Fuzzy GMDH and its application to forecasting financial processes

Abstract

This paper is devoted to the investigation and application of the fuzzy inductive modeling method known as Group Method of Data Handling (GMDH) in problems of Data Mining, in particularly its application to solving the forecasting tasks in financial sphere. The advantage of the inductive modeling method GMDH is a possibility of constructing an adequate model directly in the process of algorithm run. The generalization of GMDH in case of uncertainty — a new method fuzzy GMDH is described which enables to construct fuzzy models almost automatically. The algorithm of fuzzy GMDH is considered. Fuzzy GMDH with Gaussian and bell-wise membership functions MF are considered and their similarity with triangular MF is shown. Fuzzy GMDH with different partial descriptions orthogonal polynomials of Chebyshev and Fourier are considered. The problem of adaptation of fuzzy models obtained by FGMDH is considered and the corresponding adaptation algorithm is described. The extension and generalization of fuzzy GMDH in case of fuzzy inputs is considered and its properties are analyzed. The experimental investigations of the suggested FGMDH were carried out.

Keywords

• fuzzy GMDH
• membership functions
• models adaptation
• forecasting