Theiler window
Posted: Wed Sep 21, 2016 22:56
Hello,
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,
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,
Marina