R help - Apr 2011 - Identify period length of time series automatically?

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Hi

I have 10.000 simulations for a sensitivity analysis. I have done a few
sensitivity analysis for different response variables already,
but now, as most of the simulations (if not all) show some cyclic
behaviour, see how the independent input parameter influence the
frequency of the cyclic changes and "how cyclic" they actually are.

So effectively, I have 39 values, and I want to identify automatically
the frequency / period length of the series and a kind of a measure on
"how cyclic" the series is.

How can I do that automatically without individual checking? I do not
want to do an eyeball assessment for 10.000 time series....

Thanks,

Rainer

- -- 
Rainer M. Krug, PhD (Conservation Ecology, SUN), MSc (Conservation
Biology, UCT), Dipl. Phys. (Germany)

Centre of Excellence for Invasion Biology
Stellenbosch University
South Africa

Tel :       +33 - (0)9 53 10 27 44
Cell:       +33 - (0)6 85 62 59 98
Fax :       +33 - (0)9 58 10 27 44

Fax (D):    +49 - (0)3 21 21 25 22 44

email:      Rainer at krugs.de

Skype:      RMkrug
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> Date: Thu, 14 Apr 2011 11:29:23 +0200
> From: r.m.krug at gmail.com
> To: r-help at r-project.org
> Subject: [R] Identify period length of time series automatically?
>
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>
> Hi
>
> I have 10.000 simulations for a sensitivity analysis. I have done a few
> sensitivity analysis for different response variables already,
> but now, as most of the simulations (if not all) show some cyclic
> behaviour, see how the independent input parameter influence the
> frequency of the cyclic changes and "how cyclic" they actually
are.
>
> So effectively, I have 39 values, and I want to identify automatically
> the frequency / period length of the series and a kind of a measure on
> "how cyclic" the series is.
Probably google "Digital Signal Processing" or Fourier
transform.
>From this, you resolve your time series into sinusoids of various components
and you can separate peaks in line spectra from background noise. 
Depending on what you consider to be "cyclic" the analysis details
will vary. If you look at things like amplitude and frequncy modulation
of one sine wave with another and various relationships between carrier and
modulation frequency, you can get some ideas of what to look for in spectra.

Alternatively, you can try to define exactly what you mean by "cyclic"
and maybe make a better transform that discriminates that from acyclic
but offhand I would suggest FFT and various tests on the spectra.


Just off hand I'm not sure that 39 points would be a lot to go on
but you can simulate some examples in R quite easily if you know
what the data looks like in various cases you think may exist.




>
> How can I do that automatically without individual checking? I do not
> want to do an eyeball assessment for 10.000 time series....
>
> Thanks,
>
> Rainer
>
> - --
> Rainer M. Krug, PhD (Conservation Ecology, SUN), MSc (Conservation
> Biology, UCT), Dipl. Phys. (Germany)
>
> Centre of Excellence for Invasion Biology
> Stellenbosch University
> South Africa

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On 14/04/11 11:57, Mike Marchywka wrote:
> 
> 
> 
> 
> 
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> 
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> 
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> ----------------------------------------
>> Date: Thu, 14 Apr 2011 11:29:23 +0200
>> From: r.m.krug at gmail.com
>> To: r-help at r-project.org
>> Subject: [R] Identify period length of time series automatically?
>>
>> -----BEGIN PGP SIGNED MESSAGE-----
>> Hash: SHA1
>>
>> Hi
>>
>> I have 10.000 simulations for a sensitivity analysis. I have done a few
>> sensitivity analysis for different response variables already,
>> but now, as most of the simulations (if not all) show some cyclic
>> behaviour, see how the independent input parameter influence the
>> frequency of the cyclic changes and "how cyclic" they
actually are.
>>
>> So effectively, I have 39 values, and I want to identify automatically
>> the frequency / period length of the series and a kind of a measure on
>> "how cyclic" the series is.
Hi Mike,

thanks for your answer - it confirms my fears ...
> 
> Probably google "Digital Signal Processing" or Fourier transform.
> From this, you resolve your time series into sinusoids of various
components
> and you can separate peaks in line spectra from background noise. 
> Depending on what you consider to be "cyclic" the analysis
details
> will vary. If you look at things like amplitude and frequncy modulation
> of one sine wave with another and various relationships between carrier and
> modulation frequency, you can get some ideas of what to look for in
spectra.
That is what I thought as well. As I have no idea about fourier
analysis, could you give me a small example in R, which gives me the
frequencies of the resulting sin waves after a fourier transformation?
I only see large matrices as return values when using e.g. fft().
> 
> Alternatively, you can try to define exactly what you mean by
"cyclic"
> and maybe make a better transform that discriminates that from acyclic
> but offhand I would suggest FFT and various tests on the spectra.
the shape of the fluctuations can be quite different - so no common
pattern there.
> 
> 
> Just off hand I'm not sure that 39 points would be a lot to go on
> but you can simulate some examples in R quite easily if you know
> what the data looks like in various cases you think may exist.
Well - the data is over a year summed up data from daily data points, so
I could easily go to daily data, which would be 365*39. But that would
make the analysis probably more difficult, as I have seasonal
fluctuations, and fluctuations over several years (1, 2, 3, 4, ...?;
depending on the parameters used for the simulation).

Any ideas on how to do this in R?

I have the feeling, that the quesion id more difficult then I thought...

Rainer

> 
> 
> 
> 
> 
>>
>> How can I do that automatically without individual checking? I do not
>> want to do an eyeball assessment for 10.000 time series....
>>
>> Thanks,
>>
>> Rainer
>>
>> - --
>> Rainer M. Krug, PhD (Conservation Ecology, SUN), MSc (Conservation
>> Biology, UCT), Dipl. Phys. (Germany)
>>
>> Centre of Excellence for Invasion Biology
>> Stellenbosch University
>> South Africa
> 
>  		 	   		  

- -- 
Rainer M. Krug, PhD (Conservation Ecology, SUN), MSc (Conservation
Biology, UCT), Dipl. Phys. (Germany)

Centre of Excellence for Invasion Biology
Stellenbosch University
South Africa

Tel :       +33 - (0)9 53 10 27 44
Cell:       +33 - (0)6 85 62 59 98
Fax :       +33 - (0)9 58 10 27 44

Fax (D):    +49 - (0)3 21 21 25 22 44

email:      Rainer at krugs.de

Skype:      RMkrug
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