I am working with a data set of 42 countries of monthly migration. I want to extract factors using PCA, and find non stationary errors of my model, so I am working in first difference. However there is barely any correlation in first difference. My idea is that correlation on a monthly basis might be bit of stretch working with migration data, so I am aggregating the data on 2,3,4,5 and 6 months basis, to see if there is a robust pattern. My questions are: (i) Do I take differences before or after aggregating the data? (ii) I have simulated a dataset consisting of 42 random walks, and aggregating data on a 6 month level does seem to create some correlation, both with differencing before and after aggregating the data. Is it the correct way to handle aggregration in data sets? Or do i create spurios correlation by aggregating non stationary series?
Answers or references to relevant articles are most appreciated!