<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:st1="urn:schemas-microsoft-com:office:smarttags" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=us-ascii">
<meta name=Generator content="Microsoft Word 11 (filtered medium)">
<!--[if !mso]>
<style>
v\:* {behavior:url(#default#VML);}
o\:* {behavior:url(#default#VML);}
w\:* {behavior:url(#default#VML);}
.shape {behavior:url(#default#VML);}
</style>
<![endif]--><o:SmartTagType
namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="PersonName"/>
<!--[if !mso]>
<style>
st1\:*{behavior:url(#default#ieooui) }
</style>
<![endif]-->
<style>
<!--
/* Font Definitions */
@font-face
{font-family:Tahoma;
panose-1:2 11 6 4 3 5 4 4 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0cm;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman";}
h1
{margin-top:24.0pt;
margin-right:0cm;
margin-bottom:0cm;
margin-left:35.8pt;
margin-bottom:.0001pt;
text-indent:-21.6pt;
line-height:150%;
page-break-after:avoid;
mso-list:l0 level1 lfo9;
font-size:12.0pt;
font-family:"Times New Roman";}
h2
{margin-top:24.0pt;
margin-right:0cm;
margin-bottom:6.0pt;
margin-left:28.8pt;
text-indent:-28.8pt;
line-height:150%;
page-break-after:avoid;
mso-list:l0 level2 lfo9;
font-size:12.0pt;
font-family:"Times New Roman";}
h3
{margin-top:24.0pt;
margin-right:0cm;
margin-bottom:3.0pt;
margin-left:36.0pt;
text-indent:-36.0pt;
line-height:150%;
page-break-after:avoid;
mso-list:l0 level3 lfo9;
font-size:12.0pt;
font-family:"Times New Roman";
font-weight:normal;}
h4
{margin-top:12.0pt;
margin-right:0cm;
margin-bottom:6.0pt;
margin-left:57.4pt;
text-indent:-43.2pt;
page-break-after:avoid;
mso-list:l0 level4 lfo9;
font-size:12.0pt;
font-family:"Times New Roman";
font-weight:normal;}
h5
{margin-top:18.0pt;
margin-right:0cm;
margin-bottom:12.0pt;
margin-left:64.6pt;
text-indent:-50.4pt;
mso-list:l0 level5 lfo9;
font-size:12.0pt;
font-family:"Times New Roman";
font-weight:normal;}
h6
{margin-top:12.0pt;
margin-right:0cm;
margin-bottom:3.0pt;
margin-left:71.8pt;
text-indent:-57.6pt;
mso-list:l0 level6 lfo9;
font-size:12.0pt;
font-family:"Times New Roman";}
p.MsoHeading7, li.MsoHeading7, div.MsoHeading7
{margin-top:12.0pt;
margin-right:0cm;
margin-bottom:3.0pt;
margin-left:79.0pt;
text-indent:-64.8pt;
mso-list:l0 level7 lfo9;
font-size:12.0pt;
font-family:"Times New Roman";}
p.MsoHeading8, li.MsoHeading8, div.MsoHeading8
{margin-top:12.0pt;
margin-right:0cm;
margin-bottom:3.0pt;
margin-left:86.2pt;
text-indent:-72.0pt;
mso-list:l0 level8 lfo9;
font-size:12.0pt;
font-family:"Times New Roman";
font-style:italic;}
p.MsoHeading9, li.MsoHeading9, div.MsoHeading9
{margin-top:12.0pt;
margin-right:0cm;
margin-bottom:3.0pt;
margin-left:93.4pt;
text-indent:-79.2pt;
mso-list:l0 level9 lfo9;
font-size:12.0pt;
font-family:"Times New Roman";}
p.MsoToc1, li.MsoToc1, div.MsoToc1
{margin:0cm;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman";}
p.MsoToc2, li.MsoToc2, div.MsoToc2
{margin-top:0cm;
margin-right:0cm;
margin-bottom:0cm;
margin-left:11.0pt;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman";}
p.MsoToc3, li.MsoToc3, div.MsoToc3
{margin-top:0cm;
margin-right:0cm;
margin-bottom:0cm;
margin-left:22.0pt;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman";}
p.MsoToc4, li.MsoToc4, div.MsoToc4
{margin-top:0cm;
margin-right:0cm;
margin-bottom:0cm;
margin-left:33.0pt;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman";}
p.MsoToc5, li.MsoToc5, div.MsoToc5
{margin-top:0cm;
margin-right:0cm;
margin-bottom:0cm;
margin-left:44.0pt;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman";}
p.MsoToc6, li.MsoToc6, div.MsoToc6
{margin-top:0cm;
margin-right:0cm;
margin-bottom:0cm;
margin-left:55.0pt;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman";}
p.MsoToc7, li.MsoToc7, div.MsoToc7
{margin-top:0cm;
margin-right:0cm;
margin-bottom:0cm;
margin-left:66.0pt;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman";}
p.MsoToc8, li.MsoToc8, div.MsoToc8
{margin-top:0cm;
margin-right:0cm;
margin-bottom:0cm;
margin-left:77.0pt;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman";}
p.MsoToc9, li.MsoToc9, div.MsoToc9
{margin-top:0cm;
margin-right:0cm;
margin-bottom:0cm;
margin-left:88.0pt;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman";}
p.MsoFootnoteText, li.MsoFootnoteText, div.MsoFootnoteText
{margin:0cm;
margin-bottom:.0001pt;
font-size:10.0pt;
font-family:"Times New Roman";}
p.MsoCommentText, li.MsoCommentText, div.MsoCommentText
{margin:0cm;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman";}
p.MsoHeader, li.MsoHeader, div.MsoHeader
{margin:0cm;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman";}
p.MsoFooter, li.MsoFooter, div.MsoFooter
{margin:0cm;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman";}
p.MsoCaption, li.MsoCaption, div.MsoCaption
{margin-top:6.0pt;
margin-right:0cm;
margin-bottom:12.0pt;
margin-left:0cm;
font-size:12.0pt;
font-family:"Times New Roman";
font-weight:bold;}
span.MsoFootnoteReference
{vertical-align:super;}
p.MsoBodyText, li.MsoBodyText, div.MsoBodyText
{margin-top:0cm;
margin-right:0cm;
margin-bottom:6.0pt;
margin-left:0cm;
text-align:justify;
line-height:12.0pt;
font-size:12.0pt;
font-family:"Times New Roman";}
p.MsoBodyTextIndent, li.MsoBodyTextIndent, div.MsoBodyTextIndent
{margin-top:0cm;
margin-right:0cm;
margin-bottom:0cm;
margin-left:141.6pt;
margin-bottom:.0001pt;
text-indent:-141.6pt;
line-height:12.0pt;
font-size:12.0pt;
font-family:"Times New Roman";}
p.MsoBodyText2, li.MsoBodyText2, div.MsoBodyText2
{margin:0cm;
margin-bottom:.0001pt;
font-size:8.0pt;
font-family:"Times New Roman";
font-weight:bold;}
a:link, span.MsoHyperlink
{color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{color:blue;
text-decoration:underline;}
p.MsoAcetate, li.MsoAcetate, div.MsoAcetate
{margin:0cm;
margin-bottom:.0001pt;
font-size:8.0pt;
font-family:Tahoma;}
p.BeschriftungBild, li.BeschriftungBild, div.BeschriftungBild
{margin-top:6.0pt;
margin-right:0cm;
margin-bottom:12.0pt;
margin-left:0cm;
font-size:12.0pt;
font-family:"Times New Roman";
font-weight:bold;}
span.BeschriftungZchn
{font-family:Arial;
font-weight:bold;}
span.BeschriftungBildZchn
{font-family:Arial;
font-weight:bold;}
p.BeschriftungTabelle, li.BeschriftungTabelle, div.BeschriftungTabelle
{margin-top:12.0pt;
margin-right:0cm;
margin-bottom:6.0pt;
margin-left:0cm;
page-break-after:avoid;
font-size:12.0pt;
font-family:"Times New Roman";
font-weight:bold;}
p.Bild, li.Bild, div.Bild
{margin-top:0cm;
margin-right:0cm;
margin-bottom:6.0pt;
margin-left:0cm;
text-align:justify;
line-height:5.0pt;
page-break-after:avoid;
font-size:4.0pt;
font-family:"Times New Roman";}
p.Bild1, li.Bild1, div.Bild1
{margin:0cm;
margin-bottom:.0001pt;
page-break-after:avoid;
font-size:8.0pt;
font-family:"Times New Roman";}
p.Tabelle, li.Tabelle, div.Tabelle
{margin-top:6.0pt;
margin-right:0cm;
margin-bottom:6.0pt;
margin-left:0cm;
text-align:justify;
line-height:12.0pt;
font-size:12.0pt;
font-family:"Times New Roman";}
span.E-MailFormatvorlage47
{mso-style-type:personal-reply;
font-family:Arial;
color:navy;}
@page Section1
{size:595.3pt 841.9pt;
margin:70.85pt 70.85pt 2.0cm 70.85pt;}
div.Section1
{page:Section1;}
/* List Definitions */
@list l0
{mso-list-id:115372087;
mso-list-template-ids:1018211050;}
@list l0:level1
{mso-level-style-link:"Überschrift 1";
mso-level-text:%1;
mso-level-tab-stop:35.8pt;
mso-level-number-position:left;
margin-left:35.8pt;
text-indent:-21.6pt;}
@list l0:level2
{mso-level-style-link:"Überschrift 2";
mso-level-text:"%1\.%2";
mso-level-tab-stop:28.8pt;
mso-level-number-position:left;
margin-left:28.8pt;
text-indent:-28.8pt;}
@list l0:level3
{mso-level-style-link:"Überschrift 3";
mso-level-text:"%1\.%2\.%3";
mso-level-tab-stop:36.0pt;
mso-level-number-position:left;
margin-left:36.0pt;
text-indent:-36.0pt;}
@list l0:level4
{mso-level-style-link:"Überschrift 4";
mso-level-text:"%1\.%2\.%3\.%4";
mso-level-tab-stop:57.4pt;
mso-level-number-position:left;
margin-left:57.4pt;
text-indent:-43.2pt;}
@list l0:level5
{mso-level-style-link:"Überschrift 5";
mso-level-text:"%1\.%2\.%3\.%4\.%5";
mso-level-tab-stop:64.6pt;
mso-level-number-position:left;
margin-left:64.6pt;
text-indent:-50.4pt;}
@list l0:level6
{mso-level-style-link:"Überschrift 6";
mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6";
mso-level-tab-stop:71.8pt;
mso-level-number-position:left;
margin-left:71.8pt;
text-indent:-57.6pt;}
@list l0:level7
{mso-level-style-link:"Überschrift 7";
mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7";
mso-level-tab-stop:79.0pt;
mso-level-number-position:left;
margin-left:79.0pt;
text-indent:-64.8pt;}
@list l0:level8
{mso-level-style-link:"Überschrift 8";
mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8";
mso-level-tab-stop:86.2pt;
mso-level-number-position:left;
margin-left:86.2pt;
text-indent:-72.0pt;}
@list l0:level9
{mso-level-style-link:"Überschrift 9";
mso-level-text:"%1\.%2\.%3\.%4\.%5\.%6\.%7\.%8\.%9";
mso-level-tab-stop:93.4pt;
mso-level-number-position:left;
margin-left:93.4pt;
text-indent:-79.2pt;}
ol
{margin-bottom:0cm;}
ul
{margin-bottom:0cm;}
-->
</style>
<!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]-->
</head>
<body lang=DE link=blue vlink=blue>
<div class=Section1>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Hi,<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span 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'>sorry, of course I meant
seasonality.<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 time series consists
of longer term trends, short term noise and short time seasonality. <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'>oscillations /
seasonality, if any, it is most likely to be nonharmonic. I look for distinct
frequencies.<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'>When I did a FFT plot of
the original time series there was noise only in the spectrum.<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'>I will give it a run with
the differenciated series / the log of the 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'>There is still the
question how to test for significance of the found seasonality. <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>
<div>
<div>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Stephan</span></font><font color=navy><span
style='color:navy'><o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 color=navy face="Times New Roman"><span
style='font-size:12.0pt;color:navy'> <o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 color=navy face="Times New Roman"><span
style='font-size:12.0pt;color:navy'> </span></font><o:p></o:p></p>
</div>
</div>
<div>
<div class=MsoNormal align=center style='text-align:center'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>
<hr size=2 width="100%" align=center tabindex=-1>
</span></font></div>
<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> Freitag, 18. November
2011 00:34<br>
<b><span style='font-weight:bold'>An:</span></b> users@lists.scilab.org<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'>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>
<div>
<p class=MsoNormal><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">Mike@page-one.waitrose.com</a>>
wrote:<o:p></o:p></span></font></p>
<p class=MsoNormal><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>
<span class=hoenzb>Mike.</span></span></font><o:p></o:p></span></font></p>
<div>
<div>
<p class=MsoNormal style='margin-bottom:12.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'><br>
<br>
-----Original Message-----<br>
From: Petter Wingren [mailto:<a href="mailto:petterwr@gmail.com">petterwr@gmail.com</a>]<br>
Sent: 17 November 2011 17:18<br>
To: <a href="mailto:users@lists.scilab.org">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">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>
><br>
<br>
<o:p></o:p></span></font></p>
</div>
</div>
</div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</div>
</body>
</html>