I am dealing with a problem where the decision of applying a power/log transformation on time series data has to be done statistically. I know it can be done visually but I have to build model for multiple time series so visualizing it won't automate the problem. One of the approach I am following now is check for skewness and if skewness is out of the range of -1,1 then apply power transformation. Note: I don't wan't to apply Box cox if I don't have evidence it has to be applied.
EDIT: After a lot of research I found a solution. So one way to figure out if you should log the time series before analysis is to fit a linear regression model using time series data. And afterwards using fitted regression model's results run Goldfeld-Quandt Test. Using the result of Goldfeld-Quandt Test(test for checking heteroskedasticity) we can determine if it could be helpful to scale down the time series data.