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?
recurrence threshold

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 Norbert
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 Affiliation (Univ., Inst., Dept.): Potsdam Institute for Climate Impact Research, Germany
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 Location: Potsdam Institute for Climate Impact Research, Germany
Re: recurrence threshold
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 noiserelated structures will strongly bias the final results.ajay singh wrote: ↑Tue Mar 2, 2021 14:07 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?
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.

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 Affiliation (Univ., Inst., Dept.): zhengzhou university Henan China
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 Research field: Bearing fault diagnosis
Re: recurrence threshold
Dir sir：Norbert wrote: ↑Wed Mar 3, 2021 15:24No, 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 noiserelated structures will strongly bias the final results.ajay singh wrote: ↑Tue Mar 2, 2021 14:07 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?
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.
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？？
Last edited by Yuzhi233 on Fri Mar 12, 2021 14:01, edited 1 time in total.

 Junior
 Posts: 4
 Joined: Sat Feb 27, 2021 10:30
 Affiliation (Univ., Inst., Dept.): IIT Ropar
 Location: Ropar, Punjab, India
 Research field: Engine combustion
Re: recurrence threshold
Thanks sir for replying
 Norbert
 Expert
 Posts: 183
 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: recurrence threshold
So many questions …Yuzhi233 wrote: ↑Thu Mar 11, 2021 23:28
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？？
 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.
 If you disable the normalisation by the argument 'nonorm', you will see that this σ will vanish.
 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 nonnormalised time series, simply use the 'nonorm' flag in these functions.

 Junior
 Posts: 3
 Joined: Wed Mar 10, 2021 04:21
 Affiliation (Univ., Inst., Dept.): zhengzhou university Henan China
 Location: china Henan zhengzhou
 Research field: Bearing fault diagnosis
Re: recurrence threshold
thank U sir .I finally figured it out, thank you very muchNorbert wrote: ↑Wed May 5, 2021 16:15So many questions …Yuzhi233 wrote: ↑Thu Mar 11, 2021 23:28
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？？
 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.
 If you disable the normalisation by the argument 'nonorm', you will see that this σ will vanish.
 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 nonnormalised time series, simply use the 'nonorm' flag in these functions.