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| In practical time series analysis
we are dealing with samples of finite size $T$, often $10 \ll T < 1000$.
On an ordinal level,
such a sample forms an ordinal pattern (OP).
If there are no tied ranks, the OP is
a permutation of $(1,2,\ldots,T)$.
If the series is a finite realization of a
continuous iid process, each possible OP occurs with the same probability $1/T!$.
This is called completely unordered behavior.
However, a given process might not generate all these permutations.
This holds especially for chaotic time series.
In the talk some proposals are made
to detect order by a recurrence analysis within an OP
leading to entropy--like quantities. |
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