Cross-section correlations in panel data

Let's say we have 3 variables and T = 1000.
Let's say we don't know if the variables follow a stationary or non-stationary process.
We plot graphs and we see that variance seems not constant, so we prefere using the Kendall coefficient and not the Pearson.

My question is: does it make sense to calculate the cross-section correlations for the 3 variables?
Are those informative?

My aim is a descriptive analysis, not an inference about causes.