sphere are estimated. The Sect. 6.2 contains the problem formulation. In the Sect. 6.3 main principles and ideas of GMDH are considered. In the Sect. 6.4 the generalization of GMDH in case of uncertainty—new method fuzzy GMDH suggested by authors is described which enables to construct fuzzy models almost automatically. The Sect. 6.5 contains the algorithm of fuzzy GMDH. In the Sect. 6.6 the fuzzy GMDH with Gaussian and bell-wise membership functions MF are considered and their similarity with triangular MF is shown. In the Sect. 6.7. fuzzy GMDH with different partial descriptions in particular orthogonal polynomials of Chebyshev and Fourier are considered. In the Sect. 6.8 the problem of adaptation of fuzzy models obtained by GMDH is considered and the corresponding adaptation algorithms are described. The Sect. 6.9 contains the results of numerous experiments of GMDH and fuzzy GMDH application for forecasting share prices and Dow Jones index at New York stock exchange (NYSE). The extension and generalization of fuzzy GMDH in case of fuzzy inputs is considered and its properties are analyzed in the Sect. 6.11.