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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_spectrum.wasp
Title produced by softwareSpectral Analysis
Date of computationMon, 08 Dec 2008 13:14:38 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/08/t1228767327cf47h186oshs02z.htm/, Retrieved Wed, 11 Feb 2026 13:55:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30930, Retrieved Wed, 11 Feb 2026 13:55:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact393

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMPD  [Standard Deviation-Mean Plot] [SD mean plot step 1] [2008-12-08 19:47:44] [7d3039e6253bb5fb3b26df1537d500b4]
F    D    [Standard Deviation-Mean Plot] [SD mean plot step 1] [2008-12-08 19:54:49] [7d3039e6253bb5fb3b26df1537d500b4]
F RM D        [Spectral Analysis] [cumulative period...] [2008-12-08 20:14:38] [35348cd8592af0baf5f138bd59921307] [Current]
-               [Spectral Analysis] [cumulative period...] [2008-12-08 20:28:31] [7d3039e6253bb5fb3b26df1537d500b4]
F RMPD            [ARIMA Forecasting] [Arima forecasting...] [2008-12-15 19:14:36] [7d3039e6253bb5fb3b26df1537d500b4]
-   P               [ARIMA Forecasting] [Arima Forecast st...] [2008-12-19 17:28:32] [7d3039e6253bb5fb3b26df1537d500b4]
Feedback Forum
2008-12-15 09:19:07 [Stéphanie Claes] [reply] 
Hier wordt het resultaat van de variance reduction matrix nogmaals bevestigd, we kunnen duidelijk zien dat een groot deel van de tijdreeks verklaard zal worden door de lange termijntrend (dit kunnen we zien door de stijging die we waarnemen in het cumulatief periodogram).

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.8
7.6
7.5
7.6
7.5
7.3
7.6
7.5
7.6
7.9
7.9
8.1
8.2
8.0
7.5
6.8
6.5
6.6
7.6
8.0
8.0
7.7
7.5
7.6
7.7
7.9
7.8
7.5
7.5
7.1
7.5
7.5
7.6
7.7
7.7
7.9
8.1
8.2
8.2
8.1
7.9
7.3
6.9
6.6
6.7
6.9
7.0
7.1
7.2
7.1
6.9
7.0
6.8
6.4
6.7
6.7
6.4
6.3
6.2
6.5
6.8
6.8
6.5
6.3
5.9
5.9
6.4
6.4

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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=30930&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=30930&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30930&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Raw Periodogram
ParameterValue
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
0.0139 (72)1.726714
0.0278 (36)0.834892
0.0417 (24)0.091965
0.0556 (18)0.059025
0.0694 (14.4)1.213165
0.0833 (12)1.197437
0.0972 (10.2857)0.310561
0.1111 (9)0.432599
0.125 (8)0.158174
0.1389 (7.2)0.445747
0.1528 (6.5455)0.278538
0.1667 (6)0.354847
0.1806 (5.5385)0.022982
0.1944 (5.1429)0.141298
0.2083 (4.8)0.018387
0.2222 (4.5)0.01064
0.2361 (4.2353)0.012779
0.25 (4)0.010796
0.2639 (3.7895)0.010331
0.2778 (3.6)0.00783
0.2917 (3.4286)0.003521
0.3056 (3.2727)0.009278
0.3194 (3.1304)0.00072
0.3333 (3)0.053931
0.3472 (2.88)0.005201
0.3611 (2.7692)0.000445
0.375 (2.6667)0.017472
0.3889 (2.5714)0.000291
0.4028 (2.4828)0.007875
0.4167 (2.4)0.046376
0.4306 (2.3226)0.00673
0.4444 (2.25)0.000815
0.4583 (2.1818)0.001641
0.4722 (2.1176)0.00011
0.4861 (2.0571)0.008962
0.5 (2)0.011647

\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
0.0139 (72) & 1.726714 \tabularnewline
0.0278 (36) & 0.834892 \tabularnewline
0.0417 (24) & 0.091965 \tabularnewline
0.0556 (18) & 0.059025 \tabularnewline
0.0694 (14.4) & 1.213165 \tabularnewline
0.0833 (12) & 1.197437 \tabularnewline
0.0972 (10.2857) & 0.310561 \tabularnewline
0.1111 (9) & 0.432599 \tabularnewline
0.125 (8) & 0.158174 \tabularnewline
0.1389 (7.2) & 0.445747 \tabularnewline
0.1528 (6.5455) & 0.278538 \tabularnewline
0.1667 (6) & 0.354847 \tabularnewline
0.1806 (5.5385) & 0.022982 \tabularnewline
0.1944 (5.1429) & 0.141298 \tabularnewline
0.2083 (4.8) & 0.018387 \tabularnewline
0.2222 (4.5) & 0.01064 \tabularnewline
0.2361 (4.2353) & 0.012779 \tabularnewline
0.25 (4) & 0.010796 \tabularnewline
0.2639 (3.7895) & 0.010331 \tabularnewline
0.2778 (3.6) & 0.00783 \tabularnewline
0.2917 (3.4286) & 0.003521 \tabularnewline
0.3056 (3.2727) & 0.009278 \tabularnewline
0.3194 (3.1304) & 0.00072 \tabularnewline
0.3333 (3) & 0.053931 \tabularnewline
0.3472 (2.88) & 0.005201 \tabularnewline
0.3611 (2.7692) & 0.000445 \tabularnewline
0.375 (2.6667) & 0.017472 \tabularnewline
0.3889 (2.5714) & 0.000291 \tabularnewline
0.4028 (2.4828) & 0.007875 \tabularnewline
0.4167 (2.4) & 0.046376 \tabularnewline
0.4306 (2.3226) & 0.00673 \tabularnewline
0.4444 (2.25) & 0.000815 \tabularnewline
0.4583 (2.1818) & 0.001641 \tabularnewline
0.4722 (2.1176) & 0.00011 \tabularnewline
0.4861 (2.0571) & 0.008962 \tabularnewline
0.5 (2) & 0.011647 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30930&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]0.0139 (72)[/C][C]1.726714[/C][/ROW]
[ROW][C]0.0278 (36)[/C][C]0.834892[/C][/ROW]
[ROW][C]0.0417 (24)[/C][C]0.091965[/C][/ROW]
[ROW][C]0.0556 (18)[/C][C]0.059025[/C][/ROW]
[ROW][C]0.0694 (14.4)[/C][C]1.213165[/C][/ROW]
[ROW][C]0.0833 (12)[/C][C]1.197437[/C][/ROW]
[ROW][C]0.0972 (10.2857)[/C][C]0.310561[/C][/ROW]
[ROW][C]0.1111 (9)[/C][C]0.432599[/C][/ROW]
[ROW][C]0.125 (8)[/C][C]0.158174[/C][/ROW]
[ROW][C]0.1389 (7.2)[/C][C]0.445747[/C][/ROW]
[ROW][C]0.1528 (6.5455)[/C][C]0.278538[/C][/ROW]
[ROW][C]0.1667 (6)[/C][C]0.354847[/C][/ROW]
[ROW][C]0.1806 (5.5385)[/C][C]0.022982[/C][/ROW]
[ROW][C]0.1944 (5.1429)[/C][C]0.141298[/C][/ROW]
[ROW][C]0.2083 (4.8)[/C][C]0.018387[/C][/ROW]
[ROW][C]0.2222 (4.5)[/C][C]0.01064[/C][/ROW]
[ROW][C]0.2361 (4.2353)[/C][C]0.012779[/C][/ROW]
[ROW][C]0.25 (4)[/C][C]0.010796[/C][/ROW]
[ROW][C]0.2639 (3.7895)[/C][C]0.010331[/C][/ROW]
[ROW][C]0.2778 (3.6)[/C][C]0.00783[/C][/ROW]
[ROW][C]0.2917 (3.4286)[/C][C]0.003521[/C][/ROW]
[ROW][C]0.3056 (3.2727)[/C][C]0.009278[/C][/ROW]
[ROW][C]0.3194 (3.1304)[/C][C]0.00072[/C][/ROW]
[ROW][C]0.3333 (3)[/C][C]0.053931[/C][/ROW]
[ROW][C]0.3472 (2.88)[/C][C]0.005201[/C][/ROW]
[ROW][C]0.3611 (2.7692)[/C][C]0.000445[/C][/ROW]
[ROW][C]0.375 (2.6667)[/C][C]0.017472[/C][/ROW]
[ROW][C]0.3889 (2.5714)[/C][C]0.000291[/C][/ROW]
[ROW][C]0.4028 (2.4828)[/C][C]0.007875[/C][/ROW]
[ROW][C]0.4167 (2.4)[/C][C]0.046376[/C][/ROW]
[ROW][C]0.4306 (2.3226)[/C][C]0.00673[/C][/ROW]
[ROW][C]0.4444 (2.25)[/C][C]0.000815[/C][/ROW]
[ROW][C]0.4583 (2.1818)[/C][C]0.001641[/C][/ROW]
[ROW][C]0.4722 (2.1176)[/C][C]0.00011[/C][/ROW]
[ROW][C]0.4861 (2.0571)[/C][C]0.008962[/C][/ROW]
[ROW][C]0.5 (2)[/C][C]0.011647[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30930&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30930&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Raw Periodogram
ParameterValue
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
0.0139 (72)1.726714
0.0278 (36)0.834892
0.0417 (24)0.091965
0.0556 (18)0.059025
0.0694 (14.4)1.213165
0.0833 (12)1.197437
0.0972 (10.2857)0.310561
0.1111 (9)0.432599
0.125 (8)0.158174
0.1389 (7.2)0.445747
0.1528 (6.5455)0.278538
0.1667 (6)0.354847
0.1806 (5.5385)0.022982
0.1944 (5.1429)0.141298
0.2083 (4.8)0.018387
0.2222 (4.5)0.01064
0.2361 (4.2353)0.012779
0.25 (4)0.010796
0.2639 (3.7895)0.010331
0.2778 (3.6)0.00783
0.2917 (3.4286)0.003521
0.3056 (3.2727)0.009278
0.3194 (3.1304)0.00072
0.3333 (3)0.053931
0.3472 (2.88)0.005201
0.3611 (2.7692)0.000445
0.375 (2.6667)0.017472
0.3889 (2.5714)0.000291
0.4028 (2.4828)0.007875
0.4167 (2.4)0.046376
0.4306 (2.3226)0.00673
0.4444 (2.25)0.000815
0.4583 (2.1818)0.001641
0.4722 (2.1176)0.00011
0.4861 (2.0571)0.008962
0.5 (2)0.011647


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 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')