recurrence threshold

[ajay singh]

Dear all,
For a noisy time series, it is mentioned in the literature that the threshold should be around 5*sigma. I wanted to ask if this sigma is the standard deviation of the time series?

[Norbert]

Dear all,
For a noisy time series, it is mentioned in the literature that the threshold should be around 5*sigma. I wanted to ask if this sigma is the standard deviation of the time series?

No, it is the standard deviation of the observation noise. This threshold value (5σ) is actually much too high. The study which you refer to is more a theoretical consideration. This choice for the threshold means that the structures in the RP will be preserved. But it will also include additional structures that are related to noise. These new noise-related structures will strongly bias the final results.

Optimal theshold selection depends on the research question. This was summarized in several papers, e.g., in http://dx.doi.org/10.1016/j.physrep.2006.11.001 or http://dx.doi.org/10.1142/S0218127411029008.

[Yuzhi233]

Dear all,
For a noisy time series, it is mentioned in the literature that the threshold should be around 5*sigma. I wanted to ask if this sigma is the standard deviation of the time series?

No, it is the standard deviation of the observation noise. This threshold value (5σ) is actually much too high. The study which you refer to is more a theoretical consideration. This choice for the threshold means that the structures in the RP will be preserved. But it will also include additional structures that are related to noise. These new noise-related structures will strongly bias the final results.

Optimal theshold selection depends on the research question. This was summarized in several papers, e.g., in http://dx.doi.org/10.1016/j.physrep.2006.11.001 or http://dx.doi.org/10.1142/S0218127411029008.

Dir sir：
I use CRP toolbox ，i have some puzzle about the function ‘crp(x,m,t,e)’ and ‘pss’； e represent the threshold，but when i choose the norm
‘euclidean’，and set the e =2，like 'crp(x,3,1,2,'euclidean')',I noticed that there is a title on the picture ‘Dimention:3 Delay:1 threshold: 2σ’ ，i dont konw what ‘2σ’ mans，what is the σ？？ Is σ equal to 1？？（x is normalized when use crp？？） Or σ is the origin sequence's Standard deviation before normalize？？‘2’ means.
i know the 'pss' function can calculate the max phase space radius ， and set it to 0.1*pss(x,m,t,'euclidean'),but the result can be imported directly into crp （Do I need use (0.1*maxdist)/std(x) )????
tks sir , i am really need some help



And if the time sequemce have pulse，threshold calculate by 10% phase radiu is big ，it make the rp almost black what should i do？？

[ajay singh]

Thanks sir for replying

[Norbert]

Dir sir：
I use CRP toolbox ，i have some puzzle about the function ‘crp(x,m,t,e)’ and ‘pss’； e represent the threshold，but when i choose the norm
‘euclidean’，and set the e =2，like 'crp(x,3,1,2,'euclidean')',I noticed that there is a title on the picture ‘Dimention:3 Delay:1 threshold: 2σ’ ，i dont konw what ‘2σ’ mans，what is the σ？？ Is σ equal to 1？？（x is normalized when use crp？？） Or σ is the origin sequence's Standard deviation before normalize？？‘2’ means.
i know the 'pss' function can calculate the max phase space radius ， and set it to 0.1*pss(x,m,t,'euclidean'),but the result can be imported directly into crp （Do I need use (0.1*maxdist)/std(x) )????
tks sir , i am really need some help



And if the time sequemce have pulse，threshold calculate by 10% phase radiu is big ，it make the rp almost black what should i do？？

So many questions …

1. The default is that the time series will be automatically normalized to have standard deviation σ=1. Therefore, the threshold is in units of σ.
2. If you disable the normalisation by the argument 'nonorm', you will see that this σ will vanish.
3. I do not understand clearly your question on 'pss'. This function also normalises the time series to have σ=1. If you prefer to work with non-normalised time series, simply use the 'nonorm' flag in these functions.

[Yuzhi233]

Dir sir：
I use CRP toolbox ，i have some puzzle about the function ‘crp(x,m,t,e)’ and ‘pss’； e represent the threshold，but when i choose the norm
‘euclidean’，and set the e =2，like 'crp(x,3,1,2,'euclidean')',I noticed that there is a title on the picture ‘Dimention:3 Delay:1 threshold: 2σ’ ，i dont konw what ‘2σ’ mans，what is the σ？？ Is σ equal to 1？？（x is normalized when use crp？？） Or σ is the origin sequence's Standard deviation before normalize？？‘2’ means.
i know the 'pss' function can calculate the max phase space radius ， and set it to 0.1*pss(x,m,t,'euclidean'),but the result can be imported directly into crp （Do I need use (0.1*maxdist)/std(x) )????
tks sir , i am really need some help



And if the time sequemce have pulse，threshold calculate by 10% phase radiu is big ，it make the rp almost black what should i do？？

So many questions …

1. The default is that the time series will be automatically normalized to have standard deviation σ=1. Therefore, the threshold is in units of σ.
2. If you disable the normalisation by the argument 'nonorm', you will see that this σ will vanish.
3. I do not understand clearly your question on 'pss'. This function also normalises the time series to have σ=1. If you prefer to work with non-normalised time series, simply use the 'nonorm' flag in these functions.

thank U sir .I finally figured it out, thank you very much