I am trying to construct a financial stress index. I have selected 12 variables that I use as indicators of financial market stress. These are all time series of daily data (VIX, credit spreads, etc.). I am trying to use principal component analysis (PCA) to decide on the weights these variables should get in my index. I am using Stata. If I run the pca
command I get 12 components with eigenvalues. I then select only the components that have eigenvalue > 1 (Kaiser rule) and now I'm left with 3 components.
Stata commands:
pca $varlist, mineigen(1)
estat loadings
predict pc1 pc2 pc3, score
I now have 3 time series pc1, pc2, pc3
which are, if I understand correctly, the first three principal components.
I don't understand how I create an index out of a combination of these 3 components. What is the logical step to take now and how should I interpret the different factor loadings of the different variables in the different components?
Main question: what steps should I take to derive a time series of my financial stress index?
If you need any additional info to answer my question please say so and I'll try my best to make it as clear as possible.
pc1
is the best single summary of your variables. You won't improve on it by mushing it together with other PCs. How far you can do better is a key but open question. It's worth underlining that the PCA pays no attention whatsoever to e.g. trend, periodicities or serial dependence in the data; the same values shuffled randomly would yield the same PCs. What would also be missed, or rather mushed together in the calculations, is any of the original variables responding with different lags to outside stimuli. $\endgroup$