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<div class=Section1>
<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-GB
style='font-size:10.0pt;font-family:Arial;color:navy'>Filtering temporal spikes
is a good idea, since there are some of them. I will try that.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-GB
style='font-size:10.0pt;font-family:Arial;color:navy'>The data sample as around
7000 data points, the frequency I look for is around 1/10 * sample rate.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-GB
style='font-size:10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-GB
style='font-size:10.0pt;font-family:Arial;color:navy'>May be there are methods
that are better suited for identifying frequency components in that kind of
data?<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-GB
style='font-size:10.0pt;font-family:Arial;color:navy'>FFT always describes the
time series by harmonic oszillations, which might not work well<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-GB
style='font-size:10.0pt;font-family:Arial;color:navy'>if oscillations are not (strictly)
harmonic.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-GB
style='font-size:10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-GB
style='font-size:10.0pt;font-family:Arial;color:navy'>What about wavelets (don’t
know much about it yet, though)?<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-GB
style='font-size:10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-GB
style='font-size:10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
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<div>
<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-GB
style='font-size:10.0pt;font-family:Arial;color:navy'>Stephan</span></font><font
color=navy><span lang=EN-GB style='color:navy'><o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 color=navy face="Times New Roman"><span
lang=EN-GB style='font-size:12.0pt;color:navy'> <o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 color=navy face="Times New Roman"><span
lang=EN-GB style='font-size:12.0pt;color:navy'> </span></font><span
lang=EN-GB><o:p></o:p></span></p>
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<p class=MsoNormal><b><font size=2 face=Tahoma><span style='font-size:10.0pt;
font-family:Tahoma;font-weight:bold'>Von:</span></font></b><font size=2
face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma'> Charles Warner
[mailto:cwarner.cw711@gmail.com] <br>
<b><span style='font-weight:bold'>Gesendet:</span></b> Samstag, 19. November
2011 05:12<br>
<b><span style='font-weight:bold'>An:</span></b> <st1:PersonName w:st="on">users@lists.scilab.org</st1:PersonName><br>
<b><span style='font-weight:bold'>Betreff:</span></b> Re: [scilab-Users]
saisonality in time series</span></font><o:p></o:p></p>
</div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoNormal style='margin-bottom:12.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>Another trick I have
found that greatly reduces FFT noise it to temporarily mask any localized
"spikes" in the data (such spikes, with a narrow temporal profile
have a very broad spectral distribution). One can also try to eliminate
any offset by subtracting the mean (or the geometric mean or harmonic mean- the
appropriate mean would be dictated by the nature of the data). This
should hopefully reduce the scale of the FFT amplitude, making it easier to
spot any (especially low-frequency, or seasonal) potential frequency
components.<o:p></o:p></span></font></p>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>On Fri, Nov 18, 2011 at 3:09 AM, <st1:PersonName w:st="on">Schreckenbach
Stephan</st1:PersonName> <<a href="mailto:s.schreckenbach@truma.com">s.schreckenbach@truma.com</a>>
wrote:<o:p></o:p></span></font></p>
<div link=blue vlink=blue>
<div>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><font
size=2 color=navy face=Arial><span style='font-size:10.0pt;font-family:Arial;
color:navy'>Hi,</span></font><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><font
size=2 color=navy face=Arial><span style='font-size:10.0pt;font-family:Arial;
color:navy'> </span></font><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><font
size=2 color=navy face=Arial><span lang=EN-GB style='font-size:10.0pt;
font-family:Arial;color:navy'>sorry, of course I meant seasonality.</span></font><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><font
size=2 color=navy face=Arial><span lang=EN-GB style='font-size:10.0pt;
font-family:Arial;color:navy'>The time series consists of longer term trends,
short term noise and short time seasonality. </span></font><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><font
size=2 color=navy face=Arial><span lang=EN-GB style='font-size:10.0pt;
font-family:Arial;color:navy'>oscillations / seasonality, if any, it is most
likely to be nonharmonic. I look for distinct frequencies.</span></font><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><font
size=2 color=navy face=Arial><span lang=EN-GB style='font-size:10.0pt;
font-family:Arial;color:navy'>When I did a FFT plot of the original time series
there was noise only in the spectrum.</span></font><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><font
size=2 color=navy face=Arial><span lang=EN-GB style='font-size:10.0pt;
font-family:Arial;color:navy'>I will give it a run with the differenciated
series / the log of the data. </span></font><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><font
size=2 color=navy face=Arial><span lang=EN-GB style='font-size:10.0pt;
font-family:Arial;color:navy'>There is still the question how to test for
significance of the found seasonality. </span></font><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><font
size=2 color=navy face=Arial><span lang=EN-GB style='font-size:10.0pt;
font-family:Arial;color:navy'> </span></font><o:p></o:p></p>
<div>
<div>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><font
size=2 color=navy face=Arial><span style='font-size:10.0pt;font-family:Arial;
color:navy'>Stephan</span></font><o:p></o:p></p>
</div>
<div>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><font
size=3 color=navy face="Times New Roman"><span style='font-size:12.0pt;
color:navy'> </span></font><o:p></o:p></p>
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<div>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><font
size=3 color=navy face="Times New Roman"><span style='font-size:12.0pt;
color:navy'> </span></font><o:p></o:p></p>
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face="Times New Roman"><span style='font-size:12.0pt'>
<hr size=2 width="100%" align=center>
</span></font></div>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b><font
size=2 face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma;font-weight:
bold'>Von:</span></font></b><font size=2 face=Tahoma><span style='font-size:
10.0pt;font-family:Tahoma'> Charles Warner [mailto:<a
href="mailto:cwarner.cw711@gmail.com" target="_blank">cwarner.cw711@gmail.com</a>]
<br>
<b><span style='font-weight:bold'>Gesendet:</span></b> Freitag, 18. November
2011 00:34<br>
<b><span style='font-weight:bold'>An:</span></b> <a
href="mailto:users@lists.scilab.org" target="_blank">users@lists.scilab.org</a><br>
<b><span style='font-weight:bold'>Betreff:</span></b> Re: [scilab-Users]
saisonality in time series</span></font><o:p></o:p></p>
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<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><font
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<p class=MsoNormal style='mso-margin-top-alt:auto;margin-bottom:12.0pt'><font
size=3 face="Times New Roman"><span style='font-size:12.0pt'>Although
"seasonality" is not the term I use for long term trends hidden in
noisy data, I have had some success by taking the log of the data, and running
an FFT on the log data. Usually, I have some prior knowledge of the
long-term periodic trends I expect, so it is relatively easy to determine
quickly if this method works. Plotting the log of the data also gives one
a good feel for whether the data is stationary, or whether there are windows of
data that can be treated as stationary. Any changing magnitude effect is,
of course, reduced when on works with logs, but such effects can help one
understand what the raw data is really telling you.<br>
<br>
Charlie<o:p></o:p></span></font></p>
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<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><font
size=3 face="Times New Roman"><span style='font-size:12.0pt'>On Thu, Nov 17,
2011 at 12:40 PM, Mike Page <<a href="mailto:Mike@page-one.waitrose.com"
target="_blank">Mike@page-one.waitrose.com</a>> wrote:<o:p></o:p></span></font></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><font
size=3 face="Times New Roman"><span style='font-size:12.0pt'>Hi,<br>
<br>
I don't know much about this application, but the Cepstrum can be used to<br>
find hidden periodicity in time series. Might be worth trying? I
have used<br>
it for finding rotational components in the vibration signatures from<br>
rotating machinery. There's a simple example here<br>
(<a href="http://www.dliengineering.com/downloads/cepstrum%20analysis.pdf"
target="_blank">http://www.dliengineering.com/downloads/cepstrum%20analysis.pdf</a>).<br>
<font color="#888888"><span style='color:#888888'><br>
Mike.</span></font><o:p></o:p></span></font></p>
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<br>
-----Original Message-----<br>
From: Petter Wingren [mailto:<a href="mailto:petterwr@gmail.com" target="_blank">petterwr@gmail.com</a>]<br>
Sent: 17 November 2011 17:18<br>
To: <a href="mailto:users@lists.scilab.org" target="_blank">users@lists.scilab.org</a><br>
Subject: Re: [scilab-Users] saisonality in time series<br>
<br>
<br>
Did a quick search but couldnt find anything obvious. I suppose the<br>
word you are looking for is seasonality - maybe that helps in finding<br>
something useful.<br>
<br>
On Thu, Nov 17, 2011 at 3:36 PM, <st1:PersonName w:st="on">Schreckenbach
Stephan</st1:PersonName><br>
<<a href="mailto:s.schreckenbach@truma.com" target="_blank">s.schreckenbach@truma.com</a>>
wrote:<br>
><br>
> Hi,<br>
><br>
> I look for a test of saisonality in time series.<br>
> The time series might be instationary and nonlinear and the saisonality<br>
> / oscillation might have a changing amplitude. Furthermore the<br>
> distribution<br>
> might be unknown as well.<br>
> I need something to test for significant saisonality without knowing /<br>
> estimating a (linear) model of the time series.<br>
><br>
> ideas I got so far: Chi Square Test for independency:<br>
> I could test for independence of saison and mean value of the data<br>
><br>
> Chi Square Test to test for different means of two data groups.<br>
> I could test for a difference of the mean between several seasons.<br>
><br>
> Any more or better ideas?<br>
><br>
> Thanks in advance, Stephan<br>
><br>
><o:p></o:p></span></font></p>
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