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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 12:13:18 -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/t1228763626rq3b8ot9ap0knch.htm/, Retrieved Thu, 16 May 2024 19:50:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30755, Retrieved Thu, 16 May 2024 19:50:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact187

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]
F RMP   [Variance Reduction Matrix] [step1.1] [2008-12-08 18:32:25] [922d8ae7bd2fd460a62d9020ccd4931a]
F RMP     [(Partial) Autocorrelation Function] [step2] [2008-12-08 18:51:58] [922d8ae7bd2fd460a62d9020ccd4931a]
F    D      [(Partial) Autocorrelation Function] [step22é] [2008-12-08 18:59:41] [922d8ae7bd2fd460a62d9020ccd4931a]
-   PD        [(Partial) Autocorrelation Function] [step223] [2008-12-08 19:02:36] [922d8ae7bd2fd460a62d9020ccd4931a]
F RMP             [Spectral Analysis] [step45] [2008-12-08 19:13:18] [89a49ebb3ece8e9a225c7f9f53a14c57] [Current]
-   P               [Spectral Analysis] [step221] [2008-12-08 19:14:54] [922d8ae7bd2fd460a62d9020ccd4931a]
Feedback Forum
2008-12-16 17:33:16 [Lana Van Wesemael] [reply] 
Met behulp van de spectraal analyse kunnen we ook beslissen welke differentiaties nodig zijn om de tijdreeks stationair te maken. Wanneer het cumulatief periodogram in het begin een steil stijgend verloop kent dan wijst dit op een lange termijn trend - dit is niet het geval in deze grafiek, er zit dus geen lange termijn trend in deze tijdreeks. Als er dan ook nog een duidelijke trapbeweging aanwezig is dan zit er seizonaliteit in de tijdreeks.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
97.8
107.4
117.5
105.6
97.4
99.5
98
104.3
100.6
101.1
103.9
96.9
95.5
108.4
117
103.8
100.8
110.6
104
112.6
107.3
98.9
109.8
104.9
102.2
123.9
124.9
112.7
121.9
100.6
104.3
120.4
107.5
102.9
125.6
107.5
108.8
128.4
121.1
119.5
128.7
108.7
105.5
119.8
111.3
110.6
120.1
97.5
107.7
127.3
117.2
119.8
116.2
111
112.4
130.6
109.1
118.8
123.9
101.6
112.8
128
129.6
125.8
119.5
115.7
113.6
129.7
112
116.8
127
112.1
114.2
121.1
131.6
125
120.4
117.7
117.5
120.6
127.5
112.3
124.5
115.2
105.4

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=30755&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=30755&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30755&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
0.0111 (90)81.069803
0.0222 (45)65.502698
0.0333 (30)33.175616
0.0444 (22.5)18.951451
0.0556 (18)20.541794
0.0667 (15)4.820333
0.0778 (12.8571)189.088316
0.0889 (11.25)131.93974
0.1 (10)15.315248
0.1111 (9)26.04137
0.1222 (8.1818)7.329473
0.1333 (7.5)9.824598
0.1444 (6.9231)30.416963
0.1556 (6.4286)36.408004
0.1667 (6)448.873144
0.1778 (5.625)13.521702
0.1889 (5.2941)15.360719
0.2 (5)17.039745
0.2111 (4.7368)4.171542
0.2222 (4.5)36.65874
0.2333 (4.2857)69.822661
0.2444 (4.0909)81.417362
0.2556 (3.913)54.815472
0.2667 (3.75)14.352225
0.2778 (3.6)3.031994
0.2889 (3.4615)7.879319
0.3 (3.3333)32.439885
0.3111 (3.2143)11.851111
0.3222 (3.1034)66.70327
0.3333 (3)641.747813
0.3444 (2.9032)381.826992
0.3556 (2.8125)28.703424
0.3667 (2.7273)11.079918
0.3778 (2.6471)6.276319
0.3889 (2.5714)3.30985
0.4 (2.5)23.809674
0.4111 (2.4324)36.648229
0.4222 (2.3684)29.754999
0.4333 (2.3077)34.554603
0.4444 (2.25)10.024647
0.4556 (2.1951)1.560193
0.4667 (2.1429)0.403627
0.4778 (2.093)37.455847
0.4889 (2.0455)3.930398
0.5 (2)0.690507

\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
0.0111 (90) & 81.069803 \tabularnewline
0.0222 (45) & 65.502698 \tabularnewline
0.0333 (30) & 33.175616 \tabularnewline
0.0444 (22.5) & 18.951451 \tabularnewline
0.0556 (18) & 20.541794 \tabularnewline
0.0667 (15) & 4.820333 \tabularnewline
0.0778 (12.8571) & 189.088316 \tabularnewline
0.0889 (11.25) & 131.93974 \tabularnewline
0.1 (10) & 15.315248 \tabularnewline
0.1111 (9) & 26.04137 \tabularnewline
0.1222 (8.1818) & 7.329473 \tabularnewline
0.1333 (7.5) & 9.824598 \tabularnewline
0.1444 (6.9231) & 30.416963 \tabularnewline
0.1556 (6.4286) & 36.408004 \tabularnewline
0.1667 (6) & 448.873144 \tabularnewline
0.1778 (5.625) & 13.521702 \tabularnewline
0.1889 (5.2941) & 15.360719 \tabularnewline
0.2 (5) & 17.039745 \tabularnewline
0.2111 (4.7368) & 4.171542 \tabularnewline
0.2222 (4.5) & 36.65874 \tabularnewline
0.2333 (4.2857) & 69.822661 \tabularnewline
0.2444 (4.0909) & 81.417362 \tabularnewline
0.2556 (3.913) & 54.815472 \tabularnewline
0.2667 (3.75) & 14.352225 \tabularnewline
0.2778 (3.6) & 3.031994 \tabularnewline
0.2889 (3.4615) & 7.879319 \tabularnewline
0.3 (3.3333) & 32.439885 \tabularnewline
0.3111 (3.2143) & 11.851111 \tabularnewline
0.3222 (3.1034) & 66.70327 \tabularnewline
0.3333 (3) & 641.747813 \tabularnewline
0.3444 (2.9032) & 381.826992 \tabularnewline
0.3556 (2.8125) & 28.703424 \tabularnewline
0.3667 (2.7273) & 11.079918 \tabularnewline
0.3778 (2.6471) & 6.276319 \tabularnewline
0.3889 (2.5714) & 3.30985 \tabularnewline
0.4 (2.5) & 23.809674 \tabularnewline
0.4111 (2.4324) & 36.648229 \tabularnewline
0.4222 (2.3684) & 29.754999 \tabularnewline
0.4333 (2.3077) & 34.554603 \tabularnewline
0.4444 (2.25) & 10.024647 \tabularnewline
0.4556 (2.1951) & 1.560193 \tabularnewline
0.4667 (2.1429) & 0.403627 \tabularnewline
0.4778 (2.093) & 37.455847 \tabularnewline
0.4889 (2.0455) & 3.930398 \tabularnewline
0.5 (2) & 0.690507 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30755&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]0.0111 (90)[/C][C]81.069803[/C][/ROW]
[ROW][C]0.0222 (45)[/C][C]65.502698[/C][/ROW]
[ROW][C]0.0333 (30)[/C][C]33.175616[/C][/ROW]
[ROW][C]0.0444 (22.5)[/C][C]18.951451[/C][/ROW]
[ROW][C]0.0556 (18)[/C][C]20.541794[/C][/ROW]
[ROW][C]0.0667 (15)[/C][C]4.820333[/C][/ROW]
[ROW][C]0.0778 (12.8571)[/C][C]189.088316[/C][/ROW]
[ROW][C]0.0889 (11.25)[/C][C]131.93974[/C][/ROW]
[ROW][C]0.1 (10)[/C][C]15.315248[/C][/ROW]
[ROW][C]0.1111 (9)[/C][C]26.04137[/C][/ROW]
[ROW][C]0.1222 (8.1818)[/C][C]7.329473[/C][/ROW]
[ROW][C]0.1333 (7.5)[/C][C]9.824598[/C][/ROW]
[ROW][C]0.1444 (6.9231)[/C][C]30.416963[/C][/ROW]
[ROW][C]0.1556 (6.4286)[/C][C]36.408004[/C][/ROW]
[ROW][C]0.1667 (6)[/C][C]448.873144[/C][/ROW]
[ROW][C]0.1778 (5.625)[/C][C]13.521702[/C][/ROW]
[ROW][C]0.1889 (5.2941)[/C][C]15.360719[/C][/ROW]
[ROW][C]0.2 (5)[/C][C]17.039745[/C][/ROW]
[ROW][C]0.2111 (4.7368)[/C][C]4.171542[/C][/ROW]
[ROW][C]0.2222 (4.5)[/C][C]36.65874[/C][/ROW]
[ROW][C]0.2333 (4.2857)[/C][C]69.822661[/C][/ROW]
[ROW][C]0.2444 (4.0909)[/C][C]81.417362[/C][/ROW]
[ROW][C]0.2556 (3.913)[/C][C]54.815472[/C][/ROW]
[ROW][C]0.2667 (3.75)[/C][C]14.352225[/C][/ROW]
[ROW][C]0.2778 (3.6)[/C][C]3.031994[/C][/ROW]
[ROW][C]0.2889 (3.4615)[/C][C]7.879319[/C][/ROW]
[ROW][C]0.3 (3.3333)[/C][C]32.439885[/C][/ROW]
[ROW][C]0.3111 (3.2143)[/C][C]11.851111[/C][/ROW]
[ROW][C]0.3222 (3.1034)[/C][C]66.70327[/C][/ROW]
[ROW][C]0.3333 (3)[/C][C]641.747813[/C][/ROW]
[ROW][C]0.3444 (2.9032)[/C][C]381.826992[/C][/ROW]
[ROW][C]0.3556 (2.8125)[/C][C]28.703424[/C][/ROW]
[ROW][C]0.3667 (2.7273)[/C][C]11.079918[/C][/ROW]
[ROW][C]0.3778 (2.6471)[/C][C]6.276319[/C][/ROW]
[ROW][C]0.3889 (2.5714)[/C][C]3.30985[/C][/ROW]
[ROW][C]0.4 (2.5)[/C][C]23.809674[/C][/ROW]
[ROW][C]0.4111 (2.4324)[/C][C]36.648229[/C][/ROW]
[ROW][C]0.4222 (2.3684)[/C][C]29.754999[/C][/ROW]
[ROW][C]0.4333 (2.3077)[/C][C]34.554603[/C][/ROW]
[ROW][C]0.4444 (2.25)[/C][C]10.024647[/C][/ROW]
[ROW][C]0.4556 (2.1951)[/C][C]1.560193[/C][/ROW]
[ROW][C]0.4667 (2.1429)[/C][C]0.403627[/C][/ROW]
[ROW][C]0.4778 (2.093)[/C][C]37.455847[/C][/ROW]
[ROW][C]0.4889 (2.0455)[/C][C]3.930398[/C][/ROW]
[ROW][C]0.5 (2)[/C][C]0.690507[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30755&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30755&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
0.0111 (90)81.069803
0.0222 (45)65.502698
0.0333 (30)33.175616
0.0444 (22.5)18.951451
0.0556 (18)20.541794
0.0667 (15)4.820333
0.0778 (12.8571)189.088316
0.0889 (11.25)131.93974
0.1 (10)15.315248
0.1111 (9)26.04137
0.1222 (8.1818)7.329473
0.1333 (7.5)9.824598
0.1444 (6.9231)30.416963
0.1556 (6.4286)36.408004
0.1667 (6)448.873144
0.1778 (5.625)13.521702
0.1889 (5.2941)15.360719
0.2 (5)17.039745
0.2111 (4.7368)4.171542
0.2222 (4.5)36.65874
0.2333 (4.2857)69.822661
0.2444 (4.0909)81.417362
0.2556 (3.913)54.815472
0.2667 (3.75)14.352225
0.2778 (3.6)3.031994
0.2889 (3.4615)7.879319
0.3 (3.3333)32.439885
0.3111 (3.2143)11.851111
0.3222 (3.1034)66.70327
0.3333 (3)641.747813
0.3444 (2.9032)381.826992
0.3556 (2.8125)28.703424
0.3667 (2.7273)11.079918
0.3778 (2.6471)6.276319
0.3889 (2.5714)3.30985
0.4 (2.5)23.809674
0.4111 (2.4324)36.648229
0.4222 (2.3684)29.754999
0.4333 (2.3077)34.554603
0.4444 (2.25)10.024647
0.4556 (2.1951)1.560193
0.4667 (2.1429)0.403627
0.4778 (2.093)37.455847
0.4889 (2.0455)3.930398
0.5 (2)0.690507


Figures (Output of Computation)

Input Parameters & R Code

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')