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.
Best Answer
First, I think this calls for factor analysis, not principal component analysis. A "financial stress index" is a latent variable - that is, a variable that cannot be directly measured.
However, you are likely to get similar results. If you want a single index, then you want the first factor. If that factor does not explain much of the variance, then it's just not a very good index.