The Effect of Inverse Transformation on the Unit Mean and Constant Variance Assumptions of a Multiplicative Error Model Whose Error Component has a Gamma Distribution.

Abstract

In this paper, the effect of inverse transformation on the unit mean and constant variance assumptions of a multiplicative error model whose error component is Gamma distributed was studied. From the results of the study, it was discovered that the unit mean assumption is violated after inverse transformation. The mean and variance of the inverse-transformed gamma error component were found to be smaller than those of the untransformed error. Furthermore this decrease in mean,  was modeled and was found to increase per unit increase in ?, the shape parameter while that of the variance was found to decrease per unit increase in the shape parameter and their relationships (predictive equations) were determined. Finally, it was discovered that in order to achieve the unit mean condition after inverse transformation, the condition is unavoidable, where ? and ? are respectively the shape and location parameters of the Gamma distribution, otherwise inverse transformation would not be successful.

Keywords: Multiplicative Error Model; Gamma distribution; Inverse Transformation; Mean; Variance