# [R] Identify period length of time series automatically?

Rainer M Krug r.m.krug at gmail.com
Thu Apr 14 12:42:28 CEST 2011

```-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1

On 14/04/11 11:57, Mike Marchywka wrote:
>
>
>
>
>
>
>
>
>
>
> ----------------------------------------
>> 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,

>
> 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
-----BEGIN PGP SIGNATURE-----
Version: GnuPG v1.4.10 (GNU/Linux)
Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org/

iEYEARECAAYFAk2mz5QACgkQoYgNqgF2egqZ8QCfZrtSmYczWo+Gq9NgY25mtP5Q
LHwAn3qaWKoo2wkc4pjTe9skZhcW7UL+
=4uTI
-----END PGP SIGNATURE-----

```