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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 computationThu, 01 Dec 2011 08:54:06 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/01/t132274766346bjsqayjuexp16.htm/, Retrieved Tue, 10 Feb 2026 18:46:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=149621, Retrieved Tue, 10 Feb 2026 18:46:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact381

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]
- RMP   [Spectral Analysis] [Unemployment] [2010-11-29 09:21:38] [b98453cac15ba1066b407e146608df68]
-    D    [Spectral Analysis] [Workshop 9, Cumul...] [2010-12-05 17:58:39] [3635fb7041b1998c5a1332cf9de22bce]
- R PD        [Spectral Analysis] [] [2011-12-01 13:54:06] [e232377fd09030116200e3da7df6eeaf] [Current]
-    D          [Spectral Analysis] [] [2011-12-01 13:56:02] [d6b4d011b409693eac2700c83288e3e7]
- RM              [Standard Deviation-Mean Plot] [] [2011-12-01 14:20:55] [d6b4d011b409693eac2700c83288e3e7]
- R PD          [Spectral Analysis] [] [2011-12-13 16:49:42] [d6b4d011b409693eac2700c83288e3e7]
- R PD          [Spectral Analysis] [] [2011-12-13 16:50:14] [d6b4d011b409693eac2700c83288e3e7]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9 676
8 642
9 402
9 610
9 294
9 448
10 319
9 548
9 801
9 596
8 923
9 746
9 829
9 125
9 782
9 441
9 162
9 915
10 444
10 209
9 985
9 842
9 429
10 132
9 849
9 172
10 313
9 819
9 955
10 048
10 082
10 541
10 208
10 233
9 439
9 963
10 158
9 225
10 474
9 757
10 490
10 281
10 444
10 640
10 695
10 786
9 832
9 747
10 411
9 511
10 402
9 701
10 540
10 112
10 915
11 183
10 384
10 834
9 886
10 216
10 943
9 867
10 203
10 837
10 573
10 647
11 502
10 656
10 866
10 835
9 945
10 331

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149621&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149621&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149621&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






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)2173.328865
0.0278 (36)26801.54856
0.0417 (24)29842.045678
0.0556 (18)50969.111115
0.0694 (14.4)54503.065648
0.0833 (12)1592032.43228
0.0972 (10.2857)64426.055904
0.1111 (9)46206.120901
0.125 (8)134.744867
0.1389 (7.2)15889.236601
0.1528 (6.5455)100467.568983
0.1667 (6)343962.635527
0.1806 (5.5385)42601.810666
0.1944 (5.1429)112806.376009
0.2083 (4.8)66321.063161
0.2222 (4.5)53286.606628
0.2361 (4.2353)118563.955103
0.25 (4)154462.586045
0.2639 (3.7895)36393.440304
0.2778 (3.6)41394.179478
0.2917 (3.4286)32050.218345
0.3056 (3.2727)22589.522154
0.3194 (3.1304)64997.812444
0.3333 (3)904507.252944
0.3472 (2.88)392060.387532
0.3611 (2.7692)4869.324537
0.375 (2.6667)103419.019259
0.3889 (2.5714)82822.09535
0.4028 (2.4828)289703.723391
0.4167 (2.4)748675.314682
0.4306 (2.3226)295357.005247
0.4444 (2.25)7182.590795
0.4583 (2.1818)16119.622052
0.4722 (2.1176)41464.082252
0.4861 (2.0571)43304.306868
0.5 (2)308457.097081

\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) & 2173.328865 \tabularnewline
0.0278 (36) & 26801.54856 \tabularnewline
0.0417 (24) & 29842.045678 \tabularnewline
0.0556 (18) & 50969.111115 \tabularnewline
0.0694 (14.4) & 54503.065648 \tabularnewline
0.0833 (12) & 1592032.43228 \tabularnewline
0.0972 (10.2857) & 64426.055904 \tabularnewline
0.1111 (9) & 46206.120901 \tabularnewline
0.125 (8) & 134.744867 \tabularnewline
0.1389 (7.2) & 15889.236601 \tabularnewline
0.1528 (6.5455) & 100467.568983 \tabularnewline
0.1667 (6) & 343962.635527 \tabularnewline
0.1806 (5.5385) & 42601.810666 \tabularnewline
0.1944 (5.1429) & 112806.376009 \tabularnewline
0.2083 (4.8) & 66321.063161 \tabularnewline
0.2222 (4.5) & 53286.606628 \tabularnewline
0.2361 (4.2353) & 118563.955103 \tabularnewline
0.25 (4) & 154462.586045 \tabularnewline
0.2639 (3.7895) & 36393.440304 \tabularnewline
0.2778 (3.6) & 41394.179478 \tabularnewline
0.2917 (3.4286) & 32050.218345 \tabularnewline
0.3056 (3.2727) & 22589.522154 \tabularnewline
0.3194 (3.1304) & 64997.812444 \tabularnewline
0.3333 (3) & 904507.252944 \tabularnewline
0.3472 (2.88) & 392060.387532 \tabularnewline
0.3611 (2.7692) & 4869.324537 \tabularnewline
0.375 (2.6667) & 103419.019259 \tabularnewline
0.3889 (2.5714) & 82822.09535 \tabularnewline
0.4028 (2.4828) & 289703.723391 \tabularnewline
0.4167 (2.4) & 748675.314682 \tabularnewline
0.4306 (2.3226) & 295357.005247 \tabularnewline
0.4444 (2.25) & 7182.590795 \tabularnewline
0.4583 (2.1818) & 16119.622052 \tabularnewline
0.4722 (2.1176) & 41464.082252 \tabularnewline
0.4861 (2.0571) & 43304.306868 \tabularnewline
0.5 (2) & 308457.097081 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149621&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]2173.328865[/C][/ROW]
[ROW][C]0.0278 (36)[/C][C]26801.54856[/C][/ROW]
[ROW][C]0.0417 (24)[/C][C]29842.045678[/C][/ROW]
[ROW][C]0.0556 (18)[/C][C]50969.111115[/C][/ROW]
[ROW][C]0.0694 (14.4)[/C][C]54503.065648[/C][/ROW]
[ROW][C]0.0833 (12)[/C][C]1592032.43228[/C][/ROW]
[ROW][C]0.0972 (10.2857)[/C][C]64426.055904[/C][/ROW]
[ROW][C]0.1111 (9)[/C][C]46206.120901[/C][/ROW]
[ROW][C]0.125 (8)[/C][C]134.744867[/C][/ROW]
[ROW][C]0.1389 (7.2)[/C][C]15889.236601[/C][/ROW]
[ROW][C]0.1528 (6.5455)[/C][C]100467.568983[/C][/ROW]
[ROW][C]0.1667 (6)[/C][C]343962.635527[/C][/ROW]
[ROW][C]0.1806 (5.5385)[/C][C]42601.810666[/C][/ROW]
[ROW][C]0.1944 (5.1429)[/C][C]112806.376009[/C][/ROW]
[ROW][C]0.2083 (4.8)[/C][C]66321.063161[/C][/ROW]
[ROW][C]0.2222 (4.5)[/C][C]53286.606628[/C][/ROW]
[ROW][C]0.2361 (4.2353)[/C][C]118563.955103[/C][/ROW]
[ROW][C]0.25 (4)[/C][C]154462.586045[/C][/ROW]
[ROW][C]0.2639 (3.7895)[/C][C]36393.440304[/C][/ROW]
[ROW][C]0.2778 (3.6)[/C][C]41394.179478[/C][/ROW]
[ROW][C]0.2917 (3.4286)[/C][C]32050.218345[/C][/ROW]
[ROW][C]0.3056 (3.2727)[/C][C]22589.522154[/C][/ROW]
[ROW][C]0.3194 (3.1304)[/C][C]64997.812444[/C][/ROW]
[ROW][C]0.3333 (3)[/C][C]904507.252944[/C][/ROW]
[ROW][C]0.3472 (2.88)[/C][C]392060.387532[/C][/ROW]
[ROW][C]0.3611 (2.7692)[/C][C]4869.324537[/C][/ROW]
[ROW][C]0.375 (2.6667)[/C][C]103419.019259[/C][/ROW]
[ROW][C]0.3889 (2.5714)[/C][C]82822.09535[/C][/ROW]
[ROW][C]0.4028 (2.4828)[/C][C]289703.723391[/C][/ROW]
[ROW][C]0.4167 (2.4)[/C][C]748675.314682[/C][/ROW]
[ROW][C]0.4306 (2.3226)[/C][C]295357.005247[/C][/ROW]
[ROW][C]0.4444 (2.25)[/C][C]7182.590795[/C][/ROW]
[ROW][C]0.4583 (2.1818)[/C][C]16119.622052[/C][/ROW]
[ROW][C]0.4722 (2.1176)[/C][C]41464.082252[/C][/ROW]
[ROW][C]0.4861 (2.0571)[/C][C]43304.306868[/C][/ROW]
[ROW][C]0.5 (2)[/C][C]308457.097081[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149621&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149621&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)2173.328865
0.0278 (36)26801.54856
0.0417 (24)29842.045678
0.0556 (18)50969.111115
0.0694 (14.4)54503.065648
0.0833 (12)1592032.43228
0.0972 (10.2857)64426.055904
0.1111 (9)46206.120901
0.125 (8)134.744867
0.1389 (7.2)15889.236601
0.1528 (6.5455)100467.568983
0.1667 (6)343962.635527
0.1806 (5.5385)42601.810666
0.1944 (5.1429)112806.376009
0.2083 (4.8)66321.063161
0.2222 (4.5)53286.606628
0.2361 (4.2353)118563.955103
0.25 (4)154462.586045
0.2639 (3.7895)36393.440304
0.2778 (3.6)41394.179478
0.2917 (3.4286)32050.218345
0.3056 (3.2727)22589.522154
0.3194 (3.1304)64997.812444
0.3333 (3)904507.252944
0.3472 (2.88)392060.387532
0.3611 (2.7692)4869.324537
0.375 (2.6667)103419.019259
0.3889 (2.5714)82822.09535
0.4028 (2.4828)289703.723391
0.4167 (2.4)748675.314682
0.4306 (2.3226)295357.005247
0.4444 (2.25)7182.590795
0.4583 (2.1818)16119.622052
0.4722 (2.1176)41464.082252
0.4861 (2.0571)43304.306868
0.5 (2)308457.097081


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;
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')