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Author*The author of this computation has been verified*
R Software Modulerwasp_decompose.wasp
Title produced by softwareClassical Decomposition
Date of computationMon, 12 Dec 2016 19:51:28 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/12/t1481568700xv2epv6tqt484qp.htm/, Retrieved Sat, 04 May 2024 01:06:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298971, Retrieved Sat, 04 May 2024 01:06:52 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact87
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Classical Decomposition] [classical decompo...] [2016-12-12 18:51:28] [130d73899007e5ff8a4f636b9bcfb397] [Current]
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Dataseries X:
6155
6490
6285
6450
6240
6375
6100
5600
5505
5155
4720
4645
5210
5580
5830
6395
7265
7460
6790
6810
7040
7385
7170
6620
6485
6035
6165
6320
6430
6785
6895
8030
8115
8915
9630
9250
9535
8320
7070
6375
6535
6480
6925
7020




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298971&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298971&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298971&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Classical Decomposition by Moving Averages
tObservationsFitTrendSeasonalRandom
16155NANA212.85NA
26490NANA-249.997NA
36285NANA-476.942NA
46450NANA-249.65NA
56240NANA59.7251NA
66375NANA136.496NA
761005641.885770.62-128.747458.122
856005710.565693.3317.2251-110.558
955055690.75636.4654.239-185.697
1051555924.595615.21309.378-769.586
1147205983.615655.62327.989-1263.61
1246455730.985743.54-12.5666-1085.98
1352106030.355817.5212.85-820.35
1455805646.675896.67-249.997-66.6696
1558305534.16011.04-476.942295.9
1663955918.276167.92-249.65476.733
1772656422.646362.9259.7251842.358
1874606683.796547.29136.496776.212
1967906553.966682.71-128.747236.039
2068106772.026754.7917.225137.9832
2170406841.956787.7154.239198.053
2273857107.926798.54309.378277.08
2371707088.616760.62327.98981.386
2466206685.146697.71-12.5666-65.1418
2564856886.816673.96212.85-401.808
2660356479.176729.17-249.997-444.17
2761656347.856824.79-476.942-182.85
2863206683.686933.33-249.65-363.683
2964307159.317099.5859.7251-729.308
3067857448.167311.67136.496-663.163
3168957419.597548.33-128.747-524.586
3280307787.857770.6217.2251242.15
3381157957.787903.5454.239157.219
3489158252.927943.54309.378662.08
3596308278.27950.21327.9891351.8
3692507929.317941.87-12.56661320.69
3795358143.277930.42212.851391.73
3883207639.597889.58-249.997680.414
397070NANA-476.942NA
406375NANA-249.65NA
416535NANA59.7251NA
426480NANA136.496NA
436925NANA-128.747NA
447020NANA17.2251NA

\begin{tabular}{lllllllll}
\hline
Classical Decomposition by Moving Averages \tabularnewline
t & Observations & Fit & Trend & Seasonal & Random \tabularnewline
1 & 6155 & NA & NA & 212.85 & NA \tabularnewline
2 & 6490 & NA & NA & -249.997 & NA \tabularnewline
3 & 6285 & NA & NA & -476.942 & NA \tabularnewline
4 & 6450 & NA & NA & -249.65 & NA \tabularnewline
5 & 6240 & NA & NA & 59.7251 & NA \tabularnewline
6 & 6375 & NA & NA & 136.496 & NA \tabularnewline
7 & 6100 & 5641.88 & 5770.62 & -128.747 & 458.122 \tabularnewline
8 & 5600 & 5710.56 & 5693.33 & 17.2251 & -110.558 \tabularnewline
9 & 5505 & 5690.7 & 5636.46 & 54.239 & -185.697 \tabularnewline
10 & 5155 & 5924.59 & 5615.21 & 309.378 & -769.586 \tabularnewline
11 & 4720 & 5983.61 & 5655.62 & 327.989 & -1263.61 \tabularnewline
12 & 4645 & 5730.98 & 5743.54 & -12.5666 & -1085.98 \tabularnewline
13 & 5210 & 6030.35 & 5817.5 & 212.85 & -820.35 \tabularnewline
14 & 5580 & 5646.67 & 5896.67 & -249.997 & -66.6696 \tabularnewline
15 & 5830 & 5534.1 & 6011.04 & -476.942 & 295.9 \tabularnewline
16 & 6395 & 5918.27 & 6167.92 & -249.65 & 476.733 \tabularnewline
17 & 7265 & 6422.64 & 6362.92 & 59.7251 & 842.358 \tabularnewline
18 & 7460 & 6683.79 & 6547.29 & 136.496 & 776.212 \tabularnewline
19 & 6790 & 6553.96 & 6682.71 & -128.747 & 236.039 \tabularnewline
20 & 6810 & 6772.02 & 6754.79 & 17.2251 & 37.9832 \tabularnewline
21 & 7040 & 6841.95 & 6787.71 & 54.239 & 198.053 \tabularnewline
22 & 7385 & 7107.92 & 6798.54 & 309.378 & 277.08 \tabularnewline
23 & 7170 & 7088.61 & 6760.62 & 327.989 & 81.386 \tabularnewline
24 & 6620 & 6685.14 & 6697.71 & -12.5666 & -65.1418 \tabularnewline
25 & 6485 & 6886.81 & 6673.96 & 212.85 & -401.808 \tabularnewline
26 & 6035 & 6479.17 & 6729.17 & -249.997 & -444.17 \tabularnewline
27 & 6165 & 6347.85 & 6824.79 & -476.942 & -182.85 \tabularnewline
28 & 6320 & 6683.68 & 6933.33 & -249.65 & -363.683 \tabularnewline
29 & 6430 & 7159.31 & 7099.58 & 59.7251 & -729.308 \tabularnewline
30 & 6785 & 7448.16 & 7311.67 & 136.496 & -663.163 \tabularnewline
31 & 6895 & 7419.59 & 7548.33 & -128.747 & -524.586 \tabularnewline
32 & 8030 & 7787.85 & 7770.62 & 17.2251 & 242.15 \tabularnewline
33 & 8115 & 7957.78 & 7903.54 & 54.239 & 157.219 \tabularnewline
34 & 8915 & 8252.92 & 7943.54 & 309.378 & 662.08 \tabularnewline
35 & 9630 & 8278.2 & 7950.21 & 327.989 & 1351.8 \tabularnewline
36 & 9250 & 7929.31 & 7941.87 & -12.5666 & 1320.69 \tabularnewline
37 & 9535 & 8143.27 & 7930.42 & 212.85 & 1391.73 \tabularnewline
38 & 8320 & 7639.59 & 7889.58 & -249.997 & 680.414 \tabularnewline
39 & 7070 & NA & NA & -476.942 & NA \tabularnewline
40 & 6375 & NA & NA & -249.65 & NA \tabularnewline
41 & 6535 & NA & NA & 59.7251 & NA \tabularnewline
42 & 6480 & NA & NA & 136.496 & NA \tabularnewline
43 & 6925 & NA & NA & -128.747 & NA \tabularnewline
44 & 7020 & NA & NA & 17.2251 & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298971&T=1

[TABLE]
[ROW][C]Classical Decomposition by Moving Averages[/C][/ROW]
[ROW][C]t[/C][C]Observations[/C][C]Fit[/C][C]Trend[/C][C]Seasonal[/C][C]Random[/C][/ROW]
[ROW][C]1[/C][C]6155[/C][C]NA[/C][C]NA[/C][C]212.85[/C][C]NA[/C][/ROW]
[ROW][C]2[/C][C]6490[/C][C]NA[/C][C]NA[/C][C]-249.997[/C][C]NA[/C][/ROW]
[ROW][C]3[/C][C]6285[/C][C]NA[/C][C]NA[/C][C]-476.942[/C][C]NA[/C][/ROW]
[ROW][C]4[/C][C]6450[/C][C]NA[/C][C]NA[/C][C]-249.65[/C][C]NA[/C][/ROW]
[ROW][C]5[/C][C]6240[/C][C]NA[/C][C]NA[/C][C]59.7251[/C][C]NA[/C][/ROW]
[ROW][C]6[/C][C]6375[/C][C]NA[/C][C]NA[/C][C]136.496[/C][C]NA[/C][/ROW]
[ROW][C]7[/C][C]6100[/C][C]5641.88[/C][C]5770.62[/C][C]-128.747[/C][C]458.122[/C][/ROW]
[ROW][C]8[/C][C]5600[/C][C]5710.56[/C][C]5693.33[/C][C]17.2251[/C][C]-110.558[/C][/ROW]
[ROW][C]9[/C][C]5505[/C][C]5690.7[/C][C]5636.46[/C][C]54.239[/C][C]-185.697[/C][/ROW]
[ROW][C]10[/C][C]5155[/C][C]5924.59[/C][C]5615.21[/C][C]309.378[/C][C]-769.586[/C][/ROW]
[ROW][C]11[/C][C]4720[/C][C]5983.61[/C][C]5655.62[/C][C]327.989[/C][C]-1263.61[/C][/ROW]
[ROW][C]12[/C][C]4645[/C][C]5730.98[/C][C]5743.54[/C][C]-12.5666[/C][C]-1085.98[/C][/ROW]
[ROW][C]13[/C][C]5210[/C][C]6030.35[/C][C]5817.5[/C][C]212.85[/C][C]-820.35[/C][/ROW]
[ROW][C]14[/C][C]5580[/C][C]5646.67[/C][C]5896.67[/C][C]-249.997[/C][C]-66.6696[/C][/ROW]
[ROW][C]15[/C][C]5830[/C][C]5534.1[/C][C]6011.04[/C][C]-476.942[/C][C]295.9[/C][/ROW]
[ROW][C]16[/C][C]6395[/C][C]5918.27[/C][C]6167.92[/C][C]-249.65[/C][C]476.733[/C][/ROW]
[ROW][C]17[/C][C]7265[/C][C]6422.64[/C][C]6362.92[/C][C]59.7251[/C][C]842.358[/C][/ROW]
[ROW][C]18[/C][C]7460[/C][C]6683.79[/C][C]6547.29[/C][C]136.496[/C][C]776.212[/C][/ROW]
[ROW][C]19[/C][C]6790[/C][C]6553.96[/C][C]6682.71[/C][C]-128.747[/C][C]236.039[/C][/ROW]
[ROW][C]20[/C][C]6810[/C][C]6772.02[/C][C]6754.79[/C][C]17.2251[/C][C]37.9832[/C][/ROW]
[ROW][C]21[/C][C]7040[/C][C]6841.95[/C][C]6787.71[/C][C]54.239[/C][C]198.053[/C][/ROW]
[ROW][C]22[/C][C]7385[/C][C]7107.92[/C][C]6798.54[/C][C]309.378[/C][C]277.08[/C][/ROW]
[ROW][C]23[/C][C]7170[/C][C]7088.61[/C][C]6760.62[/C][C]327.989[/C][C]81.386[/C][/ROW]
[ROW][C]24[/C][C]6620[/C][C]6685.14[/C][C]6697.71[/C][C]-12.5666[/C][C]-65.1418[/C][/ROW]
[ROW][C]25[/C][C]6485[/C][C]6886.81[/C][C]6673.96[/C][C]212.85[/C][C]-401.808[/C][/ROW]
[ROW][C]26[/C][C]6035[/C][C]6479.17[/C][C]6729.17[/C][C]-249.997[/C][C]-444.17[/C][/ROW]
[ROW][C]27[/C][C]6165[/C][C]6347.85[/C][C]6824.79[/C][C]-476.942[/C][C]-182.85[/C][/ROW]
[ROW][C]28[/C][C]6320[/C][C]6683.68[/C][C]6933.33[/C][C]-249.65[/C][C]-363.683[/C][/ROW]
[ROW][C]29[/C][C]6430[/C][C]7159.31[/C][C]7099.58[/C][C]59.7251[/C][C]-729.308[/C][/ROW]
[ROW][C]30[/C][C]6785[/C][C]7448.16[/C][C]7311.67[/C][C]136.496[/C][C]-663.163[/C][/ROW]
[ROW][C]31[/C][C]6895[/C][C]7419.59[/C][C]7548.33[/C][C]-128.747[/C][C]-524.586[/C][/ROW]
[ROW][C]32[/C][C]8030[/C][C]7787.85[/C][C]7770.62[/C][C]17.2251[/C][C]242.15[/C][/ROW]
[ROW][C]33[/C][C]8115[/C][C]7957.78[/C][C]7903.54[/C][C]54.239[/C][C]157.219[/C][/ROW]
[ROW][C]34[/C][C]8915[/C][C]8252.92[/C][C]7943.54[/C][C]309.378[/C][C]662.08[/C][/ROW]
[ROW][C]35[/C][C]9630[/C][C]8278.2[/C][C]7950.21[/C][C]327.989[/C][C]1351.8[/C][/ROW]
[ROW][C]36[/C][C]9250[/C][C]7929.31[/C][C]7941.87[/C][C]-12.5666[/C][C]1320.69[/C][/ROW]
[ROW][C]37[/C][C]9535[/C][C]8143.27[/C][C]7930.42[/C][C]212.85[/C][C]1391.73[/C][/ROW]
[ROW][C]38[/C][C]8320[/C][C]7639.59[/C][C]7889.58[/C][C]-249.997[/C][C]680.414[/C][/ROW]
[ROW][C]39[/C][C]7070[/C][C]NA[/C][C]NA[/C][C]-476.942[/C][C]NA[/C][/ROW]
[ROW][C]40[/C][C]6375[/C][C]NA[/C][C]NA[/C][C]-249.65[/C][C]NA[/C][/ROW]
[ROW][C]41[/C][C]6535[/C][C]NA[/C][C]NA[/C][C]59.7251[/C][C]NA[/C][/ROW]
[ROW][C]42[/C][C]6480[/C][C]NA[/C][C]NA[/C][C]136.496[/C][C]NA[/C][/ROW]
[ROW][C]43[/C][C]6925[/C][C]NA[/C][C]NA[/C][C]-128.747[/C][C]NA[/C][/ROW]
[ROW][C]44[/C][C]7020[/C][C]NA[/C][C]NA[/C][C]17.2251[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298971&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298971&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Classical Decomposition by Moving Averages
tObservationsFitTrendSeasonalRandom
16155NANA212.85NA
26490NANA-249.997NA
36285NANA-476.942NA
46450NANA-249.65NA
56240NANA59.7251NA
66375NANA136.496NA
761005641.885770.62-128.747458.122
856005710.565693.3317.2251-110.558
955055690.75636.4654.239-185.697
1051555924.595615.21309.378-769.586
1147205983.615655.62327.989-1263.61
1246455730.985743.54-12.5666-1085.98
1352106030.355817.5212.85-820.35
1455805646.675896.67-249.997-66.6696
1558305534.16011.04-476.942295.9
1663955918.276167.92-249.65476.733
1772656422.646362.9259.7251842.358
1874606683.796547.29136.496776.212
1967906553.966682.71-128.747236.039
2068106772.026754.7917.225137.9832
2170406841.956787.7154.239198.053
2273857107.926798.54309.378277.08
2371707088.616760.62327.98981.386
2466206685.146697.71-12.5666-65.1418
2564856886.816673.96212.85-401.808
2660356479.176729.17-249.997-444.17
2761656347.856824.79-476.942-182.85
2863206683.686933.33-249.65-363.683
2964307159.317099.5859.7251-729.308
3067857448.167311.67136.496-663.163
3168957419.597548.33-128.747-524.586
3280307787.857770.6217.2251242.15
3381157957.787903.5454.239157.219
3489158252.927943.54309.378662.08
3596308278.27950.21327.9891351.8
3692507929.317941.87-12.56661320.69
3795358143.277930.42212.851391.73
3883207639.597889.58-249.997680.414
397070NANA-476.942NA
406375NANA-249.65NA
416535NANA59.7251NA
426480NANA136.496NA
436925NANA-128.747NA
447020NANA17.2251NA



Parameters (Session):
par1 = additive ; par2 = 12 ;
Parameters (R input):
par1 = additive ; par2 = 12 ;
R code (references can be found in the software module):
par2 <- as.numeric(par2)
x <- ts(x,freq=par2)
m <- decompose(x,type=par1)
m$figure
bitmap(file='test1.png')
plot(m)
dev.off()
mylagmax <- length(x)/2
bitmap(file='test2.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(x),lag.max = mylagmax,main='Observed')
acf(as.numeric(m$trend),na.action=na.pass,lag.max = mylagmax,main='Trend')
acf(as.numeric(m$seasonal),na.action=na.pass,lag.max = mylagmax,main='Seasonal')
acf(as.numeric(m$random),na.action=na.pass,lag.max = mylagmax,main='Random')
par(op)
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
spectrum(as.numeric(x),main='Observed')
spectrum(as.numeric(m$trend[!is.na(m$trend)]),main='Trend')
spectrum(as.numeric(m$seasonal[!is.na(m$seasonal)]),main='Seasonal')
spectrum(as.numeric(m$random[!is.na(m$random)]),main='Random')
par(op)
dev.off()
bitmap(file='test4.png')
op <- par(mfrow = c(2,2))
cpgram(as.numeric(x),main='Observed')
cpgram(as.numeric(m$trend[!is.na(m$trend)]),main='Trend')
cpgram(as.numeric(m$seasonal[!is.na(m$seasonal)]),main='Seasonal')
cpgram(as.numeric(m$random[!is.na(m$random)]),main='Random')
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Classical Decomposition by Moving Averages',6,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observations',header=TRUE)
a<-table.element(a,'Fit',header=TRUE)
a<-table.element(a,'Trend',header=TRUE)
a<-table.element(a,'Seasonal',header=TRUE)
a<-table.element(a,'Random',header=TRUE)
a<-table.row.end(a)
for (i in 1:length(m$trend)) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
if (par1 == 'additive') a<-table.element(a,signif(m$trend[i]+m$seasonal[i],6)) else a<-table.element(a,signif(m$trend[i]*m$seasonal[i],6))
a<-table.element(a,signif(m$trend[i],6))
a<-table.element(a,signif(m$seasonal[i],6))
a<-table.element(a,signif(m$random[i],6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')