GM(1,1) Model Considering the Approximate Heteroscedasticity.

The GM(1,1) model identifies the parameters by utilizing the least squares and builds its model by the function which aims at minimizing the error sum of squares of the original sequences. The least squares are established under the assumption that the error term is homoscedastic, while generalized least squares are more applicable when the heteroscedasticity of the error term occur. In this paper we first distinguish the heteroscedasticity of the GM(1,1) model by Goldfeld-Quandt testing and establish the GM (1,1) model under the significance of the generalized least squares, then provide the optimized matrix and expansion form according to the parameters of [a,b]T simultaneously. Subsequent analysis proves that multiple transformation does not change the precision of the heteroscedastic GM(1,1) model while it can reduce its morbidity. At the end of this paper, when the heteroscedasticity of the error terms occur, the case studies indicate that the effects of the heteroscedastic GM(1,1) model are more favorable than that of the GM(1,1) model. [ABSTRACT FROM AUTHOR]