What is the largest n root transformation I should consider for making a time series stationary? Currently, I am working with multiple time series and not all of them are stationary. In order to make them stationary I am considering different transformations and checking the augmented dickey fuller test. I have considered $log(x), \sqrt{x}$, and $x^\frac{1}{3}$ as well as box cox. Some of the transforms have not made my series stationary but higher order roots have such as $\frac{1}{4}, \frac{1}{5}, etc$.
My questions are:


*

*Should I consider higher order n root transformations for making a series stationary?

*If yes, then at what point is too high? So far, the highest I have used is $x^\frac{1}{7}$.
 A: SOME TRANSFORMATIONS ARE GOOD FOR YOU AND OTHERS NOT SO GOOD 

Detrending , Power Transformations .Differencing AND ARMA are all forms of transformations. Determining the minimally sufficient (parsimonious) combination requires a combination of skillful people and skillful techniques . 
Simple scripts i.e. hard and fast rules are to be studiously avoided as they limit the scope of the solution and often obfuscate like taking the nth root of anything.
Power transforms are discussed When (and why) should you take the log of a distribution (of numbers)? and some more material on transforms here : optimal Box-Cox transforms should be based upon the residuals from a useful model not necessarily the original series. .
I should also add there are two other forms of transformations often suggested by the data ...
Due to changes in parameters over time SEGMENT the data
Due to deterministic error variance change(s) over time employ Weighted Least Squares (GLS)
A very good/priceless discussion of transformations is here BOX-COX TRANSFORMATION always stabilize variance where a veritable pantheon of heavy/knowledgeable SE hitters chime in on the topic. Lots to learn here , if you are willing to follow all the threads .
