## time delay

Everything about quantification of recurrence plots.

### time delay

hello,
How can I get the time delay by using mi!
Thank you!
liujinlong
Junior

Posts: 1
Joined: Mon Nov 26, 2012 11:27

### Re: time delay

hi,

we have a time series x. you have now to calculate the mutual information MI between the x(t) and a time delayed version of this time series x(t+tau). this is analogous to the auto-correlation. then plot the MI versus the delay tau. usually, at the beginning, you will find a steep decrease with increasing tau. but after some delay, the decrease will be slower in average (or zero). the time of this change point can be used as the delay for embedding. in the example below, i would define such a change point at 3 or 4.

best regards
norbert
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Norbert
Expert

Posts: 173
Joined: Wed Jan 4, 2006 11:03
Location: Potsdam Institute for Climate Impact Research, Germany

### Re: time delay

Hi,

i try to generate a recurrence plot of a soccer match. Hence, I have lots of time series: two for each player in the soccer game. I read the post about calculating the embedding m and i read the paper "nonlinear time series analysis " from Kantz et al. to get more information about calculating the delay parameter tau. I tried an auto-correlation with one of my time series and get a continous decreasing plot.
auto-correlation of one time series
autocorr_lag_120.jpg (75.88 KiB) Viewed 5631 times
How shell i choose tau from this? Do i need new delay parameters for each time series?

I plotted the MI with tau = 80, as an attempt, versus tau and got this plot.
mi (with tau = 80) plotted versus tau
Mutual Information(tau=80,taumax=1000).jpg (54.54 KiB) Viewed 5631 times
I chose tau max = 1000. Is it right to choose a delay for embedding at 200?

Best regards
Denise
denise
Junior

Posts: 7
Joined: Sun Jun 1, 2014 13:41

### Re: time delay

Hi,

when using the ACF, I would suggest to chose a delay where the ACF value falls below 1/e.

Using MI, I agree with your selection of 200.

Regarding your question on the selection for each time series: it depends on the research question. Without knowing more about the data and the research question I cannot recommend anything.

Norbert
Expert

Posts: 173
Joined: Wed Jan 4, 2006 11:03
Location: Potsdam Institute for Climate Impact Research, Germany

### Re: time delay

Dear Prof. Marwan,

thank you very much for the immediate answer.

I will try to specifying my data: I have the positional data (X and Y) of all players for each tenth of each second over the whole soccer game.

I have already computed some "global" recurrence plots (with c#) based on the correlation of the position of each player to each second. Therefore I tried to generate quantitative and qualitative parameters out of the plot to describe the game. Secondly i generated plots based on the mean distance between the players from each second to each other second and set a value of 7 meters to get a "local" recurrence plot.

With the RQA i hope to get parameters, which describe the order of the game much better.

Back to the embedding parameters m and tau: I tried the advice you gave me. Thanks for that. But the 1/e and the ACF didn’t cross each other, so I scaled the ACF with natural logarithm. After that I got e.g. m=200 and tau = 190 for the first time series x1 (the x coordinates of the first player). But while computing an crp for this, the error occurred that the Dimension m or/and the delay T are too big.
>>RP1 = crp(x1, 200, 190, .1,'rr','silent');
Do you have an idea what is wrong?

Best regards,
Denise
denise
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Joined: Sun Jun 1, 2014 13:41