I wonder what the relationship between the empirical sample correlation of two time series in levels and the one of the differenced series is.
I know that for nonstationary variables, it makes little sense to calculate the correlation between them, so one should difference the series to make them stationary and calucate the correlation of the differenced series.
How are the "valid" correlation (between 2 differenced stationary series) and the "wrong" correlation (between 2 series in levels) related?
If the "wrong" correlation strengthens over time, does that mean that the "valid" correlation does too, always?
While intuitively, this might make sense (the two variables are coming "closer together"), it confuses me that the correlation between stationary variables should be state-dependent.