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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 computationSun, 19 Dec 2010 11:35:26 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/19/t1292758403us046x5nkzrbech.htm/, Retrieved Tue, 10 Feb 2026 19:09:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112294, Retrieved Tue, 10 Feb 2026 19:09:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact419

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Spectral Analysis] [CP_paper_uit_Voet] [2010-12-19 11:35:26] [13dfa60174f50d862e8699db2153bfc5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15
14,4
13
13,7
13,6
15,2
12,9
14
14,1
13,2
11,3
13,3
14,4
13,3
11,6
13,2
13,1
14,6
14
14,3
13,8
13,7
11
14,4
15,6
13,7
12,6
13,2
13,3
14,3
14
13,4
13,9
13,7
10,5
14,5
15
13,5
13,5
13,2
13,8
16,2
14,7
13,9
16
14,4
12,3
15,9
15,9
15,5
15,1
14,5
15,1
17,4
16,2
15,6
17,2
14,9
13,8
17,5
16,2
17,5
16,6
16,2
16,6
19,6
15,9
18
18,3
16,3
14,9
18,2
18,4
18,5
16
17,4
17,2
19,6
17,2
18,3
19,3
18,1
16,2
18,4
20,5
19
16,5
18,7
19
19,2
20,5
19,3
20,6
20,1
16,1
20,4
19,7
15,6
14,4
13,7
14,1
15
14,2
13,6
15,4
14,8
12,5
16,2
16,1
16
15,8
15,2
15,7
18,9
17,4
17
19,8
17,7
16
19,6
19,7

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112294&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112294&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112294&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Raw Periodogram
ParameterValue
Box-Cox transformation parameter (lambda)-0.6
Degree of non-seasonal differencing (d)0
Degree of seasonal differencing (D)0
Seasonal Period (s)12
Frequency (Period)Spectrum
0.008 (125)0.005782
0.016 (62.5)0.004998
0.024 (41.6667)0.002434
0.032 (31.25)0.002477
0.04 (25)0.001231
0.048 (20.8333)0.000561
0.056 (17.8571)0.000584
0.064 (15.625)0.000171
0.072 (13.8889)0.000118
0.08 (12.5)5e-04
0.088 (11.3636)0.000136
0.096 (10.4167)0.000118
0.104 (9.6154)6.5e-05
0.112 (8.9286)5e-06
0.12 (8.3333)3e-06
0.128 (7.8125)2.6e-05
0.136 (7.3529)6e-06
0.144 (6.9444)0.000113
0.152 (6.5789)0.000209
0.16 (6.25)0.000303
0.168 (5.9524)0.002902
0.176 (5.6818)3.1e-05
0.184 (5.4348)6.5e-05
0.192 (5.2083)2.9e-05
0.2 (5)1.5e-05
0.208 (4.8077)3.4e-05
0.216 (4.6296)0.000133
0.224 (4.4643)2.9e-05
0.232 (4.3103)0.000104
0.24 (4.1667)0.000138
0.248 (4.0323)0.003393
0.256 (3.9062)0.000524
0.264 (3.7879)0.000212
0.272 (3.6765)2.1e-05
0.28 (3.5714)4.5e-05
0.288 (3.4722)7e-06
0.296 (3.3784)1e-06
0.304 (3.2895)9.1e-05
0.312 (3.2051)3.5e-05
0.32 (3.125)7.2e-05
0.328 (3.0488)0.000463
0.336 (2.9762)0.002097
0.344 (2.907)0.000676
0.352 (2.8409)0.000593
0.36 (2.7778)0.000101
0.368 (2.7174)7e-06
0.376 (2.6596)5e-06
0.384 (2.6042)5.4e-05
0.392 (2.551)6.3e-05
0.4 (2.5)0.000101
0.408 (2.451)2e-05
0.416 (2.4038)0.000132
0.424 (2.3585)5.7e-05
0.432 (2.3148)0.000214
0.44 (2.2727)3e-06
0.448 (2.2321)1.3e-05
0.456 (2.193)1.4e-05
0.464 (2.1552)7e-06
0.472 (2.1186)1.7e-05
0.48 (2.0833)0.000158
0.488 (2.0492)5.4e-05
0.496 (2.0161)0.000871

\begin{tabular}{lllllllll}
\hline
Raw Periodogram \tabularnewline
Parameter & Value \tabularnewline
Box-Cox transformation parameter (lambda) & -0.6 \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
0.008 (125) & 0.005782 \tabularnewline
0.016 (62.5) & 0.004998 \tabularnewline
0.024 (41.6667) & 0.002434 \tabularnewline
0.032 (31.25) & 0.002477 \tabularnewline
0.04 (25) & 0.001231 \tabularnewline
0.048 (20.8333) & 0.000561 \tabularnewline
0.056 (17.8571) & 0.000584 \tabularnewline
0.064 (15.625) & 0.000171 \tabularnewline
0.072 (13.8889) & 0.000118 \tabularnewline
0.08 (12.5) & 5e-04 \tabularnewline
0.088 (11.3636) & 0.000136 \tabularnewline
0.096 (10.4167) & 0.000118 \tabularnewline
0.104 (9.6154) & 6.5e-05 \tabularnewline
0.112 (8.9286) & 5e-06 \tabularnewline
0.12 (8.3333) & 3e-06 \tabularnewline
0.128 (7.8125) & 2.6e-05 \tabularnewline
0.136 (7.3529) & 6e-06 \tabularnewline
0.144 (6.9444) & 0.000113 \tabularnewline
0.152 (6.5789) & 0.000209 \tabularnewline
0.16 (6.25) & 0.000303 \tabularnewline
0.168 (5.9524) & 0.002902 \tabularnewline
0.176 (5.6818) & 3.1e-05 \tabularnewline
0.184 (5.4348) & 6.5e-05 \tabularnewline
0.192 (5.2083) & 2.9e-05 \tabularnewline
0.2 (5) & 1.5e-05 \tabularnewline
0.208 (4.8077) & 3.4e-05 \tabularnewline
0.216 (4.6296) & 0.000133 \tabularnewline
0.224 (4.4643) & 2.9e-05 \tabularnewline
0.232 (4.3103) & 0.000104 \tabularnewline
0.24 (4.1667) & 0.000138 \tabularnewline
0.248 (4.0323) & 0.003393 \tabularnewline
0.256 (3.9062) & 0.000524 \tabularnewline
0.264 (3.7879) & 0.000212 \tabularnewline
0.272 (3.6765) & 2.1e-05 \tabularnewline
0.28 (3.5714) & 4.5e-05 \tabularnewline
0.288 (3.4722) & 7e-06 \tabularnewline
0.296 (3.3784) & 1e-06 \tabularnewline
0.304 (3.2895) & 9.1e-05 \tabularnewline
0.312 (3.2051) & 3.5e-05 \tabularnewline
0.32 (3.125) & 7.2e-05 \tabularnewline
0.328 (3.0488) & 0.000463 \tabularnewline
0.336 (2.9762) & 0.002097 \tabularnewline
0.344 (2.907) & 0.000676 \tabularnewline
0.352 (2.8409) & 0.000593 \tabularnewline
0.36 (2.7778) & 0.000101 \tabularnewline
0.368 (2.7174) & 7e-06 \tabularnewline
0.376 (2.6596) & 5e-06 \tabularnewline
0.384 (2.6042) & 5.4e-05 \tabularnewline
0.392 (2.551) & 6.3e-05 \tabularnewline
0.4 (2.5) & 0.000101 \tabularnewline
0.408 (2.451) & 2e-05 \tabularnewline
0.416 (2.4038) & 0.000132 \tabularnewline
0.424 (2.3585) & 5.7e-05 \tabularnewline
0.432 (2.3148) & 0.000214 \tabularnewline
0.44 (2.2727) & 3e-06 \tabularnewline
0.448 (2.2321) & 1.3e-05 \tabularnewline
0.456 (2.193) & 1.4e-05 \tabularnewline
0.464 (2.1552) & 7e-06 \tabularnewline
0.472 (2.1186) & 1.7e-05 \tabularnewline
0.48 (2.0833) & 0.000158 \tabularnewline
0.488 (2.0492) & 5.4e-05 \tabularnewline
0.496 (2.0161) & 0.000871 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112294&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]-0.6[/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]0.008 (125)[/C][C]0.005782[/C][/ROW]
[ROW][C]0.016 (62.5)[/C][C]0.004998[/C][/ROW]
[ROW][C]0.024 (41.6667)[/C][C]0.002434[/C][/ROW]
[ROW][C]0.032 (31.25)[/C][C]0.002477[/C][/ROW]
[ROW][C]0.04 (25)[/C][C]0.001231[/C][/ROW]
[ROW][C]0.048 (20.8333)[/C][C]0.000561[/C][/ROW]
[ROW][C]0.056 (17.8571)[/C][C]0.000584[/C][/ROW]
[ROW][C]0.064 (15.625)[/C][C]0.000171[/C][/ROW]
[ROW][C]0.072 (13.8889)[/C][C]0.000118[/C][/ROW]
[ROW][C]0.08 (12.5)[/C][C]5e-04[/C][/ROW]
[ROW][C]0.088 (11.3636)[/C][C]0.000136[/C][/ROW]
[ROW][C]0.096 (10.4167)[/C][C]0.000118[/C][/ROW]
[ROW][C]0.104 (9.6154)[/C][C]6.5e-05[/C][/ROW]
[ROW][C]0.112 (8.9286)[/C][C]5e-06[/C][/ROW]
[ROW][C]0.12 (8.3333)[/C][C]3e-06[/C][/ROW]
[ROW][C]0.128 (7.8125)[/C][C]2.6e-05[/C][/ROW]
[ROW][C]0.136 (7.3529)[/C][C]6e-06[/C][/ROW]
[ROW][C]0.144 (6.9444)[/C][C]0.000113[/C][/ROW]
[ROW][C]0.152 (6.5789)[/C][C]0.000209[/C][/ROW]
[ROW][C]0.16 (6.25)[/C][C]0.000303[/C][/ROW]
[ROW][C]0.168 (5.9524)[/C][C]0.002902[/C][/ROW]
[ROW][C]0.176 (5.6818)[/C][C]3.1e-05[/C][/ROW]
[ROW][C]0.184 (5.4348)[/C][C]6.5e-05[/C][/ROW]
[ROW][C]0.192 (5.2083)[/C][C]2.9e-05[/C][/ROW]
[ROW][C]0.2 (5)[/C][C]1.5e-05[/C][/ROW]
[ROW][C]0.208 (4.8077)[/C][C]3.4e-05[/C][/ROW]
[ROW][C]0.216 (4.6296)[/C][C]0.000133[/C][/ROW]
[ROW][C]0.224 (4.4643)[/C][C]2.9e-05[/C][/ROW]
[ROW][C]0.232 (4.3103)[/C][C]0.000104[/C][/ROW]
[ROW][C]0.24 (4.1667)[/C][C]0.000138[/C][/ROW]
[ROW][C]0.248 (4.0323)[/C][C]0.003393[/C][/ROW]
[ROW][C]0.256 (3.9062)[/C][C]0.000524[/C][/ROW]
[ROW][C]0.264 (3.7879)[/C][C]0.000212[/C][/ROW]
[ROW][C]0.272 (3.6765)[/C][C]2.1e-05[/C][/ROW]
[ROW][C]0.28 (3.5714)[/C][C]4.5e-05[/C][/ROW]
[ROW][C]0.288 (3.4722)[/C][C]7e-06[/C][/ROW]
[ROW][C]0.296 (3.3784)[/C][C]1e-06[/C][/ROW]
[ROW][C]0.304 (3.2895)[/C][C]9.1e-05[/C][/ROW]
[ROW][C]0.312 (3.2051)[/C][C]3.5e-05[/C][/ROW]
[ROW][C]0.32 (3.125)[/C][C]7.2e-05[/C][/ROW]
[ROW][C]0.328 (3.0488)[/C][C]0.000463[/C][/ROW]
[ROW][C]0.336 (2.9762)[/C][C]0.002097[/C][/ROW]
[ROW][C]0.344 (2.907)[/C][C]0.000676[/C][/ROW]
[ROW][C]0.352 (2.8409)[/C][C]0.000593[/C][/ROW]
[ROW][C]0.36 (2.7778)[/C][C]0.000101[/C][/ROW]
[ROW][C]0.368 (2.7174)[/C][C]7e-06[/C][/ROW]
[ROW][C]0.376 (2.6596)[/C][C]5e-06[/C][/ROW]
[ROW][C]0.384 (2.6042)[/C][C]5.4e-05[/C][/ROW]
[ROW][C]0.392 (2.551)[/C][C]6.3e-05[/C][/ROW]
[ROW][C]0.4 (2.5)[/C][C]0.000101[/C][/ROW]
[ROW][C]0.408 (2.451)[/C][C]2e-05[/C][/ROW]
[ROW][C]0.416 (2.4038)[/C][C]0.000132[/C][/ROW]
[ROW][C]0.424 (2.3585)[/C][C]5.7e-05[/C][/ROW]
[ROW][C]0.432 (2.3148)[/C][C]0.000214[/C][/ROW]
[ROW][C]0.44 (2.2727)[/C][C]3e-06[/C][/ROW]
[ROW][C]0.448 (2.2321)[/C][C]1.3e-05[/C][/ROW]
[ROW][C]0.456 (2.193)[/C][C]1.4e-05[/C][/ROW]
[ROW][C]0.464 (2.1552)[/C][C]7e-06[/C][/ROW]
[ROW][C]0.472 (2.1186)[/C][C]1.7e-05[/C][/ROW]
[ROW][C]0.48 (2.0833)[/C][C]0.000158[/C][/ROW]
[ROW][C]0.488 (2.0492)[/C][C]5.4e-05[/C][/ROW]
[ROW][C]0.496 (2.0161)[/C][C]0.000871[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112294&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112294&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)-0.6
Degree of non-seasonal differencing (d)0
Degree of seasonal differencing (D)0
Seasonal Period (s)12
Frequency (Period)Spectrum
0.008 (125)0.005782
0.016 (62.5)0.004998
0.024 (41.6667)0.002434
0.032 (31.25)0.002477
0.04 (25)0.001231
0.048 (20.8333)0.000561
0.056 (17.8571)0.000584
0.064 (15.625)0.000171
0.072 (13.8889)0.000118
0.08 (12.5)5e-04
0.088 (11.3636)0.000136
0.096 (10.4167)0.000118
0.104 (9.6154)6.5e-05
0.112 (8.9286)5e-06
0.12 (8.3333)3e-06
0.128 (7.8125)2.6e-05
0.136 (7.3529)6e-06
0.144 (6.9444)0.000113
0.152 (6.5789)0.000209
0.16 (6.25)0.000303
0.168 (5.9524)0.002902
0.176 (5.6818)3.1e-05
0.184 (5.4348)6.5e-05
0.192 (5.2083)2.9e-05
0.2 (5)1.5e-05
0.208 (4.8077)3.4e-05
0.216 (4.6296)0.000133
0.224 (4.4643)2.9e-05
0.232 (4.3103)0.000104
0.24 (4.1667)0.000138
0.248 (4.0323)0.003393
0.256 (3.9062)0.000524
0.264 (3.7879)0.000212
0.272 (3.6765)2.1e-05
0.28 (3.5714)4.5e-05
0.288 (3.4722)7e-06
0.296 (3.3784)1e-06
0.304 (3.2895)9.1e-05
0.312 (3.2051)3.5e-05
0.32 (3.125)7.2e-05
0.328 (3.0488)0.000463
0.336 (2.9762)0.002097
0.344 (2.907)0.000676
0.352 (2.8409)0.000593
0.36 (2.7778)0.000101
0.368 (2.7174)7e-06
0.376 (2.6596)5e-06
0.384 (2.6042)5.4e-05
0.392 (2.551)6.3e-05
0.4 (2.5)0.000101
0.408 (2.451)2e-05
0.416 (2.4038)0.000132
0.424 (2.3585)5.7e-05
0.432 (2.3148)0.000214
0.44 (2.2727)3e-06
0.448 (2.2321)1.3e-05
0.456 (2.193)1.4e-05
0.464 (2.1552)7e-06
0.472 (2.1186)1.7e-05
0.48 (2.0833)0.000158
0.488 (2.0492)5.4e-05
0.496 (2.0161)0.000871


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = -0.6 ; par2 = 0 ; par3 = 0 ; par4 = 12 ;
Parameters (R input):
par1 = -0.6 ; 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')