Orthogonalized??? def?

Quantamentalist · January 10th, 2007, 8:09 pm

Ive heard the term orthogonalized being used so often and in so many different ways.In finance what does it mean to "Orthogonalize" data? Thanks

attesaarela · January 10th, 2007, 8:46 pm

It's fundamentally a linear algebraic concept, even though it can also be applied to functions. For instance it can mean that if you have a set of vectors describing a given space, make the vectors orthogonal (perpendicular) to each other, "independent" in some way, for time series it means remove correlation I think..It really pays to study linear algebra pretty thoroughly, it pops up in so many places, a bit like calculus even.

Quantamentalist · January 11th, 2007, 12:26 am

Thanks, so how could one take financial data and then "orthogonalize" and hence remove the correlation between variables?I thought orthogonalize meant to order the data and then break it up into fractiles, eg. take the cross-section of a universe of stock P/Es (for example) and then order those stocks into quartiles or something. I must be completely off then...

attesaarela · January 11th, 2007, 1:39 am

QuoteOriginally posted by: QuantamentalistThanks, so how could one take financial data and then "orthogonalize" and hence remove the correlation between variables?Matlab has functions for it, but if you want to really know what you're doing, study linear algebra.

gardener3 · January 11th, 2007, 1:48 am

QuoteOriginally posted by: QuantamentalistThanks, so how could one take financial data and then "orthogonalize" and hence remove the correlation between variables?Run a linear regression of one variable on the other.

wolf87 · January 11th, 2007, 3:20 am

Quick question on the last reply (if it's dumb, I apologize in advance): Linear regression is an orthogonal projection operation, and the only resulting vector that is guaranteed to be orthogonal to the data is the vector of residuals. Thus, running a regression of one variable on another does not seem like a way to orthogonalize data. Wouldn't that require a change of basis? Or are you saying that the linear regression operation gives you the information needed to compute this change of basis?

gardener3 · January 11th, 2007, 6:18 pm

Yes the residuals by definition will be othg to the variable in question. This is what people do woth nested factor analysis. I don't understand what you mean by 'change of basis'

zeta · January 11th, 2007, 6:59 pm

the gram schmidt process takes a set of vectors and generates an orthorgonal set.you could do a QR decomp in matlab/octave to accomplish the same thing

wolf87 · January 11th, 2007, 7:02 pm

gardener3 & zeta:You basically hit what I was trying to get at. I was thinking along the lines of a principal component analysis, which is at its core a change of basis operation on a set of data vectors.