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!

  • $\begingroup$ Which model do you use after you extract principle components? What is your dependent variable? Have you considered standardization or scaling to total population or GDP of the variables prior to PCA application? For temporal aggregation issues you may look here bancaditalia.it/pubblicazioni/temi-discussione/2008/2008-0685/… $\endgroup$ – Dmitrij Celov Apr 18 '19 at 10:58
  • $\begingroup$ Thanks for your answer! The PCA is interesting in itself, as I am using it in a factor analysis context. Once I get a few models my plan is to forecast using a factor augmented VAR approach. Dependent variable? I what sense? Scaling with respect to GDP sounds interesting, I did not consider this before. However GDP and inflow of migration is not linearly correlated, so I am not completely sure what that variable would actually show. What is your intuition? Thanks for your link! That is really appreciated! $\endgroup$ – MNielsen Apr 19 '19 at 8:36
  • $\begingroup$ Still some extra details would be handy: what you try to join as FAVAR model? Are you looking at correlations between the countries? Do you want to cluster countries by their correlations (mind corrplot package for that)? Migration is better scaled by labour or population, other VAR variables could be scaled by GDP :) Intuition -- elemenate extensive effects due to population/economic trends and have comparability betweeen countries. otexts.com/fpp2/transformations.html $\endgroup$ – Dmitrij Celov Apr 25 '19 at 6:46

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