Can correlograms be made only for wide-sense stationary processes? From what I understand, a correlogram plots the autocorrelation of a stochastic process as a function of the delay. However, that is only possible in the case of wide-sense stationary processes, since the autocorrelation otherwise depends on the two precise moments in time, not just on the delay...
Am I correct in stating that correlograms can only be plotted for wide-sense stationary processes?

Your reasoning makes sense.
For a wide-sense stationary process, a correlogram can be interpreted in a straightforward way, since the population counterparts of the sample autocorrelations you see in it do actually exist.
For a process that is not wide-sense stationary, it is still technically possible to plot a correlogram. However, it loses its straightforward interpretation, as the population counterparts of sample autocorrelations do not exist. The correlogram may still be informative, though, as e.g. we can identify (or at least get a sense of) a unit-root, a long-memory or a trending process by looking at a correlogram.
