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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, 26 Dec 2010 17:33:10 +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/26/t1293384646x8m04y5bzcl5vbe.htm/, Retrieved Mon, 06 May 2024 16:28:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115742, Retrieved Mon, 06 May 2024 16:28:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact126

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [Standard Deviation-Mean Plot] [Births] [2010-11-29 10:52:49] [b98453cac15ba1066b407e146608df68]
- RMP           [(Partial) Autocorrelation Function] [WS6 - autocorrelatie] [2010-12-14 19:09:35] [8ed0bd3560b9ca2814a2ed0a29182575]
- RMP             [Spectral Analysis] [WS6 - spectrale a...] [2010-12-14 19:53:05] [8ed0bd3560b9ca2814a2ed0a29182575]
-   PD                [Spectral Analysis] [Spectral Analysis...] [2010-12-26 17:33:10] [c9d5faca36bd2ada281161976df30bf1] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.4271
7.7662
7.6289
7.5281
7.3831
7.2355
7.0617
7.1237
7.4533
7.5411
7.4978
7.3525
7.3862
7.311
7.2013
7.249
7.3321
7.59
7.9082
8.2123
8.0929
8.118
8.1206
8.2883
8.4281
8.7917
8.9168
8.9446
8.9786
9.5862
9.6533
9.4125
9.2195
9.2882
9.6774
9.6857
10.1688
10.4399
10.4675
10.149
9.9163
9.9268
10.0529
10.1622
10.083
10.1134
10.3423
10.7536
11.0967
10.8588
10.7719
10.9262
10.708
10.5062
10.0683
9.8954
9.9589
9.9177
9.7189
9.5273
9.5746
9.763
9.6117
9.6581
9.8361
10.2353
10.1285
10.1347
10.2141
10.0971
9.9651
10.1286
10.3356
10.1238
10.1326
10.2467
10.44
10.3689
10.2415
10.3899
10.3162
10.4533
10.6741
10.8957
10.7404
10.6568
10.5682
10.9833
11.0237
10.8462
10.7287
10.7809
10.2609
9.8252
9.1071
8.695
9.2205
9.0496
8.7406
8.921
9.011
9.3157
9.5786
9.6246
9.7485
9.9431
10.1152
10.1827
9.9777
9.7436
9.3462
9.2623
9.1505
8.5794
8.3245
8.6538
8.752
8.8104
9.2665
9.0895

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=115742&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=115742&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115742&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)1
Degree of seasonal differencing (D)0
Seasonal Period (s)12
Frequency (Period)Spectrum
0.0083 (120)0.019352
0.0167 (60)0.044329
0.025 (40)0.09395
0.0333 (30)0.054408
0.0417 (24)0.022275
0.05 (20)0.297825
0.0583 (17.1429)0.201828
0.0667 (15)0.024513
0.075 (13.3333)0.167727
0.0833 (12)0.002621
0.0917 (10.9091)0.014349
0.1 (10)0.146046
0.1083 (9.2308)0.072952
0.1167 (8.5714)0.048388
0.125 (8)0.081834
0.1333 (7.5)0.018426
0.1417 (7.0588)0.00146
0.15 (6.6667)0.079038
0.1583 (6.3158)0.005508
0.1667 (6)0.071841
0.175 (5.7143)0.049617
0.1833 (5.4545)0.057529
0.1917 (5.2174)0.068831
0.2 (5)0.124289
0.2083 (4.8)0.119346
0.2167 (4.6154)0.081761
0.225 (4.4444)0.17783
0.2333 (4.2857)0.022592
0.2417 (4.1379)0.068175
0.25 (4)0.056294
0.2583 (3.871)0.121485
0.2667 (3.75)0.02154
0.275 (3.6364)0.006431
0.2833 (3.5294)0.122119
0.2917 (3.4286)0.016427
0.3 (3.3333)0.010389
0.3083 (3.2432)0.014268
0.3167 (3.1579)0.019827
0.325 (3.0769)0.038496
0.3333 (3)0.034451
0.3417 (2.9268)0.012914
0.35 (2.8571)0.044591
0.3583 (2.7907)0.046193
0.3667 (2.7273)0.016488
0.375 (2.6667)0.062093
0.3833 (2.6087)0.008666
0.3917 (2.5532)0.015863
0.4 (2.5)0.021749
0.4083 (2.449)0.002963
0.4167 (2.4)0.055082
0.425 (2.3529)0.015784
0.4333 (2.3077)0.001045
0.4417 (2.2642)0.001007
0.45 (2.2222)0.042923
0.4583 (2.1818)0.004846
0.4667 (2.1429)0.052896
0.475 (2.1053)0.014475
0.4833 (2.069)0.008787
0.4917 (2.0339)0.004839
0.5 (2)0.037708

\begin{tabular}{lllllllll}
\hline
Raw Periodogram \tabularnewline
Parameter & Value \tabularnewline
Box-Cox transformation parameter (lambda) & 1 \tabularnewline
Degree of non-seasonal differencing (d) & 1 \tabularnewline
Degree of seasonal differencing (D) & 0 \tabularnewline
Seasonal Period (s) & 12 \tabularnewline
Frequency (Period) & Spectrum \tabularnewline
0.0083 (120) & 0.019352 \tabularnewline
0.0167 (60) & 0.044329 \tabularnewline
0.025 (40) & 0.09395 \tabularnewline
0.0333 (30) & 0.054408 \tabularnewline
0.0417 (24) & 0.022275 \tabularnewline
0.05 (20) & 0.297825 \tabularnewline
0.0583 (17.1429) & 0.201828 \tabularnewline
0.0667 (15) & 0.024513 \tabularnewline
0.075 (13.3333) & 0.167727 \tabularnewline
0.0833 (12) & 0.002621 \tabularnewline
0.0917 (10.9091) & 0.014349 \tabularnewline
0.1 (10) & 0.146046 \tabularnewline
0.1083 (9.2308) & 0.072952 \tabularnewline
0.1167 (8.5714) & 0.048388 \tabularnewline
0.125 (8) & 0.081834 \tabularnewline
0.1333 (7.5) & 0.018426 \tabularnewline
0.1417 (7.0588) & 0.00146 \tabularnewline
0.15 (6.6667) & 0.079038 \tabularnewline
0.1583 (6.3158) & 0.005508 \tabularnewline
0.1667 (6) & 0.071841 \tabularnewline
0.175 (5.7143) & 0.049617 \tabularnewline
0.1833 (5.4545) & 0.057529 \tabularnewline
0.1917 (5.2174) & 0.068831 \tabularnewline
0.2 (5) & 0.124289 \tabularnewline
0.2083 (4.8) & 0.119346 \tabularnewline
0.2167 (4.6154) & 0.081761 \tabularnewline
0.225 (4.4444) & 0.17783 \tabularnewline
0.2333 (4.2857) & 0.022592 \tabularnewline
0.2417 (4.1379) & 0.068175 \tabularnewline
0.25 (4) & 0.056294 \tabularnewline
0.2583 (3.871) & 0.121485 \tabularnewline
0.2667 (3.75) & 0.02154 \tabularnewline
0.275 (3.6364) & 0.006431 \tabularnewline
0.2833 (3.5294) & 0.122119 \tabularnewline
0.2917 (3.4286) & 0.016427 \tabularnewline
0.3 (3.3333) & 0.010389 \tabularnewline
0.3083 (3.2432) & 0.014268 \tabularnewline
0.3167 (3.1579) & 0.019827 \tabularnewline
0.325 (3.0769) & 0.038496 \tabularnewline
0.3333 (3) & 0.034451 \tabularnewline
0.3417 (2.9268) & 0.012914 \tabularnewline
0.35 (2.8571) & 0.044591 \tabularnewline
0.3583 (2.7907) & 0.046193 \tabularnewline
0.3667 (2.7273) & 0.016488 \tabularnewline
0.375 (2.6667) & 0.062093 \tabularnewline
0.3833 (2.6087) & 0.008666 \tabularnewline
0.3917 (2.5532) & 0.015863 \tabularnewline
0.4 (2.5) & 0.021749 \tabularnewline
0.4083 (2.449) & 0.002963 \tabularnewline
0.4167 (2.4) & 0.055082 \tabularnewline
0.425 (2.3529) & 0.015784 \tabularnewline
0.4333 (2.3077) & 0.001045 \tabularnewline
0.4417 (2.2642) & 0.001007 \tabularnewline
0.45 (2.2222) & 0.042923 \tabularnewline
0.4583 (2.1818) & 0.004846 \tabularnewline
0.4667 (2.1429) & 0.052896 \tabularnewline
0.475 (2.1053) & 0.014475 \tabularnewline
0.4833 (2.069) & 0.008787 \tabularnewline
0.4917 (2.0339) & 0.004839 \tabularnewline
0.5 (2) & 0.037708 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115742&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]1[/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]0.0083 (120)[/C][C]0.019352[/C][/ROW]
[ROW][C]0.0167 (60)[/C][C]0.044329[/C][/ROW]
[ROW][C]0.025 (40)[/C][C]0.09395[/C][/ROW]
[ROW][C]0.0333 (30)[/C][C]0.054408[/C][/ROW]
[ROW][C]0.0417 (24)[/C][C]0.022275[/C][/ROW]
[ROW][C]0.05 (20)[/C][C]0.297825[/C][/ROW]
[ROW][C]0.0583 (17.1429)[/C][C]0.201828[/C][/ROW]
[ROW][C]0.0667 (15)[/C][C]0.024513[/C][/ROW]
[ROW][C]0.075 (13.3333)[/C][C]0.167727[/C][/ROW]
[ROW][C]0.0833 (12)[/C][C]0.002621[/C][/ROW]
[ROW][C]0.0917 (10.9091)[/C][C]0.014349[/C][/ROW]
[ROW][C]0.1 (10)[/C][C]0.146046[/C][/ROW]
[ROW][C]0.1083 (9.2308)[/C][C]0.072952[/C][/ROW]
[ROW][C]0.1167 (8.5714)[/C][C]0.048388[/C][/ROW]
[ROW][C]0.125 (8)[/C][C]0.081834[/C][/ROW]
[ROW][C]0.1333 (7.5)[/C][C]0.018426[/C][/ROW]
[ROW][C]0.1417 (7.0588)[/C][C]0.00146[/C][/ROW]
[ROW][C]0.15 (6.6667)[/C][C]0.079038[/C][/ROW]
[ROW][C]0.1583 (6.3158)[/C][C]0.005508[/C][/ROW]
[ROW][C]0.1667 (6)[/C][C]0.071841[/C][/ROW]
[ROW][C]0.175 (5.7143)[/C][C]0.049617[/C][/ROW]
[ROW][C]0.1833 (5.4545)[/C][C]0.057529[/C][/ROW]
[ROW][C]0.1917 (5.2174)[/C][C]0.068831[/C][/ROW]
[ROW][C]0.2 (5)[/C][C]0.124289[/C][/ROW]
[ROW][C]0.2083 (4.8)[/C][C]0.119346[/C][/ROW]
[ROW][C]0.2167 (4.6154)[/C][C]0.081761[/C][/ROW]
[ROW][C]0.225 (4.4444)[/C][C]0.17783[/C][/ROW]
[ROW][C]0.2333 (4.2857)[/C][C]0.022592[/C][/ROW]
[ROW][C]0.2417 (4.1379)[/C][C]0.068175[/C][/ROW]
[ROW][C]0.25 (4)[/C][C]0.056294[/C][/ROW]
[ROW][C]0.2583 (3.871)[/C][C]0.121485[/C][/ROW]
[ROW][C]0.2667 (3.75)[/C][C]0.02154[/C][/ROW]
[ROW][C]0.275 (3.6364)[/C][C]0.006431[/C][/ROW]
[ROW][C]0.2833 (3.5294)[/C][C]0.122119[/C][/ROW]
[ROW][C]0.2917 (3.4286)[/C][C]0.016427[/C][/ROW]
[ROW][C]0.3 (3.3333)[/C][C]0.010389[/C][/ROW]
[ROW][C]0.3083 (3.2432)[/C][C]0.014268[/C][/ROW]
[ROW][C]0.3167 (3.1579)[/C][C]0.019827[/C][/ROW]
[ROW][C]0.325 (3.0769)[/C][C]0.038496[/C][/ROW]
[ROW][C]0.3333 (3)[/C][C]0.034451[/C][/ROW]
[ROW][C]0.3417 (2.9268)[/C][C]0.012914[/C][/ROW]
[ROW][C]0.35 (2.8571)[/C][C]0.044591[/C][/ROW]
[ROW][C]0.3583 (2.7907)[/C][C]0.046193[/C][/ROW]
[ROW][C]0.3667 (2.7273)[/C][C]0.016488[/C][/ROW]
[ROW][C]0.375 (2.6667)[/C][C]0.062093[/C][/ROW]
[ROW][C]0.3833 (2.6087)[/C][C]0.008666[/C][/ROW]
[ROW][C]0.3917 (2.5532)[/C][C]0.015863[/C][/ROW]
[ROW][C]0.4 (2.5)[/C][C]0.021749[/C][/ROW]
[ROW][C]0.4083 (2.449)[/C][C]0.002963[/C][/ROW]
[ROW][C]0.4167 (2.4)[/C][C]0.055082[/C][/ROW]
[ROW][C]0.425 (2.3529)[/C][C]0.015784[/C][/ROW]
[ROW][C]0.4333 (2.3077)[/C][C]0.001045[/C][/ROW]
[ROW][C]0.4417 (2.2642)[/C][C]0.001007[/C][/ROW]
[ROW][C]0.45 (2.2222)[/C][C]0.042923[/C][/ROW]
[ROW][C]0.4583 (2.1818)[/C][C]0.004846[/C][/ROW]
[ROW][C]0.4667 (2.1429)[/C][C]0.052896[/C][/ROW]
[ROW][C]0.475 (2.1053)[/C][C]0.014475[/C][/ROW]
[ROW][C]0.4833 (2.069)[/C][C]0.008787[/C][/ROW]
[ROW][C]0.4917 (2.0339)[/C][C]0.004839[/C][/ROW]
[ROW][C]0.5 (2)[/C][C]0.037708[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115742&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115742&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)1
Degree of seasonal differencing (D)0
Seasonal Period (s)12
Frequency (Period)Spectrum
0.0083 (120)0.019352
0.0167 (60)0.044329
0.025 (40)0.09395
0.0333 (30)0.054408
0.0417 (24)0.022275
0.05 (20)0.297825
0.0583 (17.1429)0.201828
0.0667 (15)0.024513
0.075 (13.3333)0.167727
0.0833 (12)0.002621
0.0917 (10.9091)0.014349
0.1 (10)0.146046
0.1083 (9.2308)0.072952
0.1167 (8.5714)0.048388
0.125 (8)0.081834
0.1333 (7.5)0.018426
0.1417 (7.0588)0.00146
0.15 (6.6667)0.079038
0.1583 (6.3158)0.005508
0.1667 (6)0.071841
0.175 (5.7143)0.049617
0.1833 (5.4545)0.057529
0.1917 (5.2174)0.068831
0.2 (5)0.124289
0.2083 (4.8)0.119346
0.2167 (4.6154)0.081761
0.225 (4.4444)0.17783
0.2333 (4.2857)0.022592
0.2417 (4.1379)0.068175
0.25 (4)0.056294
0.2583 (3.871)0.121485
0.2667 (3.75)0.02154
0.275 (3.6364)0.006431
0.2833 (3.5294)0.122119
0.2917 (3.4286)0.016427
0.3 (3.3333)0.010389
0.3083 (3.2432)0.014268
0.3167 (3.1579)0.019827
0.325 (3.0769)0.038496
0.3333 (3)0.034451
0.3417 (2.9268)0.012914
0.35 (2.8571)0.044591
0.3583 (2.7907)0.046193
0.3667 (2.7273)0.016488
0.375 (2.6667)0.062093
0.3833 (2.6087)0.008666
0.3917 (2.5532)0.015863
0.4 (2.5)0.021749
0.4083 (2.449)0.002963
0.4167 (2.4)0.055082
0.425 (2.3529)0.015784
0.4333 (2.3077)0.001045
0.4417 (2.2642)0.001007
0.45 (2.2222)0.042923
0.4583 (2.1818)0.004846
0.4667 (2.1429)0.052896
0.475 (2.1053)0.014475
0.4833 (2.069)0.008787
0.4917 (2.0339)0.004839
0.5 (2)0.037708


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 1 ; par2 = 1 ; 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')