Power Transformations found via a Box-Cox test http://onlinestatbook.com/2/transformations/box-cox.html  are useful/correct when a linear relationship is found between the expected value and the variability of the model errors. It has little to do with the variability of the original series. The  range of transformations is from none to a reciprocal. Care should be taken to account for pulse outliers as untreated they can distort the Box-Cox conclusions. Furthermore note that error variance may also change in discrete steps quite free of the expected value . The appropriate remedy in this case is to Generalized Least Squares or as it is often known as Weighted Least Squares.

You might look very closely at my response to http://stats.stackexchange.com/questions/6498/seeking-certain-type-of-arima-explanation/9017#9017