Re: Seminar: HILBERT SPACE MODELS COMMODITY EXCHANGES by Paul Cockshott

From: Paul Cockshott (wpc@DCS.GLA.AC.UK)
Date: Wed Sep 22 2004 - 06:27:33 EDT


I am not entirely sure on this point. I don't know enough
of the history of the derivation of the correlation coefficient,
and I have certainly used it in the past. However it looks
very like an inner product operation which only   
make sense in a vector space. 

What one is basically doing with the correlation coefficient
is measuring the angle between two vectors, or rather measuring
the cosine of the angle between normalised unit vectors going
along the same rays as the original vectors. But this whole
procedure is only well defined for vector spaces. If one has
for example a Manhattan metric, then the distance between
the origin and the point (3,4) is not 5 but 7, so that 
the normalisation condition used in the correlation coefficient
will be wrong.

-----Original Message-----
From: OPE-L [mailto:OPE-L@SUS.CSUCHICO.EDU] On Behalf Of Ian Wright
Sent: 21 September 2004 22:28
To: OPE-L@SUS.CSUCHICO.EDU
Subject: Re: Seminar: HILBERT SPACE MODELS COMMODITY EXCHANGES by Paul
Cockshott

Hi Paul

What is wrong with the Pearson correlation coefficient when comparing
(price, value) pairs? I am unsure whether this measure assumes
anything about an underlying metric space.

-Ian.


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