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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 computationWed, 14 Dec 2016 15:10:05 +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/14/t1481724630yifdnh1njrkiae0.htm/, Retrieved Fri, 03 May 2024 16:28:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299469, Retrieved Fri, 03 May 2024 16:28:25 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Classical Decomposition] [] [2016-12-14 14:10:05] [349958aef20b862f8399a5ba04d6f6e3] [Current]
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Dataseries X:
5520
3880
4840
4360
3800
4560
4560
5120
4320
5380
4860
4560
5820
4260
3720
4500
5200
4300
5460
4800
4500
4640
4600
5400
5220
3700
5180
4360
3920
4760
4600
4580
4300
4920
3940
5640
4800
4120
4940
4540
4100
4940
4660
4180
3960
4380
4480
5860
4760
4440
5020




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=299469&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=299469&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299469&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
15520NANA591.997NA
23880NANA-649.67NA
34840NANA-44.9479NA
44360NANA-172.726NA
53800NANA-213.559NA
64560NANA33.6632NA
745604836.024659.17176.858-276.024
851204716.444687.528.941403.559
943204277.94656.67-378.76742.1007
1053804930.614615.83314.774449.392
1148604474.774680-205.226385.226
1245605246.164727.5518.663-686.163
1358205346.164754.17591.997473.837
1442604128.664778.33-649.67131.337
1537204727.554772.5-44.9479-1007.55
1645004576.444749.17-172.726-76.441
1752004493.944707.5-213.559706.059
1843004765.334731.6733.6632-465.33
1954604918.524741.67176.858541.476
2048004722.274693.3328.94177.7257
2145004352.074730.83-378.767147.934
2246405100.614785.83314.774-460.608
2346004521.444726.67-205.22678.559
2454005211.164692.5518.663188.837
2552205267.834675.83591.997-47.8299
2637003981.164630.83-649.67-281.163
2751804568.394613.33-44.9479611.615
2843604443.944616.67-172.726-83.941
2939204387.274600.83-213.559-467.274
30476046174583.3333.6632143.003
3146004752.694575.83176.858-152.691
3245804604.774575.8328.941-24.7743
3343004204.574583.33-378.76795.434
3449204895.614580.83314.77424.3924
3539404390.614595.83-205.226-450.608
3656405129.54610.83518.663510.503
3748005212.834620.83591.997-412.83
38412039574606.67-649.67163.003
3949404530.894575.83-44.9479409.115
4045404366.444539.17-172.726173.559
4141004325.614539.17-213.559-225.608
4249404604.54570.8333.6632335.503
4346604755.194578.33176.858-95.191
4441804618.94459028.941-438.941
4539604227.94606.67-378.767-267.899
464380NANA314.774NA
474480NANA-205.226NA
485860NANA518.663NA
494760NANA591.997NA
504440NANA-649.67NA
515020NANA-44.9479NA

\begin{tabular}{lllllllll}
\hline
Classical Decomposition by Moving Averages \tabularnewline
t & Observations & Fit & Trend & Seasonal & Random \tabularnewline
1 & 5520 & NA & NA & 591.997 & NA \tabularnewline
2 & 3880 & NA & NA & -649.67 & NA \tabularnewline
3 & 4840 & NA & NA & -44.9479 & NA \tabularnewline
4 & 4360 & NA & NA & -172.726 & NA \tabularnewline
5 & 3800 & NA & NA & -213.559 & NA \tabularnewline
6 & 4560 & NA & NA & 33.6632 & NA \tabularnewline
7 & 4560 & 4836.02 & 4659.17 & 176.858 & -276.024 \tabularnewline
8 & 5120 & 4716.44 & 4687.5 & 28.941 & 403.559 \tabularnewline
9 & 4320 & 4277.9 & 4656.67 & -378.767 & 42.1007 \tabularnewline
10 & 5380 & 4930.61 & 4615.83 & 314.774 & 449.392 \tabularnewline
11 & 4860 & 4474.77 & 4680 & -205.226 & 385.226 \tabularnewline
12 & 4560 & 5246.16 & 4727.5 & 518.663 & -686.163 \tabularnewline
13 & 5820 & 5346.16 & 4754.17 & 591.997 & 473.837 \tabularnewline
14 & 4260 & 4128.66 & 4778.33 & -649.67 & 131.337 \tabularnewline
15 & 3720 & 4727.55 & 4772.5 & -44.9479 & -1007.55 \tabularnewline
16 & 4500 & 4576.44 & 4749.17 & -172.726 & -76.441 \tabularnewline
17 & 5200 & 4493.94 & 4707.5 & -213.559 & 706.059 \tabularnewline
18 & 4300 & 4765.33 & 4731.67 & 33.6632 & -465.33 \tabularnewline
19 & 5460 & 4918.52 & 4741.67 & 176.858 & 541.476 \tabularnewline
20 & 4800 & 4722.27 & 4693.33 & 28.941 & 77.7257 \tabularnewline
21 & 4500 & 4352.07 & 4730.83 & -378.767 & 147.934 \tabularnewline
22 & 4640 & 5100.61 & 4785.83 & 314.774 & -460.608 \tabularnewline
23 & 4600 & 4521.44 & 4726.67 & -205.226 & 78.559 \tabularnewline
24 & 5400 & 5211.16 & 4692.5 & 518.663 & 188.837 \tabularnewline
25 & 5220 & 5267.83 & 4675.83 & 591.997 & -47.8299 \tabularnewline
26 & 3700 & 3981.16 & 4630.83 & -649.67 & -281.163 \tabularnewline
27 & 5180 & 4568.39 & 4613.33 & -44.9479 & 611.615 \tabularnewline
28 & 4360 & 4443.94 & 4616.67 & -172.726 & -83.941 \tabularnewline
29 & 3920 & 4387.27 & 4600.83 & -213.559 & -467.274 \tabularnewline
30 & 4760 & 4617 & 4583.33 & 33.6632 & 143.003 \tabularnewline
31 & 4600 & 4752.69 & 4575.83 & 176.858 & -152.691 \tabularnewline
32 & 4580 & 4604.77 & 4575.83 & 28.941 & -24.7743 \tabularnewline
33 & 4300 & 4204.57 & 4583.33 & -378.767 & 95.434 \tabularnewline
34 & 4920 & 4895.61 & 4580.83 & 314.774 & 24.3924 \tabularnewline
35 & 3940 & 4390.61 & 4595.83 & -205.226 & -450.608 \tabularnewline
36 & 5640 & 5129.5 & 4610.83 & 518.663 & 510.503 \tabularnewline
37 & 4800 & 5212.83 & 4620.83 & 591.997 & -412.83 \tabularnewline
38 & 4120 & 3957 & 4606.67 & -649.67 & 163.003 \tabularnewline
39 & 4940 & 4530.89 & 4575.83 & -44.9479 & 409.115 \tabularnewline
40 & 4540 & 4366.44 & 4539.17 & -172.726 & 173.559 \tabularnewline
41 & 4100 & 4325.61 & 4539.17 & -213.559 & -225.608 \tabularnewline
42 & 4940 & 4604.5 & 4570.83 & 33.6632 & 335.503 \tabularnewline
43 & 4660 & 4755.19 & 4578.33 & 176.858 & -95.191 \tabularnewline
44 & 4180 & 4618.94 & 4590 & 28.941 & -438.941 \tabularnewline
45 & 3960 & 4227.9 & 4606.67 & -378.767 & -267.899 \tabularnewline
46 & 4380 & NA & NA & 314.774 & NA \tabularnewline
47 & 4480 & NA & NA & -205.226 & NA \tabularnewline
48 & 5860 & NA & NA & 518.663 & NA \tabularnewline
49 & 4760 & NA & NA & 591.997 & NA \tabularnewline
50 & 4440 & NA & NA & -649.67 & NA \tabularnewline
51 & 5020 & NA & NA & -44.9479 & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299469&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]5520[/C][C]NA[/C][C]NA[/C][C]591.997[/C][C]NA[/C][/ROW]
[ROW][C]2[/C][C]3880[/C][C]NA[/C][C]NA[/C][C]-649.67[/C][C]NA[/C][/ROW]
[ROW][C]3[/C][C]4840[/C][C]NA[/C][C]NA[/C][C]-44.9479[/C][C]NA[/C][/ROW]
[ROW][C]4[/C][C]4360[/C][C]NA[/C][C]NA[/C][C]-172.726[/C][C]NA[/C][/ROW]
[ROW][C]5[/C][C]3800[/C][C]NA[/C][C]NA[/C][C]-213.559[/C][C]NA[/C][/ROW]
[ROW][C]6[/C][C]4560[/C][C]NA[/C][C]NA[/C][C]33.6632[/C][C]NA[/C][/ROW]
[ROW][C]7[/C][C]4560[/C][C]4836.02[/C][C]4659.17[/C][C]176.858[/C][C]-276.024[/C][/ROW]
[ROW][C]8[/C][C]5120[/C][C]4716.44[/C][C]4687.5[/C][C]28.941[/C][C]403.559[/C][/ROW]
[ROW][C]9[/C][C]4320[/C][C]4277.9[/C][C]4656.67[/C][C]-378.767[/C][C]42.1007[/C][/ROW]
[ROW][C]10[/C][C]5380[/C][C]4930.61[/C][C]4615.83[/C][C]314.774[/C][C]449.392[/C][/ROW]
[ROW][C]11[/C][C]4860[/C][C]4474.77[/C][C]4680[/C][C]-205.226[/C][C]385.226[/C][/ROW]
[ROW][C]12[/C][C]4560[/C][C]5246.16[/C][C]4727.5[/C][C]518.663[/C][C]-686.163[/C][/ROW]
[ROW][C]13[/C][C]5820[/C][C]5346.16[/C][C]4754.17[/C][C]591.997[/C][C]473.837[/C][/ROW]
[ROW][C]14[/C][C]4260[/C][C]4128.66[/C][C]4778.33[/C][C]-649.67[/C][C]131.337[/C][/ROW]
[ROW][C]15[/C][C]3720[/C][C]4727.55[/C][C]4772.5[/C][C]-44.9479[/C][C]-1007.55[/C][/ROW]
[ROW][C]16[/C][C]4500[/C][C]4576.44[/C][C]4749.17[/C][C]-172.726[/C][C]-76.441[/C][/ROW]
[ROW][C]17[/C][C]5200[/C][C]4493.94[/C][C]4707.5[/C][C]-213.559[/C][C]706.059[/C][/ROW]
[ROW][C]18[/C][C]4300[/C][C]4765.33[/C][C]4731.67[/C][C]33.6632[/C][C]-465.33[/C][/ROW]
[ROW][C]19[/C][C]5460[/C][C]4918.52[/C][C]4741.67[/C][C]176.858[/C][C]541.476[/C][/ROW]
[ROW][C]20[/C][C]4800[/C][C]4722.27[/C][C]4693.33[/C][C]28.941[/C][C]77.7257[/C][/ROW]
[ROW][C]21[/C][C]4500[/C][C]4352.07[/C][C]4730.83[/C][C]-378.767[/C][C]147.934[/C][/ROW]
[ROW][C]22[/C][C]4640[/C][C]5100.61[/C][C]4785.83[/C][C]314.774[/C][C]-460.608[/C][/ROW]
[ROW][C]23[/C][C]4600[/C][C]4521.44[/C][C]4726.67[/C][C]-205.226[/C][C]78.559[/C][/ROW]
[ROW][C]24[/C][C]5400[/C][C]5211.16[/C][C]4692.5[/C][C]518.663[/C][C]188.837[/C][/ROW]
[ROW][C]25[/C][C]5220[/C][C]5267.83[/C][C]4675.83[/C][C]591.997[/C][C]-47.8299[/C][/ROW]
[ROW][C]26[/C][C]3700[/C][C]3981.16[/C][C]4630.83[/C][C]-649.67[/C][C]-281.163[/C][/ROW]
[ROW][C]27[/C][C]5180[/C][C]4568.39[/C][C]4613.33[/C][C]-44.9479[/C][C]611.615[/C][/ROW]
[ROW][C]28[/C][C]4360[/C][C]4443.94[/C][C]4616.67[/C][C]-172.726[/C][C]-83.941[/C][/ROW]
[ROW][C]29[/C][C]3920[/C][C]4387.27[/C][C]4600.83[/C][C]-213.559[/C][C]-467.274[/C][/ROW]
[ROW][C]30[/C][C]4760[/C][C]4617[/C][C]4583.33[/C][C]33.6632[/C][C]143.003[/C][/ROW]
[ROW][C]31[/C][C]4600[/C][C]4752.69[/C][C]4575.83[/C][C]176.858[/C][C]-152.691[/C][/ROW]
[ROW][C]32[/C][C]4580[/C][C]4604.77[/C][C]4575.83[/C][C]28.941[/C][C]-24.7743[/C][/ROW]
[ROW][C]33[/C][C]4300[/C][C]4204.57[/C][C]4583.33[/C][C]-378.767[/C][C]95.434[/C][/ROW]
[ROW][C]34[/C][C]4920[/C][C]4895.61[/C][C]4580.83[/C][C]314.774[/C][C]24.3924[/C][/ROW]
[ROW][C]35[/C][C]3940[/C][C]4390.61[/C][C]4595.83[/C][C]-205.226[/C][C]-450.608[/C][/ROW]
[ROW][C]36[/C][C]5640[/C][C]5129.5[/C][C]4610.83[/C][C]518.663[/C][C]510.503[/C][/ROW]
[ROW][C]37[/C][C]4800[/C][C]5212.83[/C][C]4620.83[/C][C]591.997[/C][C]-412.83[/C][/ROW]
[ROW][C]38[/C][C]4120[/C][C]3957[/C][C]4606.67[/C][C]-649.67[/C][C]163.003[/C][/ROW]
[ROW][C]39[/C][C]4940[/C][C]4530.89[/C][C]4575.83[/C][C]-44.9479[/C][C]409.115[/C][/ROW]
[ROW][C]40[/C][C]4540[/C][C]4366.44[/C][C]4539.17[/C][C]-172.726[/C][C]173.559[/C][/ROW]
[ROW][C]41[/C][C]4100[/C][C]4325.61[/C][C]4539.17[/C][C]-213.559[/C][C]-225.608[/C][/ROW]
[ROW][C]42[/C][C]4940[/C][C]4604.5[/C][C]4570.83[/C][C]33.6632[/C][C]335.503[/C][/ROW]
[ROW][C]43[/C][C]4660[/C][C]4755.19[/C][C]4578.33[/C][C]176.858[/C][C]-95.191[/C][/ROW]
[ROW][C]44[/C][C]4180[/C][C]4618.94[/C][C]4590[/C][C]28.941[/C][C]-438.941[/C][/ROW]
[ROW][C]45[/C][C]3960[/C][C]4227.9[/C][C]4606.67[/C][C]-378.767[/C][C]-267.899[/C][/ROW]
[ROW][C]46[/C][C]4380[/C][C]NA[/C][C]NA[/C][C]314.774[/C][C]NA[/C][/ROW]
[ROW][C]47[/C][C]4480[/C][C]NA[/C][C]NA[/C][C]-205.226[/C][C]NA[/C][/ROW]
[ROW][C]48[/C][C]5860[/C][C]NA[/C][C]NA[/C][C]518.663[/C][C]NA[/C][/ROW]
[ROW][C]49[/C][C]4760[/C][C]NA[/C][C]NA[/C][C]591.997[/C][C]NA[/C][/ROW]
[ROW][C]50[/C][C]4440[/C][C]NA[/C][C]NA[/C][C]-649.67[/C][C]NA[/C][/ROW]
[ROW][C]51[/C][C]5020[/C][C]NA[/C][C]NA[/C][C]-44.9479[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299469&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299469&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
15520NANA591.997NA
23880NANA-649.67NA
34840NANA-44.9479NA
44360NANA-172.726NA
53800NANA-213.559NA
64560NANA33.6632NA
745604836.024659.17176.858-276.024
851204716.444687.528.941403.559
943204277.94656.67-378.76742.1007
1053804930.614615.83314.774449.392
1148604474.774680-205.226385.226
1245605246.164727.5518.663-686.163
1358205346.164754.17591.997473.837
1442604128.664778.33-649.67131.337
1537204727.554772.5-44.9479-1007.55
1645004576.444749.17-172.726-76.441
1752004493.944707.5-213.559706.059
1843004765.334731.6733.6632-465.33
1954604918.524741.67176.858541.476
2048004722.274693.3328.94177.7257
2145004352.074730.83-378.767147.934
2246405100.614785.83314.774-460.608
2346004521.444726.67-205.22678.559
2454005211.164692.5518.663188.837
2552205267.834675.83591.997-47.8299
2637003981.164630.83-649.67-281.163
2751804568.394613.33-44.9479611.615
2843604443.944616.67-172.726-83.941
2939204387.274600.83-213.559-467.274
30476046174583.3333.6632143.003
3146004752.694575.83176.858-152.691
3245804604.774575.8328.941-24.7743
3343004204.574583.33-378.76795.434
3449204895.614580.83314.77424.3924
3539404390.614595.83-205.226-450.608
3656405129.54610.83518.663510.503
3748005212.834620.83591.997-412.83
38412039574606.67-649.67163.003
3949404530.894575.83-44.9479409.115
4045404366.444539.17-172.726173.559
4141004325.614539.17-213.559-225.608
4249404604.54570.8333.6632335.503
4346604755.194578.33176.858-95.191
4441804618.94459028.941-438.941
4539604227.94606.67-378.767-267.899
464380NANA314.774NA
474480NANA-205.226NA
485860NANA518.663NA
494760NANA591.997NA
504440NANA-649.67NA
515020NANA-44.9479NA



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')