Theiler window

General discussions and questions about recurrence plot and recurrence network related methods.
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Joined: Wed Sep 21, 2016 18:44
Affiliation (Univ., Inst., Dept.): University of Alicante
Location: Alicante, Spain
Research field: Petrology, Geology

Theiler window

Post by Marina »

I am not sure I understand what the Theiler Window means in practical terms. I'll explain what I think it means and my question using an example.
(A sketch is appended)
We have a time series with measurements every hour (24 measurements every day) and it has a daily seasonality. I estimate the embedding dimension, delay etc., etc. …
Let say, the system is in a state X at 15:00 April, 4 and I take a Theiler Window of 6 gaps, so the first time the system could reach the state X would be 21:00 April, 4.
Now, let's imagine the system actually recurs to the state X on April, 5 at 12:00, 13:00, 14:00 (because the periodicity is not perfect and because of the tangential movement). The next Theiler Window will encompass the times 13:00,14:00, 15:00, 16:00 and 17:00, being 18:00 the first allowed time for a possible recurrence of the state X.
By the way, if I have a time series which is partially periodic but also partially laminar, I think the Theiler Window would remove the laminarity, so maybe I shouldn’t use it.
Thanks in advance,
This is not a realistic plot. It is just a mere sketch.
This is not a realistic plot. It is just a mere sketch.
duda.jpg (88.65 KiB) Viewed 15578 times
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Joined: Wed Jan 4, 2006 11:03
Affiliation (Univ., Inst., Dept.): Potsdam Institute for Climate Impact Research, Germany
Location: Potsdam, Germany
Location: Potsdam Institute for Climate Impact Research, Germany

Re: Theiler window

Post by Norbert »

Hi Marina,

the Theiler window corrects only the recurrences that are close to the reference point. All other, "futher away" points are not corrected. For a RP it means that the Theiler window is a small band along the main diagonal.
Therefore, it will only partly affect the LAM measure.

Bes regards
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