# 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