To log or not to log? I am working on industrial output data and running a lot of tests for it, before I proceed to make an ARIMA model for it. 
Before I do that, I need to decide whether or not to "log" the data. 
I am having trouble spotting whether the data is growing exponentially or not. And even if it's not - it's logical to assume that industrial growth has constant growth and its variance goes up with time. 

Bottom line - would you advise to log the data in general (not just for ARIMA) when I do things like seasonally adjust it and smooth it, etc.
 A: Looking at the graph, there are clearly multiple things going on, and the nature of the long-term increase will be clearer if they are separated out.
However, if IPF is some sort of "amount of output" then I think you can make a good case for logs regardless of the exact shape of the distribution. This is because it makes more sense (to me, at least, but I don't think I am alone) to think about growth over time multiplicatively rather that additively. A change from 40 to 50 is more like a change from 400 to 500 than like a change from 400 to 410. 
So, I would first go with the logs because it makes substantive sense. Then you need to apply time-series tools (remove seasonality, for instance) and then see what you've got. 
A: Log or square-root transformation for ARIMA discusses answers this. In a word avoid transforming unless you have to as suggested by the relationship between ther error variance and the level of the expected value of Y. Note the variability of the observed Y is not mentioned above.
