Re: Box-counting dimension of random and Gaussian data points?
From: Roger Bagula (tftn_at_earthlink.net)
Date: 12/08/04
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Date: Wed, 08 Dec 2004 16:19:24 GMT
Dear Ross Evans,
Are you measuring a time series as:
s[n]->{s[1],s[2], s[3],...,s[n]}
Or
{r[n],s[n]},-> {{r[1],s[1]},{r[2],s[2]},{r[3],s[3]},...,{r[n],s[n]}}
The first will be one dimensional and the second should be two dimensional.
How are you producing your white noise/ normal variates?
Different randomization method of producing your distribution will
produce different
results.
Ross Evans wrote:
>I need help understanding something.
>
>The box-counting dimension of a set of random data points -- random in the
>sense that they are white noise, equally likely to occur anywhere within an
>interval -- is theoretically 2. That is computed by adding 1 to the slope
>of the log/log plot of the single-variable data points, counted at various
>sizes of box measurent..
>
>That works out empirically for me. My measured slope of such a set of data
>points is very close to 1.
>
>But what about data points that are distributed not as such white noise, but
>as Gaussian-distributed data centered around a mean. These data points
>visually do not fill the space as completely, because by definition they
>tend to be clustered around the mean. And when I measure the slope of such
>a set of points, it is only about .92.
>
>But the literature generally seems to expect a box-counting dimension of 2
>for Gaussian data, not just white noise. I don't get it.
>
>
>
>
-- Respectfully, Roger L. Bagula tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 : alternative email: rlbtftn@netscape.net URL : http://home.earthlink.net/~tftn
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