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I am also interested in resolving this problem, although, decided not to create separate thread for it yet. This is kind of continuation of previous question below. http://stats.stackexchange.com/questions/34396/im-getting-jumpy-loadings-in-rollapply-pca-in-r-can-i-fix-it In factor analysis, specifically PCA, sign of the loadings does not mean anything, ...


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Possibly she is referring to the fact that classical PCA is not robust in the sense that its asymptotic properties depend on the distribution of the data. Large deviations from normality will result in sub-optimal estimates, or estimates that are distorted. If this is what she has in mind, then you can use robust PCA instead (cf. Candes et. al.)


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The first principle component of interest rates will not help you capture the term structure better at all. It will basically remove all term structure affects you are going to see. When we decompose the returns on interest rates you are going to get 3 PC's which explain 99.9% of the variance. PC1 - Level of the interest rates (~90% of variance) PC2 - ...


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Personally, I don't find any of the answers provided to be of that much help in answering the question. Factor analysis was developed for information collected for a single point in time. It's only been in the last few decades that extensions were made to, first, two or a few time periods, and then most recently truly longitudinal models have been proposed. ...


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Let's use the following returns matrix, X 2Y 5Y 10Y -------------------------- 0.0143 0.0910 0.1451 0.1791 0.3505 0.4588 0.0572 0.1358 0.0120 0.0357 0.1809 0.2884 -0.0571 -0.1096 -0.0719 0.0286 0.0710 0.1319 0.0429 0.1806 0.2754 -0.0357 -0.0579 -0.1075 0.0714 0.2513 0.4304 -0.0214 ...


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Sounds like PCA is not the approach you're looking for. If you're looking to transform a risk vector in terms of securities V into a risk vector in terms of securities W, then the basic approach would be to perform a linear regression of V against W. The resulting regression coefficients will form a matrix B which will give a change of basis between V and W. ...


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I just want to mention that it's highly prevalent to apply PCA to rate levels in rich/cheap analyses. Personally I prefer that... There's an old MS publication that discusses this very topic and the recommendation is to use level PCA for rich/cheap, and to use change PCA for risk management. There's a really good Salomon paper (Principles of Principal ...


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The literature on cointegration in large datasets or panels is really the only place where I've seen this sort of issue discussed. Breitung and Pesaran, among other places, talks about it. I would recommend applying the PCA to the rate changes (perhaps with some kind of zero lower bound adjustment). Then, take the cumulative sum of each of the factors. ...



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