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Principal component analysis questions and issues

Discussion in 'Technical Analysis' started by fatrat, Mar 12, 2008.

1. fatrat

If I perform a PCA on the correlation matrix or the covariance matrix of the set of log-returns from 8 stocks, how exactly do I take the resulting eigenvectors corresponding to the first two or three lambdas and construct a regression model from it?

Suppose I have 8 stocks, one of them is a response, the other 7 are predictors, and we have some general linear model, like:

y = b0*X1 + b2*X2 .... + bn * XN

I take the logreturns of all of the 7 predictors, build a covariance/correlation matrix, perform PCA. Now I have a set of 7 principle components. How do I take these components back and get a reduced regression model?

I have this dumb text book that stops at explaining how certain weightings will explain most of the variance; however, I don't understand this:

I get different weightings if I apply PCA to the covariance matrix of the logreturns versus the correlation matrix. How is it I can take these different weightings and reapply them to the original data?

I can't find a textbook that walks me back through the process of using these eigenvectors to get a reduced linear regression model?