# Lambda value for BoxCox transformation in time series analysis

I was reading the online version of Forecasting: principles and practice by Rob J Hyndman and George Athana­sopou­los. I found this sentence about STL decomposition and the BoxCox transformation:

"Decompositions some way between additive and multiplicative can be obtained using a Box-Cox transformation of the data with 0<λ<1. A value of λ=0 corresponds to the multiplicative decomposition while λ=1 is equivalent to an additive decomposition."

My question is: why is it just lambda in that range could be a valid option? Why couldn't lambda equal -0.5 or 2?

• You're right; it can. You just couldn't interpret a $\lambda$ outside that range as being "between" additive and multiplicative. – whuber Nov 8 '16 at 23:54

## 1 Answer

You probably want to look at When (and why) should you take the log of a distribution (of numbers)? which discusses power transforms. Unwarranted or incorrect transformations including differences should be studiously avoided as they are often an ill-fashioned /ill-conceived attempt to deal with unidentified anomalies/level shifts/time trends or changes in parameters or changes in error variance

A classic example of this is discussed starting at slide 60 here http://www.autobox.com/cms/index.php/afs-university/intro-to-forecasting/doc_download/53-capabilities-presentation where three pulse anomalies (untreated) led to an unwarranted log transformation by early researchers. Unfortunately some of our current researchers are still making the same mistake.

The issue here ( as suggested by the op) is to be very wary of assumptions.