Re: Comparing predictors

From: Richard Ulrich (Rich.Ulrich_at_comcast.net)
Date: 06/26/04 

Date: Fri, 25 Jun 2004 21:56:58 -0400

On 25 Jun 2004 08:09:25 -0700, clemenr@wmin.ac.uk (Ross Clement)
wrote:

> Lionel Barnett <mail@lionelb.com> wrote in message news:<2k24skF16dfdnU1@uni-berlin.de>...
> > The figures are:
> >
> > corr(Y',Y'') = 0.8851
> > corr(Y'-Y,Y''-Y) = 0.9991 (!)
>
> I must say that I agree with the addition of the exclamation mark to
> your figures. I'm not quite sure how you get a correlation for the
> error so much higher than the correlation of the raw values. By that I

It is not hard to see that there can be a high correlation
for residuals in a time series, and for it to be not-very-
useful or interesting.

Consider the hourly price quotations by a stock;
model it by the 1-day average versus the 24-hour (running) average.
Both 'models' will miss just about all that 'noise' of the
daily fluctuations, and the residuals will be practically
the same. The total variance of the prices will depend on
how much the price varied over the total duration of the
model, compared to its daily fluctuations -- it could be near zero,
or a lot. The correlations with criterion of the two 'models'
would vary accordingly.

Time series offers that problem of 'wrong windowing' in addition
to that problem of autocorrelation. 

-- 
Rich Ulrich, wpilib@pitt.edu
http://www.pitt.edu/~wpilib/index.html

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