Practical problems with correlation dimension

Karl karlknoblich at yahoo.de
Wed Jan 21 08:00:32 EST 2004


Hallo!

I want to calculate the correlation dimension of a time serie.

What I have done
I calculated the correlation integral C(r) (number of point having a
distance smaller than r) for different embedding dimensions. Taking
the slopes of the curve of log C(r) against log r for the different
embedding dimensions and plotting them against the embedding dimension
should result in a limes of the slopes: the correlation dimension.

My problem
Which slope shall I take?

In examples I saw in text books there is a nice limit of the slopes
with higher embedding dimensions. In my data I do not know which slope
I should take because the slope of the curve varies. If I take the
slope at a certain value of log r I can not get a limes.

My curves (log C(r) against log r) can be seen in
http://karlknoblich.4t.com/korrdim.jpg


What to do? Does anybody knows such data and how to handle it?

Hope somebody can help!

Karl



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