Can I perform cross correlation on non-stationary data? I have level data which need different level of integration to be stationary. I would like to know how to perform a correlation analysis. Can I perform this on raw data or must the data be stationary?
 A: You can calculate correlation for non-stationary variables, but you have to think carefully about why you are doing so and what you hope to learn.  As @stans-ReinstateMonica suggested, reading up on co-integration would be a good start.  
As @RichardHardy points out, one problem is that your estimates will depend on your estimation window.  Imagine we have two integrated processes that are just straight lines through the origin with opposite slopes. Their correlation is -1.  Now add some shared stationary noise to each of them, and the correlation will increase towards 1 as the variance of the noise becomes large relative to the variance of the lines.  Unfortunately, that variance is proportional to the square of the width of the observation window, so changing the window changes the correlation.
Because of problems like this, I find it hard to think of examples where calculating the correlation of nonstationary variables would be useful.  If in doubt I suggest you difference for stationarity but, as always in statistics, in the answer to what you should calculate should be determined by the inference you wish to draw from the result.
