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Author

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R Software Module

rwasp_spectrum.wasp

Title produced by software

Spectral Analysis

Date of computation

Mon, 01 Dec 2008 08:52:17 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/01/t1228146782v9rvpdr5yu94idf.htm/, Retrieved Sun, 05 May 2024 14:37:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26958, Retrieved Sun, 05 May 2024 14:37:51 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

222

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

F     [Law of Averages] [Random Walk Simul...] [2008-11-25 18:40:39] [b98453cac15ba1066b407e146608df68]
F       [Law of Averages] [Random Walk Simul...] [2008-11-27 19:45:04] [58bf45a666dc5198906262e8815a9722]
F RMPD    [Standard Deviation-Mean Plot] [Standard Deviatio...] [2008-11-27 22:08:29] [58bf45a666dc5198906262e8815a9722]
- RMPD      [Spectral Analysis] [Spectral Analysis...] [2008-11-27 23:04:22] [58bf45a666dc5198906262e8815a9722]
F   P           [Spectral Analysis] [Q4] [2008-12-01 15:52:17] [7ed4ec9f8cdf7df79ef87b9dc09dff20] [Current]

Feedback Forum

2008-12-03 10:02:11 [Romina Machiels] [reply] 
Deze vraag werd correct beantwoord.
2008-12-08 18:10:35 [Jeroen Aerts] [reply] 
Volgens mij heb je een verkeerde bewerking uitgevoerd, aangezien de berekening het volgende resultaat zou moeten weergeven: Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/08/t122875972365i3oa4nz2ydpud.htm, Retrieved Mon, 08 Dec 2008 18:08:51 +0000 
 
 
Het spectrum geeft een verband tussen de intensiteit van de onafhankelijke golfbewegingen van de reeks met hun frequentie. 
 
Spectrum = amplitude / frequentie 
Spectrum = amplitude / (1 /periode) 
Spectrum = amplitude * periode 
 
De hoogste spectrumwaarde is te zien bij een waarde 0.Het Cumulative Periodogram toont een verband tussen de cumulatieve intensiteit van de golven samen met de perioden. 
 
Amplitude / periode 
=> amplitude / (1/ frequentie) 
=> amplitude * frequentie 
 
Bij grote frequenties moeten de waarden in de grafiek dus ook groot zijn. 
Via deze methode kunnen we controleren welke waarde van een bepaalde frequentie een bepaald aantal % van de reeks verklaard. 
Is de frequentie 0, dan verklaren we niets. Is de frequentie 0,1 dan verklaren we bijna alles. Hieruit kunnen we afleiden dat wanneer de frequentie klein is, de periode groot (lang) zal zijn. We stelden eerder al dat een lange periode niet-seizoenale autocorrelatie impliceert. We bevestigen dus wederom onze eerdere bevindingen.
2008-12-08 18:33:39 [Yara Van Overstraeten] [reply] 
Hier werd inderdaad de verkeerde berekening gemaakt. 
Jeroen heeft de correcte berekening geblogt.

Post a new message

Dataseries X:

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Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26958&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26958&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26958&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Raw Periodogram
Parameter	Value
Box-Cox transformation parameter (lambda)	1
Degree of non-seasonal differencing (d)	1
Degree of seasonal differencing (D)	0
Seasonal Period (s)	12
Frequency (Period)	Spectrum
0.0167 (60)	6.082551
0.0333 (30)	1.941143
0.05 (20)	1.226396
0.0667 (15)	3.919919
0.0833 (12)	32.602553
0.1 (10)	5.970416
0.1167 (8.5714)	0.358131
0.1333 (7.5)	12.544647
0.15 (6.6667)	12.157077
0.1667 (6)	204.748373
0.1833 (5.4545)	30.555585
0.2 (5)	6.064001
0.2167 (4.6154)	15.27164
0.2333 (4.2857)	30.700182
0.25 (4)	340.142319
0.2667 (3.75)	56.630993
0.2833 (3.5294)	152.753931
0.3 (3.3333)	144.004398
0.3167 (3.1579)	206.112155
0.3333 (3)	919.831219
0.35 (2.8571)	866.842121
0.3667 (2.7273)	63.740289
0.3833 (2.6087)	62.33013
0.4 (2.5)	50.016858
0.4167 (2.4)	307.692014
0.4333 (2.3077)	73.627839
0.45 (2.2222)	15.078035
0.4667 (2.1429)	2.573648
0.4833 (2.069)	254.401028
0.5 (2)	103.952847

\begin{tabular}{lllllllll}
\hline
Raw Periodogram \tabularnewline
Parameter & Value \tabularnewline
Box-Cox transformation parameter (lambda) & 1 \tabularnewline
Degree of non-seasonal differencing (d) & 1 \tabularnewline
Degree of seasonal differencing (D) & 0 \tabularnewline
Seasonal Period (s) & 12 \tabularnewline
Frequency (Period) & Spectrum \tabularnewline
0.0167 (60) & 6.082551 \tabularnewline
0.0333 (30) & 1.941143 \tabularnewline
0.05 (20) & 1.226396 \tabularnewline
0.0667 (15) & 3.919919 \tabularnewline
0.0833 (12) & 32.602553 \tabularnewline
0.1 (10) & 5.970416 \tabularnewline
0.1167 (8.5714) & 0.358131 \tabularnewline
0.1333 (7.5) & 12.544647 \tabularnewline
0.15 (6.6667) & 12.157077 \tabularnewline
0.1667 (6) & 204.748373 \tabularnewline
0.1833 (5.4545) & 30.555585 \tabularnewline
0.2 (5) & 6.064001 \tabularnewline
0.2167 (4.6154) & 15.27164 \tabularnewline
0.2333 (4.2857) & 30.700182 \tabularnewline
0.25 (4) & 340.142319 \tabularnewline
0.2667 (3.75) & 56.630993 \tabularnewline
0.2833 (3.5294) & 152.753931 \tabularnewline
0.3 (3.3333) & 144.004398 \tabularnewline
0.3167 (3.1579) & 206.112155 \tabularnewline
0.3333 (3) & 919.831219 \tabularnewline
0.35 (2.8571) & 866.842121 \tabularnewline
0.3667 (2.7273) & 63.740289 \tabularnewline
0.3833 (2.6087) & 62.33013 \tabularnewline
0.4 (2.5) & 50.016858 \tabularnewline
0.4167 (2.4) & 307.692014 \tabularnewline
0.4333 (2.3077) & 73.627839 \tabularnewline
0.45 (2.2222) & 15.078035 \tabularnewline
0.4667 (2.1429) & 2.573648 \tabularnewline
0.4833 (2.069) & 254.401028 \tabularnewline
0.5 (2) & 103.952847 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26958&T=1

[TABLE]
[ROW][C]Raw Periodogram[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]Box-Cox transformation parameter (lambda)[/C][C]1[/C][/ROW]
[ROW][C]Degree of non-seasonal differencing (d)[/C][C]1[/C][/ROW]
[ROW][C]Degree of seasonal differencing (D)[/C][C]0[/C][/ROW]
[ROW][C]Seasonal Period (s)[/C][C]12[/C][/ROW]
[ROW][C]Frequency (Period)[/C][C]Spectrum[/C][/ROW]
[ROW][C]0.0167 (60)[/C][C]6.082551[/C][/ROW]
[ROW][C]0.0333 (30)[/C][C]1.941143[/C][/ROW]
[ROW][C]0.05 (20)[/C][C]1.226396[/C][/ROW]
[ROW][C]0.0667 (15)[/C][C]3.919919[/C][/ROW]
[ROW][C]0.0833 (12)[/C][C]32.602553[/C][/ROW]
[ROW][C]0.1 (10)[/C][C]5.970416[/C][/ROW]
[ROW][C]0.1167 (8.5714)[/C][C]0.358131[/C][/ROW]
[ROW][C]0.1333 (7.5)[/C][C]12.544647[/C][/ROW]
[ROW][C]0.15 (6.6667)[/C][C]12.157077[/C][/ROW]
[ROW][C]0.1667 (6)[/C][C]204.748373[/C][/ROW]
[ROW][C]0.1833 (5.4545)[/C][C]30.555585[/C][/ROW]
[ROW][C]0.2 (5)[/C][C]6.064001[/C][/ROW]
[ROW][C]0.2167 (4.6154)[/C][C]15.27164[/C][/ROW]
[ROW][C]0.2333 (4.2857)[/C][C]30.700182[/C][/ROW]
[ROW][C]0.25 (4)[/C][C]340.142319[/C][/ROW]
[ROW][C]0.2667 (3.75)[/C][C]56.630993[/C][/ROW]
[ROW][C]0.2833 (3.5294)[/C][C]152.753931[/C][/ROW]
[ROW][C]0.3 (3.3333)[/C][C]144.004398[/C][/ROW]
[ROW][C]0.3167 (3.1579)[/C][C]206.112155[/C][/ROW]
[ROW][C]0.3333 (3)[/C][C]919.831219[/C][/ROW]
[ROW][C]0.35 (2.8571)[/C][C]866.842121[/C][/ROW]
[ROW][C]0.3667 (2.7273)[/C][C]63.740289[/C][/ROW]
[ROW][C]0.3833 (2.6087)[/C][C]62.33013[/C][/ROW]
[ROW][C]0.4 (2.5)[/C][C]50.016858[/C][/ROW]
[ROW][C]0.4167 (2.4)[/C][C]307.692014[/C][/ROW]
[ROW][C]0.4333 (2.3077)[/C][C]73.627839[/C][/ROW]
[ROW][C]0.45 (2.2222)[/C][C]15.078035[/C][/ROW]
[ROW][C]0.4667 (2.1429)[/C][C]2.573648[/C][/ROW]
[ROW][C]0.4833 (2.069)[/C][C]254.401028[/C][/ROW]
[ROW][C]0.5 (2)[/C][C]103.952847[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26958&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26958&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Raw Periodogram
Parameter	Value
Box-Cox transformation parameter (lambda)	1
Degree of non-seasonal differencing (d)	1
Degree of seasonal differencing (D)	0
Seasonal Period (s)	12
Frequency (Period)	Spectrum
0.0167 (60)	6.082551
0.0333 (30)	1.941143
0.05 (20)	1.226396
0.0667 (15)	3.919919
0.0833 (12)	32.602553
0.1 (10)	5.970416
0.1167 (8.5714)	0.358131
0.1333 (7.5)	12.544647
0.15 (6.6667)	12.157077
0.1667 (6)	204.748373
0.1833 (5.4545)	30.555585
0.2 (5)	6.064001
0.2167 (4.6154)	15.27164
0.2333 (4.2857)	30.700182
0.25 (4)	340.142319
0.2667 (3.75)	56.630993
0.2833 (3.5294)	152.753931
0.3 (3.3333)	144.004398
0.3167 (3.1579)	206.112155
0.3333 (3)	919.831219
0.35 (2.8571)	866.842121
0.3667 (2.7273)	63.740289
0.3833 (2.6087)	62.33013
0.4 (2.5)	50.016858
0.4167 (2.4)	307.692014
0.4333 (2.3077)	73.627839
0.45 (2.2222)	15.078035
0.4667 (2.1429)	2.573648
0.4833 (2.069)	254.401028
0.5 (2)	103.952847

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 1 ; par3 = 0 ; par4 = 12 ;

Parameters (R input):

par1 = 1 ; par2 = 1 ; par3 = 0 ; par4 = 12 ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
if (par1 == 0) {
x <- log(x)
} else {
x <- (x ^ par1 - 1) / par1
}
if (par2 > 0) x <- diff(x,lag=1,difference=par2)
if (par3 > 0) x <- diff(x,lag=par4,difference=par3)
bitmap(file='test1.png')
r <- spectrum(x,main='Raw Periodogram')
dev.off()
bitmap(file='test2.png')
cpgram(x,main='Cumulative Periodogram')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Raw Periodogram',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Box-Cox transformation parameter (lambda)',header=TRUE)
a<-table.element(a,par1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Degree of non-seasonal differencing (d)',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Degree of seasonal differencing (D)',header=TRUE)
a<-table.element(a,par3)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Seasonal Period (s)',header=TRUE)
a<-table.element(a,par4)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Frequency (Period)',header=TRUE)
a<-table.element(a,'Spectrum',header=TRUE)
a<-table.row.end(a)
for (i in 1:length(r$freq)) {
a<-table.row.start(a)
mylab <- round(r$freq[i],4)
mylab <- paste(mylab,' (',sep='')
mylab <- paste(mylab,round(1/r$freq[i],4),sep='')
mylab <- paste(mylab,')',sep='')
a<-table.element(a,mylab,header=TRUE)
a<-table.element(a,round(r$spec[i],6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code