PCA princomp help please

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bartu gulen
bartu gulen 2011-12-26
Hi friends, I am using princomp to perform a pca algo on N stock returns going back M days.
my aim is to find a residual for the a basic multifactor model.
stockreturn1(t)= (beta1*factor1(t)) + (beta2*factor2(t))+ residual
I perform Princomp for N stocks (each column is time series for equity(n)). ..
I use princomp()'s "scores" matrix for factor1(t), and factor2(t), basicly scores(1:2,1).
I use princomp()'s coefs matrix for beta1, and beta2. coefs(1:2,1)
then I multiply matrices
fairreturn(t)=coefs(1:2,1)*transpose(scores(1:2,1))
finaly stockreturn1(t)- fairreturn(t)=residual
do you see anything wrong by using princomp in this way? this is some part of my code, An I wanna be sure that I dont get sth wrong fundamentally about princomp. thanks very much,Best...

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bym
bym 2011-12-26
In my opinion, this is not an appropriate use for PCA as you have described it. Principal components are used to reduce the dimensions of the predictors against the regressed value.
For example, say you wanted to predict the Dow Jones Industrial Average, but didn't want to use all 30 stocks. You could perform a PCA on a n by 30 matrix and see which stocks have the highest influence (taking into account price weighting & scaling)on the index. Then calculate the prediction using the reduced number of stocks and subtracting the actual DJIA to get the residual

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Richard Willey
Richard Willey 2011-12-27
There are some examples where Principal Component Analysis is used for regression.
Traditional regression analysis assumes that all the variance in the model is associated with the Y variable. So-called orthogonal regression assigns the variance equally across both X and Y.
The following demo provides a good introduction to this technique:
http://www.mathworks.com/products/statistics/demos.html?file=/products/demos/shipping/stats/orthoregdemo.html
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bartu gulen
bartu gulen 2011-12-27
great source for validation thanks very much richard.

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