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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 computationSat, 06 Dec 2008 11:04:18 -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/06/t1228586757u3og88t6v6pxdfi.htm/, Retrieved Sat, 18 May 2024 20:42:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29777, Retrieved Sat, 18 May 2024 20:42:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact198

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] [step 2] [2008-12-06 09:12:19] [9f5bfe3b95f9ec3d2ed4c0a560a9648a]
F RMPD      [Spectral Analysis] [step 2] [2008-12-06 18:04:18] [a9e6d7cd6e144e8b311d9f96a24c5a25] [Current]
Feedback Forum
2008-12-13 11:14:24 [Sam De Cuyper] [reply] 
Er is een lange termijn trend aanwezig. Klopt, ongeveer 60% van de waarnemingen worden verklaard door de trend op lange termijn.
2008-12-16 19:04:17 [Kevin Vermeiren] [reply] 
Uit het cumulative periodogram blijkt inderdaad dat er een trend aanwezig is. De student staaft zijn antwoord goed door te vermelden dat dit te zien is aan het steil begin van de curve. Het is tevens ook juist dat deze trend verwijderd moet worden door de parameter d= 1 te gebruiken. Verder had de student nog mogen vermelden dat er ook sprake is van seizoenaliteit daar de curve een trapsgewijs verloop weergeeft.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2648,9
2669,6
3042,3
2604,2
2732,1
2621,7
2483,7
2479,3
2684,6
2834,7
2566,1
2251,2
2350
2299,8
2542,8
2530,2
2508,1
2616,8
2534,1
2181,8
2578,9
2841,9
2529,9
2103,2
2326,2
2452,6
2782,1
2727,3
2648,2
2760,7
2613
2225,4
2713,9
2923,3
2707
2473,9
2521
2531,8
3068,8
2826,9
2674,2
2966,6
2798,8
2629,6
3124,6
3115,7
3083
2863,9
2728,7
2789,4
3225,7
3148,2
2836,5
3153,5
2656,9
2834,7
3172,5
2998,8
3103,1
2735,6
2818,1
2874,4
3438,5
2949,1
3306,8
3530
3003,8
3206,4
3514,6
3522,6
3525,5
2996,2
3231,1
3030
3541,7
3113,2
3390,8
3424,2
3079,8
3123,4
3317,1
3579,9
3317,9
2668,1
3609,2
3535,2
3644,7
3925,7
3663,2
3905,3
3990
3695,8

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=29777&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=29777&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29777&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
0.0104 (96)95191.12615
0.0208 (48)68967.280458
0.0312 (32)78474.092735
0.0417 (24)47652.990223
0.0521 (19.2)111331.733989
0.0625 (16)15670.686023
0.0729 (13.7143)5682.701752
0.0833 (12)86290.707082
0.0938 (10.6667)703.582732
0.1042 (9.6)42683.847425
0.1146 (8.7273)32003.400008
0.125 (8)437.356648
0.1354 (7.3846)1523.376764
0.1458 (6.8571)5475.778701
0.1562 (6.4)15741.924043
0.1667 (6)611425.827188
0.1771 (5.6471)34415.40764
0.1875 (5.3333)20966.710204
0.1979 (5.0526)22246.657189
0.2083 (4.8)19139.236183
0.2187 (4.5714)2702.256453
0.2292 (4.3636)46742.225916
0.2396 (4.1739)18672.104571
0.25 (4)340176.716143
0.2604 (3.84)18472.803464
0.2708 (3.6923)34410.652317
0.2812 (3.5556)4510.50159
0.2917 (3.4286)4503.811713
0.3021 (3.3103)38140.486487
0.3125 (3.2)23130.973395
0.3229 (3.0968)8304.099574
0.3333 (3)96680.922989
0.3438 (2.9091)169832.706255
0.3542 (2.8235)31097.284151
0.3646 (2.7429)12120.111557
0.375 (2.6667)7853.246875
0.3854 (2.5946)23756.69718
0.3958 (2.5263)12929.542204
0.4062 (2.4615)22101.912594
0.4167 (2.4)121508.377948
0.4271 (2.3415)57576.030165
0.4375 (2.2857)7112.73831
0.4479 (2.2326)5554.70863
0.4583 (2.1818)2997.346844
0.4688 (2.1333)3179.099883
0.4792 (2.087)22572.33111
0.4896 (2.0426)6529.64968
0.5 (2)133913.908232

\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
0.0104 (96) & 95191.12615 \tabularnewline
0.0208 (48) & 68967.280458 \tabularnewline
0.0312 (32) & 78474.092735 \tabularnewline
0.0417 (24) & 47652.990223 \tabularnewline
0.0521 (19.2) & 111331.733989 \tabularnewline
0.0625 (16) & 15670.686023 \tabularnewline
0.0729 (13.7143) & 5682.701752 \tabularnewline
0.0833 (12) & 86290.707082 \tabularnewline
0.0938 (10.6667) & 703.582732 \tabularnewline
0.1042 (9.6) & 42683.847425 \tabularnewline
0.1146 (8.7273) & 32003.400008 \tabularnewline
0.125 (8) & 437.356648 \tabularnewline
0.1354 (7.3846) & 1523.376764 \tabularnewline
0.1458 (6.8571) & 5475.778701 \tabularnewline
0.1562 (6.4) & 15741.924043 \tabularnewline
0.1667 (6) & 611425.827188 \tabularnewline
0.1771 (5.6471) & 34415.40764 \tabularnewline
0.1875 (5.3333) & 20966.710204 \tabularnewline
0.1979 (5.0526) & 22246.657189 \tabularnewline
0.2083 (4.8) & 19139.236183 \tabularnewline
0.2187 (4.5714) & 2702.256453 \tabularnewline
0.2292 (4.3636) & 46742.225916 \tabularnewline
0.2396 (4.1739) & 18672.104571 \tabularnewline
0.25 (4) & 340176.716143 \tabularnewline
0.2604 (3.84) & 18472.803464 \tabularnewline
0.2708 (3.6923) & 34410.652317 \tabularnewline
0.2812 (3.5556) & 4510.50159 \tabularnewline
0.2917 (3.4286) & 4503.811713 \tabularnewline
0.3021 (3.3103) & 38140.486487 \tabularnewline
0.3125 (3.2) & 23130.973395 \tabularnewline
0.3229 (3.0968) & 8304.099574 \tabularnewline
0.3333 (3) & 96680.922989 \tabularnewline
0.3438 (2.9091) & 169832.706255 \tabularnewline
0.3542 (2.8235) & 31097.284151 \tabularnewline
0.3646 (2.7429) & 12120.111557 \tabularnewline
0.375 (2.6667) & 7853.246875 \tabularnewline
0.3854 (2.5946) & 23756.69718 \tabularnewline
0.3958 (2.5263) & 12929.542204 \tabularnewline
0.4062 (2.4615) & 22101.912594 \tabularnewline
0.4167 (2.4) & 121508.377948 \tabularnewline
0.4271 (2.3415) & 57576.030165 \tabularnewline
0.4375 (2.2857) & 7112.73831 \tabularnewline
0.4479 (2.2326) & 5554.70863 \tabularnewline
0.4583 (2.1818) & 2997.346844 \tabularnewline
0.4688 (2.1333) & 3179.099883 \tabularnewline
0.4792 (2.087) & 22572.33111 \tabularnewline
0.4896 (2.0426) & 6529.64968 \tabularnewline
0.5 (2) & 133913.908232 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29777&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]0.0104 (96)[/C][C]95191.12615[/C][/ROW]
[ROW][C]0.0208 (48)[/C][C]68967.280458[/C][/ROW]
[ROW][C]0.0312 (32)[/C][C]78474.092735[/C][/ROW]
[ROW][C]0.0417 (24)[/C][C]47652.990223[/C][/ROW]
[ROW][C]0.0521 (19.2)[/C][C]111331.733989[/C][/ROW]
[ROW][C]0.0625 (16)[/C][C]15670.686023[/C][/ROW]
[ROW][C]0.0729 (13.7143)[/C][C]5682.701752[/C][/ROW]
[ROW][C]0.0833 (12)[/C][C]86290.707082[/C][/ROW]
[ROW][C]0.0938 (10.6667)[/C][C]703.582732[/C][/ROW]
[ROW][C]0.1042 (9.6)[/C][C]42683.847425[/C][/ROW]
[ROW][C]0.1146 (8.7273)[/C][C]32003.400008[/C][/ROW]
[ROW][C]0.125 (8)[/C][C]437.356648[/C][/ROW]
[ROW][C]0.1354 (7.3846)[/C][C]1523.376764[/C][/ROW]
[ROW][C]0.1458 (6.8571)[/C][C]5475.778701[/C][/ROW]
[ROW][C]0.1562 (6.4)[/C][C]15741.924043[/C][/ROW]
[ROW][C]0.1667 (6)[/C][C]611425.827188[/C][/ROW]
[ROW][C]0.1771 (5.6471)[/C][C]34415.40764[/C][/ROW]
[ROW][C]0.1875 (5.3333)[/C][C]20966.710204[/C][/ROW]
[ROW][C]0.1979 (5.0526)[/C][C]22246.657189[/C][/ROW]
[ROW][C]0.2083 (4.8)[/C][C]19139.236183[/C][/ROW]
[ROW][C]0.2187 (4.5714)[/C][C]2702.256453[/C][/ROW]
[ROW][C]0.2292 (4.3636)[/C][C]46742.225916[/C][/ROW]
[ROW][C]0.2396 (4.1739)[/C][C]18672.104571[/C][/ROW]
[ROW][C]0.25 (4)[/C][C]340176.716143[/C][/ROW]
[ROW][C]0.2604 (3.84)[/C][C]18472.803464[/C][/ROW]
[ROW][C]0.2708 (3.6923)[/C][C]34410.652317[/C][/ROW]
[ROW][C]0.2812 (3.5556)[/C][C]4510.50159[/C][/ROW]
[ROW][C]0.2917 (3.4286)[/C][C]4503.811713[/C][/ROW]
[ROW][C]0.3021 (3.3103)[/C][C]38140.486487[/C][/ROW]
[ROW][C]0.3125 (3.2)[/C][C]23130.973395[/C][/ROW]
[ROW][C]0.3229 (3.0968)[/C][C]8304.099574[/C][/ROW]
[ROW][C]0.3333 (3)[/C][C]96680.922989[/C][/ROW]
[ROW][C]0.3438 (2.9091)[/C][C]169832.706255[/C][/ROW]
[ROW][C]0.3542 (2.8235)[/C][C]31097.284151[/C][/ROW]
[ROW][C]0.3646 (2.7429)[/C][C]12120.111557[/C][/ROW]
[ROW][C]0.375 (2.6667)[/C][C]7853.246875[/C][/ROW]
[ROW][C]0.3854 (2.5946)[/C][C]23756.69718[/C][/ROW]
[ROW][C]0.3958 (2.5263)[/C][C]12929.542204[/C][/ROW]
[ROW][C]0.4062 (2.4615)[/C][C]22101.912594[/C][/ROW]
[ROW][C]0.4167 (2.4)[/C][C]121508.377948[/C][/ROW]
[ROW][C]0.4271 (2.3415)[/C][C]57576.030165[/C][/ROW]
[ROW][C]0.4375 (2.2857)[/C][C]7112.73831[/C][/ROW]
[ROW][C]0.4479 (2.2326)[/C][C]5554.70863[/C][/ROW]
[ROW][C]0.4583 (2.1818)[/C][C]2997.346844[/C][/ROW]
[ROW][C]0.4688 (2.1333)[/C][C]3179.099883[/C][/ROW]
[ROW][C]0.4792 (2.087)[/C][C]22572.33111[/C][/ROW]
[ROW][C]0.4896 (2.0426)[/C][C]6529.64968[/C][/ROW]
[ROW][C]0.5 (2)[/C][C]133913.908232[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29777&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29777&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
0.0104 (96)95191.12615
0.0208 (48)68967.280458
0.0312 (32)78474.092735
0.0417 (24)47652.990223
0.0521 (19.2)111331.733989
0.0625 (16)15670.686023
0.0729 (13.7143)5682.701752
0.0833 (12)86290.707082
0.0938 (10.6667)703.582732
0.1042 (9.6)42683.847425
0.1146 (8.7273)32003.400008
0.125 (8)437.356648
0.1354 (7.3846)1523.376764
0.1458 (6.8571)5475.778701
0.1562 (6.4)15741.924043
0.1667 (6)611425.827188
0.1771 (5.6471)34415.40764
0.1875 (5.3333)20966.710204
0.1979 (5.0526)22246.657189
0.2083 (4.8)19139.236183
0.2187 (4.5714)2702.256453
0.2292 (4.3636)46742.225916
0.2396 (4.1739)18672.104571
0.25 (4)340176.716143
0.2604 (3.84)18472.803464
0.2708 (3.6923)34410.652317
0.2812 (3.5556)4510.50159
0.2917 (3.4286)4503.811713
0.3021 (3.3103)38140.486487
0.3125 (3.2)23130.973395
0.3229 (3.0968)8304.099574
0.3333 (3)96680.922989
0.3438 (2.9091)169832.706255
0.3542 (2.8235)31097.284151
0.3646 (2.7429)12120.111557
0.375 (2.6667)7853.246875
0.3854 (2.5946)23756.69718
0.3958 (2.5263)12929.542204
0.4062 (2.4615)22101.912594
0.4167 (2.4)121508.377948
0.4271 (2.3415)57576.030165
0.4375 (2.2857)7112.73831
0.4479 (2.2326)5554.70863
0.4583 (2.1818)2997.346844
0.4688 (2.1333)3179.099883
0.4792 (2.087)22572.33111
0.4896 (2.0426)6529.64968
0.5 (2)133913.908232


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')