DISPERSION OF THE ERRORS IS NON-CONSTANT AND RELATED TO THE MEAN

• Consider a regression : Y(t) = v0*X(t) + e(t) where e has a variance that is proportional to the mean such that as the mean gets larger the variance increases proportionally. This phenomena is often reported in financial data.
  
  
  This is referred to in the statistical literature as a heteroscedastic circumstance. .
  
  Heteroscedasticticity of the variance ( i.e. lack of homogenity ) can arise in a mumber of ways. In this section we treat the case where the remedy is simply a power transformation. The determination of the best power transformation is handled by the Box-Cox test. Consider the following:
  
  transform = -1 means reciprocals
  transform = 0 means logarithms
  transform = .5 means square roots
  transform = 1 means no transform
  
  

• Consider a regression : Y(t) = v0*X(t) + e(t) where e has a standard deviation that is proportional to the mean such that as the mean gets larger the standard deviation increases proportionally. This phenomena is often reported in financial data.
  
  The remedy in this case is to use a square root transformation.