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Author's title

Author

*Unverified author*

R Software Module

rwasp_spectrum.wasp

Title produced by software

Spectral Analysis

Date of computation

Wed, 03 Dec 2008 01:09:26 -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/03/t1228291817hlvg7d1fn0wcek2.htm/, Retrieved Wed, 11 Feb 2026 02:19:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28568, Retrieved Wed, 11 Feb 2026 02:19:45 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

450

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

F       [Spectral Analysis] [] [2008-12-03 08:09:26] [e02910eed3830f1815f587e12f46cbdb] [Current]

Feedback Forum

2008-12-06 11:11:29 [Angelique Van de Vijver] [reply] 
Goede berekening en conclusies van de student 
Goede interpretatie van de grafieken door de student. 
Op het raw periodogram zien we inderdaad een langzaam dalend verloop=> langetermijntrend. De steil stijgende lijn aan linkerkant bij het cumulatieve periodogram wijst op de langetermijntrend. Deze lijn is ook ‘getrapt’ en dit wijst op de seizoenaliteit. 
De student kon ook nog iets vermelden over de tabel: In de tabel zien we dat er in het begin zeer hoge spectrumwaarden zijn. Dit wijst op een lage frequentie dat overeenkomt met een lange periode. Dit wijst op een langetermijntrend.

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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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28568&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28568&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28568&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	'Gwilym Jenkins' @ 72.249.127.135

Raw Periodogram
Parameter	Value
Box-Cox transformation parameter (lambda)	1
Degree of non-seasonal differencing (d)	0
Degree of seasonal differencing (D)	0
Seasonal Period (s)	12
Frequency (Period)	Spectrum
0.0167 (60)	10835.978345
0.0333 (30)	1139.261519
0.05 (20)	627.57256
0.0667 (15)	1769.473067
0.0833 (12)	2128.263481
0.1 (10)	192.872891
0.1167 (8.5714)	71.914885
0.1333 (7.5)	14.558517
0.15 (6.6667)	34.732703
0.1667 (6)	21.420757
0.1833 (5.4545)	6.108128
0.2 (5)	64.372902
0.2167 (4.6154)	24.488962
0.2333 (4.2857)	50.010345
0.25 (4)	73.986282
0.2667 (3.75)	11.468697
0.2833 (3.5294)	11.963502
0.3 (3.3333)	28.551884
0.3167 (3.1579)	19.818555
0.3333 (3)	25.203505
0.35 (2.8571)	6.745583
0.3667 (2.7273)	7.699368
0.3833 (2.6087)	0.706557
0.4 (2.5)	0.76876
0.4167 (2.4)	2.190154
0.4333 (2.3077)	11.161359
0.45 (2.2222)	0.297739
0.4667 (2.1429)	3.584528
0.4833 (2.069)	3.151464
0.5 (2)	1.138508

\begin{tabular}{lllllllll}
\hline
Raw Periodogram \tabularnewline
Parameter & Value \tabularnewline
Box-Cox transformation parameter (lambda) & 1 \tabularnewline
Degree of non-seasonal differencing (d) & 0 \tabularnewline
Degree of seasonal differencing (D) & 0 \tabularnewline
Seasonal Period (s) & 12 \tabularnewline
Frequency (Period) & Spectrum \tabularnewline
0.0167 (60) & 10835.978345 \tabularnewline
0.0333 (30) & 1139.261519 \tabularnewline
0.05 (20) & 627.57256 \tabularnewline
0.0667 (15) & 1769.473067 \tabularnewline
0.0833 (12) & 2128.263481 \tabularnewline
0.1 (10) & 192.872891 \tabularnewline
0.1167 (8.5714) & 71.914885 \tabularnewline
0.1333 (7.5) & 14.558517 \tabularnewline
0.15 (6.6667) & 34.732703 \tabularnewline
0.1667 (6) & 21.420757 \tabularnewline
0.1833 (5.4545) & 6.108128 \tabularnewline
0.2 (5) & 64.372902 \tabularnewline
0.2167 (4.6154) & 24.488962 \tabularnewline
0.2333 (4.2857) & 50.010345 \tabularnewline
0.25 (4) & 73.986282 \tabularnewline
0.2667 (3.75) & 11.468697 \tabularnewline
0.2833 (3.5294) & 11.963502 \tabularnewline
0.3 (3.3333) & 28.551884 \tabularnewline
0.3167 (3.1579) & 19.818555 \tabularnewline
0.3333 (3) & 25.203505 \tabularnewline
0.35 (2.8571) & 6.745583 \tabularnewline
0.3667 (2.7273) & 7.699368 \tabularnewline
0.3833 (2.6087) & 0.706557 \tabularnewline
0.4 (2.5) & 0.76876 \tabularnewline
0.4167 (2.4) & 2.190154 \tabularnewline
0.4333 (2.3077) & 11.161359 \tabularnewline
0.45 (2.2222) & 0.297739 \tabularnewline
0.4667 (2.1429) & 3.584528 \tabularnewline
0.4833 (2.069) & 3.151464 \tabularnewline
0.5 (2) & 1.138508 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28568&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]0[/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]10835.978345[/C][/ROW]
[ROW][C]0.0333 (30)[/C][C]1139.261519[/C][/ROW]
[ROW][C]0.05 (20)[/C][C]627.57256[/C][/ROW]
[ROW][C]0.0667 (15)[/C][C]1769.473067[/C][/ROW]
[ROW][C]0.0833 (12)[/C][C]2128.263481[/C][/ROW]
[ROW][C]0.1 (10)[/C][C]192.872891[/C][/ROW]
[ROW][C]0.1167 (8.5714)[/C][C]71.914885[/C][/ROW]
[ROW][C]0.1333 (7.5)[/C][C]14.558517[/C][/ROW]
[ROW][C]0.15 (6.6667)[/C][C]34.732703[/C][/ROW]
[ROW][C]0.1667 (6)[/C][C]21.420757[/C][/ROW]
[ROW][C]0.1833 (5.4545)[/C][C]6.108128[/C][/ROW]
[ROW][C]0.2 (5)[/C][C]64.372902[/C][/ROW]
[ROW][C]0.2167 (4.6154)[/C][C]24.488962[/C][/ROW]
[ROW][C]0.2333 (4.2857)[/C][C]50.010345[/C][/ROW]
[ROW][C]0.25 (4)[/C][C]73.986282[/C][/ROW]
[ROW][C]0.2667 (3.75)[/C][C]11.468697[/C][/ROW]
[ROW][C]0.2833 (3.5294)[/C][C]11.963502[/C][/ROW]
[ROW][C]0.3 (3.3333)[/C][C]28.551884[/C][/ROW]
[ROW][C]0.3167 (3.1579)[/C][C]19.818555[/C][/ROW]
[ROW][C]0.3333 (3)[/C][C]25.203505[/C][/ROW]
[ROW][C]0.35 (2.8571)[/C][C]6.745583[/C][/ROW]
[ROW][C]0.3667 (2.7273)[/C][C]7.699368[/C][/ROW]
[ROW][C]0.3833 (2.6087)[/C][C]0.706557[/C][/ROW]
[ROW][C]0.4 (2.5)[/C][C]0.76876[/C][/ROW]
[ROW][C]0.4167 (2.4)[/C][C]2.190154[/C][/ROW]
[ROW][C]0.4333 (2.3077)[/C][C]11.161359[/C][/ROW]
[ROW][C]0.45 (2.2222)[/C][C]0.297739[/C][/ROW]
[ROW][C]0.4667 (2.1429)[/C][C]3.584528[/C][/ROW]
[ROW][C]0.4833 (2.069)[/C][C]3.151464[/C][/ROW]
[ROW][C]0.5 (2)[/C][C]1.138508[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28568&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28568&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)	0
Degree of seasonal differencing (D)	0
Seasonal Period (s)	12
Frequency (Period)	Spectrum
0.0167 (60)	10835.978345
0.0333 (30)	1139.261519
0.05 (20)	627.57256
0.0667 (15)	1769.473067
0.0833 (12)	2128.263481
0.1 (10)	192.872891
0.1167 (8.5714)	71.914885
0.1333 (7.5)	14.558517
0.15 (6.6667)	34.732703
0.1667 (6)	21.420757
0.1833 (5.4545)	6.108128
0.2 (5)	64.372902
0.2167 (4.6154)	24.488962
0.2333 (4.2857)	50.010345
0.25 (4)	73.986282
0.2667 (3.75)	11.468697
0.2833 (3.5294)	11.963502
0.3 (3.3333)	28.551884
0.3167 (3.1579)	19.818555
0.3333 (3)	25.203505
0.35 (2.8571)	6.745583
0.3667 (2.7273)	7.699368
0.3833 (2.6087)	0.706557
0.4 (2.5)	0.76876
0.4167 (2.4)	2.190154
0.4333 (2.3077)	11.161359
0.45 (2.2222)	0.297739
0.4667 (2.1429)	3.584528
0.4833 (2.069)	3.151464
0.5 (2)	1.138508

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = 1 ; par2 = 0 ; 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