Cross-lagged correlation

Hey everybody,

I am currently writing on my bachelor's thesis. For the evaluation of my data I am using the so-called cross-lagged correlation design. My problem is that I have never used this method before so I am a bit confused about how to apply it.
I have longitudinal data and I have to correlate data at time 1 with data at time 2.
I should have 6 correlations in the end (PX1X2, PY1Y2, PX1Y1, PX2Y2, PX1Y2 and PY1X2).
My question is now, whether I am using normal Spearman/ Pearson correlations or is there a special formula. I have tried to test this method by calculating the cross correlations with data from another study but the results were totally different. :(

I hope someone of you has already worked with this method and can help me.

Thanks a lot in advance :)