Box-cox transformation and the problem of heteroscedasticity

Abstract

It is known that heteroscedasticity in the context of the well-known family of power transformations suggested by Box and Cox creates complications because it depends upon the heteros- cedasticity of the original values of the dependent variable in a regression model set-up) as well as upon the transforma- tion parameter In this paper we attempt at generalizing the original Box-Cox model in this direction, and suggest maximum likelihood method of estimation for the parameters of the model. Through illustrative examples we show the seriousness of the problem of heteroscedasticity in the context of this trans- formation, and indicate how one can separate out the problem of non-linearity from the influence of stabilization of error variance in an estimate of the transformation parameter in our generalized model.

Keywords:

• Box-cox model
• functionaz fom
• hatoaos- cedasticity
• nonnoamcvlity
• powzr transformation