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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 19:45:02 +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/t1481568316jrhiqn4hk3n5ulc.htm/, Retrieved Fri, 03 May 2024 20:26:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298964, Retrieved Fri, 03 May 2024 20:26:31 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
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 18:45:02] [130d73899007e5ff8a4f636b9bcfb397] [Current]
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Dataseries X:
4650
4800
3500
3850
9100
4400
8500
6000
2850
7450
6000
4950
6400
5550
6900
9900
6400
8000
5450
6800
6150
8600
8700
4000
8300
4950
4100
4200
6600
8050
8950
10850
3750
6800
3650
3600
3400
3400
3750
5100
3700
4850
7700
2800
5750
6200
5150
4300
4500
3450
5600




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298964&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298964&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298964&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 time2 seconds
R ServerBig Analytics Cloud Computing Center







Classical Decomposition by Moving Averages
tObservationsFitTrendSeasonalRandom
14650NANA30.353NA
24800NANA-1314.09NA
33500NANA-1026.59NA
43850NANA433.825NA
59100NANA-370.341NA
64400NANA1050.49NA
785007422.895577.081845.81077.11
860006505.185681.25823.929-505.179
928504682.785854.17-1171.38-1832.78
1074507730.356247.921482.44-280.353
1160006427.586387.540.0752-427.575
1249504600.496425-1824.51349.508
1364006478.276447.9230.353-78.2697
1455505040.086354.17-1314.09509.925
1569005498.416525-1026.591401.59
1699007144.246710.42433.8252755.76
1764006500.496870.83-370.341-100.492
1880007994.246943.751050.495.7581
1954508829.146983.331845.8-3379.14
2068007861.437037.5823.929-1061.43
2161505724.456895.83-1171.38425.55
2286008024.16541.671482.44575.897
2387006352.586312.540.07522347.42
2440004498.416322.92-1824.51-498.409
2583006501.196470.8330.3531798.81
2649505471.336785.42-1314.09-521.325
2741005827.586854.17-1026.59-1727.58
2842007112.996679.17433.825-2912.99
2966006023.416393.75-370.341576.591
3080507217.166166.671050.49832.841
3189507791.645945.831845.81158.36
32108506501.015677.08823.9294348.99
3337504426.535597.92-1171.38-676.534
3468007103.275620.831482.44-303.27
3536505577.585537.540.0752-1927.58
3636003458.835283.33-1824.51141.175
3734005128.275097.9230.353-1728.27
3834003396.334710.42-1314.093.67477
3937503431.744458.33-1026.59318.258
4051004950.494516.67433.825149.508
4137004183.834554.17-370.341-483.825
4248505696.334645.831050.49-846.325
4377006566.644720.831845.81133.36
4428005592.684768.75823.929-2792.68
4557503676.534847.92-1171.382073.47
466200NANA1482.44NA
475150NANA40.0752NA
484300NANA-1824.51NA
494500NANA30.353NA
503450NANA-1314.09NA
515600NANA-1026.59NA

\begin{tabular}{lllllllll}
\hline
Classical Decomposition by Moving Averages \tabularnewline
t & Observations & Fit & Trend & Seasonal & Random \tabularnewline
1 & 4650 & NA & NA & 30.353 & NA \tabularnewline
2 & 4800 & NA & NA & -1314.09 & NA \tabularnewline
3 & 3500 & NA & NA & -1026.59 & NA \tabularnewline
4 & 3850 & NA & NA & 433.825 & NA \tabularnewline
5 & 9100 & NA & NA & -370.341 & NA \tabularnewline
6 & 4400 & NA & NA & 1050.49 & NA \tabularnewline
7 & 8500 & 7422.89 & 5577.08 & 1845.8 & 1077.11 \tabularnewline
8 & 6000 & 6505.18 & 5681.25 & 823.929 & -505.179 \tabularnewline
9 & 2850 & 4682.78 & 5854.17 & -1171.38 & -1832.78 \tabularnewline
10 & 7450 & 7730.35 & 6247.92 & 1482.44 & -280.353 \tabularnewline
11 & 6000 & 6427.58 & 6387.5 & 40.0752 & -427.575 \tabularnewline
12 & 4950 & 4600.49 & 6425 & -1824.51 & 349.508 \tabularnewline
13 & 6400 & 6478.27 & 6447.92 & 30.353 & -78.2697 \tabularnewline
14 & 5550 & 5040.08 & 6354.17 & -1314.09 & 509.925 \tabularnewline
15 & 6900 & 5498.41 & 6525 & -1026.59 & 1401.59 \tabularnewline
16 & 9900 & 7144.24 & 6710.42 & 433.825 & 2755.76 \tabularnewline
17 & 6400 & 6500.49 & 6870.83 & -370.341 & -100.492 \tabularnewline
18 & 8000 & 7994.24 & 6943.75 & 1050.49 & 5.7581 \tabularnewline
19 & 5450 & 8829.14 & 6983.33 & 1845.8 & -3379.14 \tabularnewline
20 & 6800 & 7861.43 & 7037.5 & 823.929 & -1061.43 \tabularnewline
21 & 6150 & 5724.45 & 6895.83 & -1171.38 & 425.55 \tabularnewline
22 & 8600 & 8024.1 & 6541.67 & 1482.44 & 575.897 \tabularnewline
23 & 8700 & 6352.58 & 6312.5 & 40.0752 & 2347.42 \tabularnewline
24 & 4000 & 4498.41 & 6322.92 & -1824.51 & -498.409 \tabularnewline
25 & 8300 & 6501.19 & 6470.83 & 30.353 & 1798.81 \tabularnewline
26 & 4950 & 5471.33 & 6785.42 & -1314.09 & -521.325 \tabularnewline
27 & 4100 & 5827.58 & 6854.17 & -1026.59 & -1727.58 \tabularnewline
28 & 4200 & 7112.99 & 6679.17 & 433.825 & -2912.99 \tabularnewline
29 & 6600 & 6023.41 & 6393.75 & -370.341 & 576.591 \tabularnewline
30 & 8050 & 7217.16 & 6166.67 & 1050.49 & 832.841 \tabularnewline
31 & 8950 & 7791.64 & 5945.83 & 1845.8 & 1158.36 \tabularnewline
32 & 10850 & 6501.01 & 5677.08 & 823.929 & 4348.99 \tabularnewline
33 & 3750 & 4426.53 & 5597.92 & -1171.38 & -676.534 \tabularnewline
34 & 6800 & 7103.27 & 5620.83 & 1482.44 & -303.27 \tabularnewline
35 & 3650 & 5577.58 & 5537.5 & 40.0752 & -1927.58 \tabularnewline
36 & 3600 & 3458.83 & 5283.33 & -1824.51 & 141.175 \tabularnewline
37 & 3400 & 5128.27 & 5097.92 & 30.353 & -1728.27 \tabularnewline
38 & 3400 & 3396.33 & 4710.42 & -1314.09 & 3.67477 \tabularnewline
39 & 3750 & 3431.74 & 4458.33 & -1026.59 & 318.258 \tabularnewline
40 & 5100 & 4950.49 & 4516.67 & 433.825 & 149.508 \tabularnewline
41 & 3700 & 4183.83 & 4554.17 & -370.341 & -483.825 \tabularnewline
42 & 4850 & 5696.33 & 4645.83 & 1050.49 & -846.325 \tabularnewline
43 & 7700 & 6566.64 & 4720.83 & 1845.8 & 1133.36 \tabularnewline
44 & 2800 & 5592.68 & 4768.75 & 823.929 & -2792.68 \tabularnewline
45 & 5750 & 3676.53 & 4847.92 & -1171.38 & 2073.47 \tabularnewline
46 & 6200 & NA & NA & 1482.44 & NA \tabularnewline
47 & 5150 & NA & NA & 40.0752 & NA \tabularnewline
48 & 4300 & NA & NA & -1824.51 & NA \tabularnewline
49 & 4500 & NA & NA & 30.353 & NA \tabularnewline
50 & 3450 & NA & NA & -1314.09 & NA \tabularnewline
51 & 5600 & NA & NA & -1026.59 & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298964&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]4650[/C][C]NA[/C][C]NA[/C][C]30.353[/C][C]NA[/C][/ROW]
[ROW][C]2[/C][C]4800[/C][C]NA[/C][C]NA[/C][C]-1314.09[/C][C]NA[/C][/ROW]
[ROW][C]3[/C][C]3500[/C][C]NA[/C][C]NA[/C][C]-1026.59[/C][C]NA[/C][/ROW]
[ROW][C]4[/C][C]3850[/C][C]NA[/C][C]NA[/C][C]433.825[/C][C]NA[/C][/ROW]
[ROW][C]5[/C][C]9100[/C][C]NA[/C][C]NA[/C][C]-370.341[/C][C]NA[/C][/ROW]
[ROW][C]6[/C][C]4400[/C][C]NA[/C][C]NA[/C][C]1050.49[/C][C]NA[/C][/ROW]
[ROW][C]7[/C][C]8500[/C][C]7422.89[/C][C]5577.08[/C][C]1845.8[/C][C]1077.11[/C][/ROW]
[ROW][C]8[/C][C]6000[/C][C]6505.18[/C][C]5681.25[/C][C]823.929[/C][C]-505.179[/C][/ROW]
[ROW][C]9[/C][C]2850[/C][C]4682.78[/C][C]5854.17[/C][C]-1171.38[/C][C]-1832.78[/C][/ROW]
[ROW][C]10[/C][C]7450[/C][C]7730.35[/C][C]6247.92[/C][C]1482.44[/C][C]-280.353[/C][/ROW]
[ROW][C]11[/C][C]6000[/C][C]6427.58[/C][C]6387.5[/C][C]40.0752[/C][C]-427.575[/C][/ROW]
[ROW][C]12[/C][C]4950[/C][C]4600.49[/C][C]6425[/C][C]-1824.51[/C][C]349.508[/C][/ROW]
[ROW][C]13[/C][C]6400[/C][C]6478.27[/C][C]6447.92[/C][C]30.353[/C][C]-78.2697[/C][/ROW]
[ROW][C]14[/C][C]5550[/C][C]5040.08[/C][C]6354.17[/C][C]-1314.09[/C][C]509.925[/C][/ROW]
[ROW][C]15[/C][C]6900[/C][C]5498.41[/C][C]6525[/C][C]-1026.59[/C][C]1401.59[/C][/ROW]
[ROW][C]16[/C][C]9900[/C][C]7144.24[/C][C]6710.42[/C][C]433.825[/C][C]2755.76[/C][/ROW]
[ROW][C]17[/C][C]6400[/C][C]6500.49[/C][C]6870.83[/C][C]-370.341[/C][C]-100.492[/C][/ROW]
[ROW][C]18[/C][C]8000[/C][C]7994.24[/C][C]6943.75[/C][C]1050.49[/C][C]5.7581[/C][/ROW]
[ROW][C]19[/C][C]5450[/C][C]8829.14[/C][C]6983.33[/C][C]1845.8[/C][C]-3379.14[/C][/ROW]
[ROW][C]20[/C][C]6800[/C][C]7861.43[/C][C]7037.5[/C][C]823.929[/C][C]-1061.43[/C][/ROW]
[ROW][C]21[/C][C]6150[/C][C]5724.45[/C][C]6895.83[/C][C]-1171.38[/C][C]425.55[/C][/ROW]
[ROW][C]22[/C][C]8600[/C][C]8024.1[/C][C]6541.67[/C][C]1482.44[/C][C]575.897[/C][/ROW]
[ROW][C]23[/C][C]8700[/C][C]6352.58[/C][C]6312.5[/C][C]40.0752[/C][C]2347.42[/C][/ROW]
[ROW][C]24[/C][C]4000[/C][C]4498.41[/C][C]6322.92[/C][C]-1824.51[/C][C]-498.409[/C][/ROW]
[ROW][C]25[/C][C]8300[/C][C]6501.19[/C][C]6470.83[/C][C]30.353[/C][C]1798.81[/C][/ROW]
[ROW][C]26[/C][C]4950[/C][C]5471.33[/C][C]6785.42[/C][C]-1314.09[/C][C]-521.325[/C][/ROW]
[ROW][C]27[/C][C]4100[/C][C]5827.58[/C][C]6854.17[/C][C]-1026.59[/C][C]-1727.58[/C][/ROW]
[ROW][C]28[/C][C]4200[/C][C]7112.99[/C][C]6679.17[/C][C]433.825[/C][C]-2912.99[/C][/ROW]
[ROW][C]29[/C][C]6600[/C][C]6023.41[/C][C]6393.75[/C][C]-370.341[/C][C]576.591[/C][/ROW]
[ROW][C]30[/C][C]8050[/C][C]7217.16[/C][C]6166.67[/C][C]1050.49[/C][C]832.841[/C][/ROW]
[ROW][C]31[/C][C]8950[/C][C]7791.64[/C][C]5945.83[/C][C]1845.8[/C][C]1158.36[/C][/ROW]
[ROW][C]32[/C][C]10850[/C][C]6501.01[/C][C]5677.08[/C][C]823.929[/C][C]4348.99[/C][/ROW]
[ROW][C]33[/C][C]3750[/C][C]4426.53[/C][C]5597.92[/C][C]-1171.38[/C][C]-676.534[/C][/ROW]
[ROW][C]34[/C][C]6800[/C][C]7103.27[/C][C]5620.83[/C][C]1482.44[/C][C]-303.27[/C][/ROW]
[ROW][C]35[/C][C]3650[/C][C]5577.58[/C][C]5537.5[/C][C]40.0752[/C][C]-1927.58[/C][/ROW]
[ROW][C]36[/C][C]3600[/C][C]3458.83[/C][C]5283.33[/C][C]-1824.51[/C][C]141.175[/C][/ROW]
[ROW][C]37[/C][C]3400[/C][C]5128.27[/C][C]5097.92[/C][C]30.353[/C][C]-1728.27[/C][/ROW]
[ROW][C]38[/C][C]3400[/C][C]3396.33[/C][C]4710.42[/C][C]-1314.09[/C][C]3.67477[/C][/ROW]
[ROW][C]39[/C][C]3750[/C][C]3431.74[/C][C]4458.33[/C][C]-1026.59[/C][C]318.258[/C][/ROW]
[ROW][C]40[/C][C]5100[/C][C]4950.49[/C][C]4516.67[/C][C]433.825[/C][C]149.508[/C][/ROW]
[ROW][C]41[/C][C]3700[/C][C]4183.83[/C][C]4554.17[/C][C]-370.341[/C][C]-483.825[/C][/ROW]
[ROW][C]42[/C][C]4850[/C][C]5696.33[/C][C]4645.83[/C][C]1050.49[/C][C]-846.325[/C][/ROW]
[ROW][C]43[/C][C]7700[/C][C]6566.64[/C][C]4720.83[/C][C]1845.8[/C][C]1133.36[/C][/ROW]
[ROW][C]44[/C][C]2800[/C][C]5592.68[/C][C]4768.75[/C][C]823.929[/C][C]-2792.68[/C][/ROW]
[ROW][C]45[/C][C]5750[/C][C]3676.53[/C][C]4847.92[/C][C]-1171.38[/C][C]2073.47[/C][/ROW]
[ROW][C]46[/C][C]6200[/C][C]NA[/C][C]NA[/C][C]1482.44[/C][C]NA[/C][/ROW]
[ROW][C]47[/C][C]5150[/C][C]NA[/C][C]NA[/C][C]40.0752[/C][C]NA[/C][/ROW]
[ROW][C]48[/C][C]4300[/C][C]NA[/C][C]NA[/C][C]-1824.51[/C][C]NA[/C][/ROW]
[ROW][C]49[/C][C]4500[/C][C]NA[/C][C]NA[/C][C]30.353[/C][C]NA[/C][/ROW]
[ROW][C]50[/C][C]3450[/C][C]NA[/C][C]NA[/C][C]-1314.09[/C][C]NA[/C][/ROW]
[ROW][C]51[/C][C]5600[/C][C]NA[/C][C]NA[/C][C]-1026.59[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298964&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298964&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
14650NANA30.353NA
24800NANA-1314.09NA
33500NANA-1026.59NA
43850NANA433.825NA
59100NANA-370.341NA
64400NANA1050.49NA
785007422.895577.081845.81077.11
860006505.185681.25823.929-505.179
928504682.785854.17-1171.38-1832.78
1074507730.356247.921482.44-280.353
1160006427.586387.540.0752-427.575
1249504600.496425-1824.51349.508
1364006478.276447.9230.353-78.2697
1455505040.086354.17-1314.09509.925
1569005498.416525-1026.591401.59
1699007144.246710.42433.8252755.76
1764006500.496870.83-370.341-100.492
1880007994.246943.751050.495.7581
1954508829.146983.331845.8-3379.14
2068007861.437037.5823.929-1061.43
2161505724.456895.83-1171.38425.55
2286008024.16541.671482.44575.897
2387006352.586312.540.07522347.42
2440004498.416322.92-1824.51-498.409
2583006501.196470.8330.3531798.81
2649505471.336785.42-1314.09-521.325
2741005827.586854.17-1026.59-1727.58
2842007112.996679.17433.825-2912.99
2966006023.416393.75-370.341576.591
3080507217.166166.671050.49832.841
3189507791.645945.831845.81158.36
32108506501.015677.08823.9294348.99
3337504426.535597.92-1171.38-676.534
3468007103.275620.831482.44-303.27
3536505577.585537.540.0752-1927.58
3636003458.835283.33-1824.51141.175
3734005128.275097.9230.353-1728.27
3834003396.334710.42-1314.093.67477
3937503431.744458.33-1026.59318.258
4051004950.494516.67433.825149.508
4137004183.834554.17-370.341-483.825
4248505696.334645.831050.49-846.325
4377006566.644720.831845.81133.36
4428005592.684768.75823.929-2792.68
4557503676.534847.92-1171.382073.47
466200NANA1482.44NA
475150NANA40.0752NA
484300NANA-1824.51NA
494500NANA30.353NA
503450NANA-1314.09NA
515600NANA-1026.59NA



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')