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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 computationFri, 21 Nov 2014 16:55:18 +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/2014/Nov/21/t1416589185pszzxc8juiuubzw.htm/, Retrieved Sun, 26 Apr 2026 08:58:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=257681, Retrieved Sun, 26 Apr 2026 08:58:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact367

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] [] [2008-12-14 11:54:22] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [Variance Reduction Matrix] [] [2014-11-21 16:29:18] [cc401d1001c65f55a3dfc6f2420e9570]
- RMP     [(Partial) Autocorrelation Function] [] [2014-11-21 16:38:49] [cc401d1001c65f55a3dfc6f2420e9570]
- RM          [Spectral Analysis] [] [2014-11-21 16:55:18] [37e054ac358b2aa7c2a1d0b751dfa890] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
46
62
66
59
58
61
41
27
58
70
49
59
44
36
72
45
56
54
53
35
61
52
47
51
52
63
74
45
51
64
36
30
55
64
39
40
63
45
59
55
40
64
27
28
45
57
45
69
60
56
58
50
51
53
37
22
55
70
62
58
39
49
58
47
42
62
39
40
72
70
54
65

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'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257681&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257681&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257681&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'Gertrude Mary Cox' @ cox.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)37.172984
0.0278 (36)16.777311
0.0417 (24)61.667156
0.0556 (18)3.459588
0.0694 (14.4)2.654066
0.0833 (12)490.080334
0.0972 (10.2857)322.817014
0.1111 (9)58.239244
0.125 (8)136.316719
0.1389 (7.2)51.746414
0.1528 (6.5455)12.037638
0.1667 (6)630.128237
0.1806 (5.5385)96.475133
0.1944 (5.1429)73.594184
0.2083 (4.8)165.695915
0.2222 (4.5)7.217566
0.2361 (4.2353)16.865451
0.25 (4)768.790823
0.2639 (3.7895)34.302105
0.2778 (3.6)146.29514
0.2917 (3.4286)14.935392
0.3056 (3.2727)19.223259
0.3194 (3.1304)33.618802
0.3333 (3)1237.847229
0.3472 (2.88)2.818635
0.3611 (2.7692)82.415566
0.375 (2.6667)94.091159
0.3889 (2.5714)58.556555
0.4028 (2.4828)103.157416
0.4167 (2.4)27.524318
0.4306 (2.3226)1.455437
0.4444 (2.25)172.747502
0.4583 (2.1818)4.346182
0.4722 (2.1176)56.85265
0.4861 (2.0571)117.20025
0.5 (2)0.739491

\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) & 37.172984 \tabularnewline
0.0278 (36) & 16.777311 \tabularnewline
0.0417 (24) & 61.667156 \tabularnewline
0.0556 (18) & 3.459588 \tabularnewline
0.0694 (14.4) & 2.654066 \tabularnewline
0.0833 (12) & 490.080334 \tabularnewline
0.0972 (10.2857) & 322.817014 \tabularnewline
0.1111 (9) & 58.239244 \tabularnewline
0.125 (8) & 136.316719 \tabularnewline
0.1389 (7.2) & 51.746414 \tabularnewline
0.1528 (6.5455) & 12.037638 \tabularnewline
0.1667 (6) & 630.128237 \tabularnewline
0.1806 (5.5385) & 96.475133 \tabularnewline
0.1944 (5.1429) & 73.594184 \tabularnewline
0.2083 (4.8) & 165.695915 \tabularnewline
0.2222 (4.5) & 7.217566 \tabularnewline
0.2361 (4.2353) & 16.865451 \tabularnewline
0.25 (4) & 768.790823 \tabularnewline
0.2639 (3.7895) & 34.302105 \tabularnewline
0.2778 (3.6) & 146.29514 \tabularnewline
0.2917 (3.4286) & 14.935392 \tabularnewline
0.3056 (3.2727) & 19.223259 \tabularnewline
0.3194 (3.1304) & 33.618802 \tabularnewline
0.3333 (3) & 1237.847229 \tabularnewline
0.3472 (2.88) & 2.818635 \tabularnewline
0.3611 (2.7692) & 82.415566 \tabularnewline
0.375 (2.6667) & 94.091159 \tabularnewline
0.3889 (2.5714) & 58.556555 \tabularnewline
0.4028 (2.4828) & 103.157416 \tabularnewline
0.4167 (2.4) & 27.524318 \tabularnewline
0.4306 (2.3226) & 1.455437 \tabularnewline
0.4444 (2.25) & 172.747502 \tabularnewline
0.4583 (2.1818) & 4.346182 \tabularnewline
0.4722 (2.1176) & 56.85265 \tabularnewline
0.4861 (2.0571) & 117.20025 \tabularnewline
0.5 (2) & 0.739491 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257681&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]37.172984[/C][/ROW]
[ROW][C]0.0278 (36)[/C][C]16.777311[/C][/ROW]
[ROW][C]0.0417 (24)[/C][C]61.667156[/C][/ROW]
[ROW][C]0.0556 (18)[/C][C]3.459588[/C][/ROW]
[ROW][C]0.0694 (14.4)[/C][C]2.654066[/C][/ROW]
[ROW][C]0.0833 (12)[/C][C]490.080334[/C][/ROW]
[ROW][C]0.0972 (10.2857)[/C][C]322.817014[/C][/ROW]
[ROW][C]0.1111 (9)[/C][C]58.239244[/C][/ROW]
[ROW][C]0.125 (8)[/C][C]136.316719[/C][/ROW]
[ROW][C]0.1389 (7.2)[/C][C]51.746414[/C][/ROW]
[ROW][C]0.1528 (6.5455)[/C][C]12.037638[/C][/ROW]
[ROW][C]0.1667 (6)[/C][C]630.128237[/C][/ROW]
[ROW][C]0.1806 (5.5385)[/C][C]96.475133[/C][/ROW]
[ROW][C]0.1944 (5.1429)[/C][C]73.594184[/C][/ROW]
[ROW][C]0.2083 (4.8)[/C][C]165.695915[/C][/ROW]
[ROW][C]0.2222 (4.5)[/C][C]7.217566[/C][/ROW]
[ROW][C]0.2361 (4.2353)[/C][C]16.865451[/C][/ROW]
[ROW][C]0.25 (4)[/C][C]768.790823[/C][/ROW]
[ROW][C]0.2639 (3.7895)[/C][C]34.302105[/C][/ROW]
[ROW][C]0.2778 (3.6)[/C][C]146.29514[/C][/ROW]
[ROW][C]0.2917 (3.4286)[/C][C]14.935392[/C][/ROW]
[ROW][C]0.3056 (3.2727)[/C][C]19.223259[/C][/ROW]
[ROW][C]0.3194 (3.1304)[/C][C]33.618802[/C][/ROW]
[ROW][C]0.3333 (3)[/C][C]1237.847229[/C][/ROW]
[ROW][C]0.3472 (2.88)[/C][C]2.818635[/C][/ROW]
[ROW][C]0.3611 (2.7692)[/C][C]82.415566[/C][/ROW]
[ROW][C]0.375 (2.6667)[/C][C]94.091159[/C][/ROW]
[ROW][C]0.3889 (2.5714)[/C][C]58.556555[/C][/ROW]
[ROW][C]0.4028 (2.4828)[/C][C]103.157416[/C][/ROW]
[ROW][C]0.4167 (2.4)[/C][C]27.524318[/C][/ROW]
[ROW][C]0.4306 (2.3226)[/C][C]1.455437[/C][/ROW]
[ROW][C]0.4444 (2.25)[/C][C]172.747502[/C][/ROW]
[ROW][C]0.4583 (2.1818)[/C][C]4.346182[/C][/ROW]
[ROW][C]0.4722 (2.1176)[/C][C]56.85265[/C][/ROW]
[ROW][C]0.4861 (2.0571)[/C][C]117.20025[/C][/ROW]
[ROW][C]0.5 (2)[/C][C]0.739491[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257681&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257681&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)37.172984
0.0278 (36)16.777311
0.0417 (24)61.667156
0.0556 (18)3.459588
0.0694 (14.4)2.654066
0.0833 (12)490.080334
0.0972 (10.2857)322.817014
0.1111 (9)58.239244
0.125 (8)136.316719
0.1389 (7.2)51.746414
0.1528 (6.5455)12.037638
0.1667 (6)630.128237
0.1806 (5.5385)96.475133
0.1944 (5.1429)73.594184
0.2083 (4.8)165.695915
0.2222 (4.5)7.217566
0.2361 (4.2353)16.865451
0.25 (4)768.790823
0.2639 (3.7895)34.302105
0.2778 (3.6)146.29514
0.2917 (3.4286)14.935392
0.3056 (3.2727)19.223259
0.3194 (3.1304)33.618802
0.3333 (3)1237.847229
0.3472 (2.88)2.818635
0.3611 (2.7692)82.415566
0.375 (2.6667)94.091159
0.3889 (2.5714)58.556555
0.4028 (2.4828)103.157416
0.4167 (2.4)27.524318
0.4306 (2.3226)1.455437
0.4444 (2.25)172.747502
0.4583 (2.1818)4.346182
0.4722 (2.1176)56.85265
0.4861 (2.0571)117.20025
0.5 (2)0.739491


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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')