Forums > Pricing & Modelling > Selecting Principal Components & Independent Components

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 Trev Total Posts: 31 Joined: Mar 2010
 Posted: 2012-07-21 04:00 Would be interested in hearing anyone's thoughts on techniques for selecting Principal Components (PCs) and Independent Components (ICs).For PCs I'm familiar with a few techniques:1) Kaiser - select PCs with eigenvalue(s) > 1 (assuming standardized rv's)2) Scree - using some type of ROC algorithm, find the "bend" in the plot of the eigenvalues and select those above/greater than that threshold.3) Specify some amount of variance to be explained and select the number of PCs that satisfy that amount.4) Using Random Matrix Theory determine those PCs that are "abnormal" and discard the rest.5) Specify a specific number of PCs to keep.I have used (1) and (2) mostly, (5) sometimes and (3)/(4) sparingly. Would love to hear any thoughts and especially any literature that practitioners have found useful/informative concerning the selection of PCs.More importantly, would be interested in any literature that proposed techniques that selected the "appropriate" amount of ICs. Currently within a larger algorithm I am calculating negentropy values for the ICs derived from the FastICA algorithm. My issue is what now? Specify a fixed amount of ICs? I don't want to attempt any step-wise approach (i.e. cycle through all the permutations of different structural forms based upon the ICs) and would prefer an unsupervised/non-parametric approach. And my goal is to use the ICs within a regression/classification framework (I.e. they are independent variables and I'm not concerned in gathering information about the rv's themselves).Thanks for any input.
 schmitty Total Posts: 46 Joined: Jun 2006
 Posted: 2012-07-21 07:14 For PCA, 4), iteratively. Attached File: Empirics_vs_RMT_in_Financial_Correlations.pdf
 Phynance471 Total Posts: 3 Joined: Jul 2012
 Posted: 2012-07-21 14:06 There are plenty of interesting courses about PCA on Avellaneda's website :http://www.math.nyu.edu/faculty/avellane/> Teaching > Quantitative Investment Strategies > Lecture 2 & 3
 Trev Total Posts: 31 Joined: Mar 2010
 Posted: 2012-07-21 16:07 @Schmitty: thanks for the paper: briefly scanned it and it looks interesting.@Phynance471: I've read some of Avellaneda's work but I haven't visited his webpage: some interesting stuff there.Thanks to the two of you.
 Trev Total Posts: 31 Joined: Mar 2010
 Posted: 2012-07-21 16:32 FYI: I stumbled across this slideshow by Gatheral (Random Matrix Theory and Covariance Estimation) which was also very interesting. And I also noticed that Avellaneda's notation was a little sloppy in spots; which for a simpleton like me is problematic.
 gnarsed Total Posts: 70 Joined: Feb 2008
 Posted: 2012-09-14 05:21 schmitty, i'm wondering what you mean by "iteratively"?
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