Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm

Abstract

Regression analysis is one of the well-known methods of multivariate analysis and it is efficiently used in many research fields, especially forecasting problems. In order for the results of regression analysis to be effective, some assumptions must be valid. One of these assumptions is the heterogeneity problem. One of the methods used to solve this problem is the weighted regression method. Weighted regression is a useful method when one of the least-squares assumptions of constant variance in the residuals is violated (heteroscedasticity). This procedure can minimize the sum of weighted squared residuals to produce residuals with a uniform variance if the appropriate weight will be used. (homoscedasticity). In this study, the Gustafson-Kessel method, one of the fuzzy clustering analysis method, is used to determine weights for weighted regression analysis. GustafsonKessel's method is based on the minimization of the sum of weighted squared distances which is used Mahalanobis distance, between the data points and the cluster centres. With the fuzzy clustering method, each observation value is bound to the specified clusters in a specific order of membership. These membership degrees will be calculated as weights in the weighted regression analysis and estimation work will be done. In application, 5 simulation and 1 real-time data were estimated by the proposed method. The results were interpreted by comparing with Robust Methods (M and S estimator) and weighted with FCM Regression analysis. 2020 Turkish Journal of Forecasting by Giresun University, Forecast Research Laboratory is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.