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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.

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  • $\begingroup$ At some point, don't you need to actually make a connection to some concept of "financial stress"? $\endgroup$
    – The Laconic
    Jun 25 '17 at 18:40
  • $\begingroup$ Do you mean to check whether the index I constructed is closely related to financial stress? There isn't a simple "stress" variable, that's why I am making the index out of many variables that serve as indicators for financial stress. Or did I miss the point you are getting at? $\endgroup$
    – Sam Naarden
    Jun 26 '17 at 13:37
  • $\begingroup$ First, echoing @TheLaconic 's point, an operationalization or definition of financial stress pre-existent to your empirical analysis is needed. Without one, you could do anything and call it stress. Second, PCA in and of itself is neither dynamic nor longitudinal but rather cross-sectional. In other words, PCA is not appropriate for time series models. Finally, PCA is implicitly a linear approach, on the other hand your variables and their relationships are highly nonlinear. For all of these reasons PCA is not an appropriate methodology. $\endgroup$
    – Mike Hunter
    Jul 2 '18 at 11:10
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    $\begingroup$ Within the framework of PCA, 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. $\endgroup$
    – Nick Cox
    Jul 2 '18 at 11:49
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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.

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  • $\begingroup$ First of all, thanks for you quick answer! Sticking to pca: So I should use the first principal component (pc1) and if this component does not explain enough of the variation, pca is not the appropriate method? In the literature concerning financial stress indices I noticed several articles mentioning they were using pca as a weighting method. I am not familiar with factor analysis but I always thought it was very closely related. $\endgroup$
    – Sam Naarden
    Jun 25 '17 at 14:25

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