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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 19:52:14 +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/t1481568746818v41kqykfu0aw.htm/, Retrieved Fri, 03 May 2024 21:59:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298972, Retrieved Fri, 03 May 2024 21:59:02 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71
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 18:52:14] [130d73899007e5ff8a4f636b9bcfb397] [Current]
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Dataseries X:
3913.98
3918.46
3920.72
3981.68
4047.83
4032.25
4054.52
4000.45
3991.03
4041.93
4048.3
4051.03
3988.96
3956.74
4020.78
4019.93
4085.91
4173.13
4209.46
4250.56
4273.58
4360.18
4446.81
4505.92
4496.46
4585.17
4656.57
4703
4782.58
4914.5
5123.02
5340.79
5526.35
5557.94
5708.63
5823.6
6049.46
6019.63
6243.26
6382.25
6501.27
6700.19
6799.1
6917.3




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=298972&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=298972&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298972&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
13913.98NANA16.7598NA
23918.46NANA-52.9845NA
33920.72NANA-37.4369NA
43981.68NANA-78.2163NA
54047.83NANA-71.61NA
64032.25NANA-33.5588NA
74054.524037.044003.3133.735617.4786
84000.454051.184008.0243.1599-50.7349
93991.034061.94013.7948.1062-70.8653
104041.934058.424019.5538.8707-16.4928
114048.34075.424022.7352.6839-27.1164
124051.034070.684030.1940.4903-19.6495
133988.964059.274042.5116.7598-70.3148
143956.744006.414059.39-52.9845-49.6676
154020.784044.154081.59-37.4369-23.3694
164019.934028.44106.62-78.2163-8.47332
174085.914064.874136.48-71.6121.0354
184173.134138.484172.04-33.558834.6459
194209.464245.884212.1433.7356-36.4181
204250.564302.634259.4743.1599-52.0728
214273.584360.254312.1548.1062-86.6749
224360.184405.974367.138.8707-45.792
234446.814477.274424.5952.6839-30.4644
244505.9245254484.5140.4903-19.0791
254496.464570.224553.4616.7598-73.7639
264585.174583.974636.96-52.98451.19911
274656.574697.144734.58-37.4369-40.5735
2847034758.474836.69-78.2163-55.4696
294782.584867.564939.17-71.61-84.9783
304914.55013.095046.65-33.5588-98.5887
315123.025199.995166.2633.7356-76.9748
325340.795333.95290.7443.15996.89342
335526.355464.725416.6248.106261.6259
345557.945591.575552.738.8707-33.6295
355708.635746.965694.2852.6839-38.3335
365823.65880.795840.340.4903-57.1857
376049.466001.35984.5416.759848.1644
386019.636067.086120.06-52.9845-47.4459
396243.26NANA-37.4369NA
406382.25NANA-78.2163NA
416501.27NANA-71.61NA
426700.19NANA-33.5588NA
436799.1NANA33.7356NA
446917.3NANA43.1599NA

\begin{tabular}{lllllllll}
\hline
Classical Decomposition by Moving Averages \tabularnewline
t & Observations & Fit & Trend & Seasonal & Random \tabularnewline
1 & 3913.98 & NA & NA & 16.7598 & NA \tabularnewline
2 & 3918.46 & NA & NA & -52.9845 & NA \tabularnewline
3 & 3920.72 & NA & NA & -37.4369 & NA \tabularnewline
4 & 3981.68 & NA & NA & -78.2163 & NA \tabularnewline
5 & 4047.83 & NA & NA & -71.61 & NA \tabularnewline
6 & 4032.25 & NA & NA & -33.5588 & NA \tabularnewline
7 & 4054.52 & 4037.04 & 4003.31 & 33.7356 & 17.4786 \tabularnewline
8 & 4000.45 & 4051.18 & 4008.02 & 43.1599 & -50.7349 \tabularnewline
9 & 3991.03 & 4061.9 & 4013.79 & 48.1062 & -70.8653 \tabularnewline
10 & 4041.93 & 4058.42 & 4019.55 & 38.8707 & -16.4928 \tabularnewline
11 & 4048.3 & 4075.42 & 4022.73 & 52.6839 & -27.1164 \tabularnewline
12 & 4051.03 & 4070.68 & 4030.19 & 40.4903 & -19.6495 \tabularnewline
13 & 3988.96 & 4059.27 & 4042.51 & 16.7598 & -70.3148 \tabularnewline
14 & 3956.74 & 4006.41 & 4059.39 & -52.9845 & -49.6676 \tabularnewline
15 & 4020.78 & 4044.15 & 4081.59 & -37.4369 & -23.3694 \tabularnewline
16 & 4019.93 & 4028.4 & 4106.62 & -78.2163 & -8.47332 \tabularnewline
17 & 4085.91 & 4064.87 & 4136.48 & -71.61 & 21.0354 \tabularnewline
18 & 4173.13 & 4138.48 & 4172.04 & -33.5588 & 34.6459 \tabularnewline
19 & 4209.46 & 4245.88 & 4212.14 & 33.7356 & -36.4181 \tabularnewline
20 & 4250.56 & 4302.63 & 4259.47 & 43.1599 & -52.0728 \tabularnewline
21 & 4273.58 & 4360.25 & 4312.15 & 48.1062 & -86.6749 \tabularnewline
22 & 4360.18 & 4405.97 & 4367.1 & 38.8707 & -45.792 \tabularnewline
23 & 4446.81 & 4477.27 & 4424.59 & 52.6839 & -30.4644 \tabularnewline
24 & 4505.92 & 4525 & 4484.51 & 40.4903 & -19.0791 \tabularnewline
25 & 4496.46 & 4570.22 & 4553.46 & 16.7598 & -73.7639 \tabularnewline
26 & 4585.17 & 4583.97 & 4636.96 & -52.9845 & 1.19911 \tabularnewline
27 & 4656.57 & 4697.14 & 4734.58 & -37.4369 & -40.5735 \tabularnewline
28 & 4703 & 4758.47 & 4836.69 & -78.2163 & -55.4696 \tabularnewline
29 & 4782.58 & 4867.56 & 4939.17 & -71.61 & -84.9783 \tabularnewline
30 & 4914.5 & 5013.09 & 5046.65 & -33.5588 & -98.5887 \tabularnewline
31 & 5123.02 & 5199.99 & 5166.26 & 33.7356 & -76.9748 \tabularnewline
32 & 5340.79 & 5333.9 & 5290.74 & 43.1599 & 6.89342 \tabularnewline
33 & 5526.35 & 5464.72 & 5416.62 & 48.1062 & 61.6259 \tabularnewline
34 & 5557.94 & 5591.57 & 5552.7 & 38.8707 & -33.6295 \tabularnewline
35 & 5708.63 & 5746.96 & 5694.28 & 52.6839 & -38.3335 \tabularnewline
36 & 5823.6 & 5880.79 & 5840.3 & 40.4903 & -57.1857 \tabularnewline
37 & 6049.46 & 6001.3 & 5984.54 & 16.7598 & 48.1644 \tabularnewline
38 & 6019.63 & 6067.08 & 6120.06 & -52.9845 & -47.4459 \tabularnewline
39 & 6243.26 & NA & NA & -37.4369 & NA \tabularnewline
40 & 6382.25 & NA & NA & -78.2163 & NA \tabularnewline
41 & 6501.27 & NA & NA & -71.61 & NA \tabularnewline
42 & 6700.19 & NA & NA & -33.5588 & NA \tabularnewline
43 & 6799.1 & NA & NA & 33.7356 & NA \tabularnewline
44 & 6917.3 & NA & NA & 43.1599 & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298972&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]3913.98[/C][C]NA[/C][C]NA[/C][C]16.7598[/C][C]NA[/C][/ROW]
[ROW][C]2[/C][C]3918.46[/C][C]NA[/C][C]NA[/C][C]-52.9845[/C][C]NA[/C][/ROW]
[ROW][C]3[/C][C]3920.72[/C][C]NA[/C][C]NA[/C][C]-37.4369[/C][C]NA[/C][/ROW]
[ROW][C]4[/C][C]3981.68[/C][C]NA[/C][C]NA[/C][C]-78.2163[/C][C]NA[/C][/ROW]
[ROW][C]5[/C][C]4047.83[/C][C]NA[/C][C]NA[/C][C]-71.61[/C][C]NA[/C][/ROW]
[ROW][C]6[/C][C]4032.25[/C][C]NA[/C][C]NA[/C][C]-33.5588[/C][C]NA[/C][/ROW]
[ROW][C]7[/C][C]4054.52[/C][C]4037.04[/C][C]4003.31[/C][C]33.7356[/C][C]17.4786[/C][/ROW]
[ROW][C]8[/C][C]4000.45[/C][C]4051.18[/C][C]4008.02[/C][C]43.1599[/C][C]-50.7349[/C][/ROW]
[ROW][C]9[/C][C]3991.03[/C][C]4061.9[/C][C]4013.79[/C][C]48.1062[/C][C]-70.8653[/C][/ROW]
[ROW][C]10[/C][C]4041.93[/C][C]4058.42[/C][C]4019.55[/C][C]38.8707[/C][C]-16.4928[/C][/ROW]
[ROW][C]11[/C][C]4048.3[/C][C]4075.42[/C][C]4022.73[/C][C]52.6839[/C][C]-27.1164[/C][/ROW]
[ROW][C]12[/C][C]4051.03[/C][C]4070.68[/C][C]4030.19[/C][C]40.4903[/C][C]-19.6495[/C][/ROW]
[ROW][C]13[/C][C]3988.96[/C][C]4059.27[/C][C]4042.51[/C][C]16.7598[/C][C]-70.3148[/C][/ROW]
[ROW][C]14[/C][C]3956.74[/C][C]4006.41[/C][C]4059.39[/C][C]-52.9845[/C][C]-49.6676[/C][/ROW]
[ROW][C]15[/C][C]4020.78[/C][C]4044.15[/C][C]4081.59[/C][C]-37.4369[/C][C]-23.3694[/C][/ROW]
[ROW][C]16[/C][C]4019.93[/C][C]4028.4[/C][C]4106.62[/C][C]-78.2163[/C][C]-8.47332[/C][/ROW]
[ROW][C]17[/C][C]4085.91[/C][C]4064.87[/C][C]4136.48[/C][C]-71.61[/C][C]21.0354[/C][/ROW]
[ROW][C]18[/C][C]4173.13[/C][C]4138.48[/C][C]4172.04[/C][C]-33.5588[/C][C]34.6459[/C][/ROW]
[ROW][C]19[/C][C]4209.46[/C][C]4245.88[/C][C]4212.14[/C][C]33.7356[/C][C]-36.4181[/C][/ROW]
[ROW][C]20[/C][C]4250.56[/C][C]4302.63[/C][C]4259.47[/C][C]43.1599[/C][C]-52.0728[/C][/ROW]
[ROW][C]21[/C][C]4273.58[/C][C]4360.25[/C][C]4312.15[/C][C]48.1062[/C][C]-86.6749[/C][/ROW]
[ROW][C]22[/C][C]4360.18[/C][C]4405.97[/C][C]4367.1[/C][C]38.8707[/C][C]-45.792[/C][/ROW]
[ROW][C]23[/C][C]4446.81[/C][C]4477.27[/C][C]4424.59[/C][C]52.6839[/C][C]-30.4644[/C][/ROW]
[ROW][C]24[/C][C]4505.92[/C][C]4525[/C][C]4484.51[/C][C]40.4903[/C][C]-19.0791[/C][/ROW]
[ROW][C]25[/C][C]4496.46[/C][C]4570.22[/C][C]4553.46[/C][C]16.7598[/C][C]-73.7639[/C][/ROW]
[ROW][C]26[/C][C]4585.17[/C][C]4583.97[/C][C]4636.96[/C][C]-52.9845[/C][C]1.19911[/C][/ROW]
[ROW][C]27[/C][C]4656.57[/C][C]4697.14[/C][C]4734.58[/C][C]-37.4369[/C][C]-40.5735[/C][/ROW]
[ROW][C]28[/C][C]4703[/C][C]4758.47[/C][C]4836.69[/C][C]-78.2163[/C][C]-55.4696[/C][/ROW]
[ROW][C]29[/C][C]4782.58[/C][C]4867.56[/C][C]4939.17[/C][C]-71.61[/C][C]-84.9783[/C][/ROW]
[ROW][C]30[/C][C]4914.5[/C][C]5013.09[/C][C]5046.65[/C][C]-33.5588[/C][C]-98.5887[/C][/ROW]
[ROW][C]31[/C][C]5123.02[/C][C]5199.99[/C][C]5166.26[/C][C]33.7356[/C][C]-76.9748[/C][/ROW]
[ROW][C]32[/C][C]5340.79[/C][C]5333.9[/C][C]5290.74[/C][C]43.1599[/C][C]6.89342[/C][/ROW]
[ROW][C]33[/C][C]5526.35[/C][C]5464.72[/C][C]5416.62[/C][C]48.1062[/C][C]61.6259[/C][/ROW]
[ROW][C]34[/C][C]5557.94[/C][C]5591.57[/C][C]5552.7[/C][C]38.8707[/C][C]-33.6295[/C][/ROW]
[ROW][C]35[/C][C]5708.63[/C][C]5746.96[/C][C]5694.28[/C][C]52.6839[/C][C]-38.3335[/C][/ROW]
[ROW][C]36[/C][C]5823.6[/C][C]5880.79[/C][C]5840.3[/C][C]40.4903[/C][C]-57.1857[/C][/ROW]
[ROW][C]37[/C][C]6049.46[/C][C]6001.3[/C][C]5984.54[/C][C]16.7598[/C][C]48.1644[/C][/ROW]
[ROW][C]38[/C][C]6019.63[/C][C]6067.08[/C][C]6120.06[/C][C]-52.9845[/C][C]-47.4459[/C][/ROW]
[ROW][C]39[/C][C]6243.26[/C][C]NA[/C][C]NA[/C][C]-37.4369[/C][C]NA[/C][/ROW]
[ROW][C]40[/C][C]6382.25[/C][C]NA[/C][C]NA[/C][C]-78.2163[/C][C]NA[/C][/ROW]
[ROW][C]41[/C][C]6501.27[/C][C]NA[/C][C]NA[/C][C]-71.61[/C][C]NA[/C][/ROW]
[ROW][C]42[/C][C]6700.19[/C][C]NA[/C][C]NA[/C][C]-33.5588[/C][C]NA[/C][/ROW]
[ROW][C]43[/C][C]6799.1[/C][C]NA[/C][C]NA[/C][C]33.7356[/C][C]NA[/C][/ROW]
[ROW][C]44[/C][C]6917.3[/C][C]NA[/C][C]NA[/C][C]43.1599[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298972&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298972&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
13913.98NANA16.7598NA
23918.46NANA-52.9845NA
33920.72NANA-37.4369NA
43981.68NANA-78.2163NA
54047.83NANA-71.61NA
64032.25NANA-33.5588NA
74054.524037.044003.3133.735617.4786
84000.454051.184008.0243.1599-50.7349
93991.034061.94013.7948.1062-70.8653
104041.934058.424019.5538.8707-16.4928
114048.34075.424022.7352.6839-27.1164
124051.034070.684030.1940.4903-19.6495
133988.964059.274042.5116.7598-70.3148
143956.744006.414059.39-52.9845-49.6676
154020.784044.154081.59-37.4369-23.3694
164019.934028.44106.62-78.2163-8.47332
174085.914064.874136.48-71.6121.0354
184173.134138.484172.04-33.558834.6459
194209.464245.884212.1433.7356-36.4181
204250.564302.634259.4743.1599-52.0728
214273.584360.254312.1548.1062-86.6749
224360.184405.974367.138.8707-45.792
234446.814477.274424.5952.6839-30.4644
244505.9245254484.5140.4903-19.0791
254496.464570.224553.4616.7598-73.7639
264585.174583.974636.96-52.98451.19911
274656.574697.144734.58-37.4369-40.5735
2847034758.474836.69-78.2163-55.4696
294782.584867.564939.17-71.61-84.9783
304914.55013.095046.65-33.5588-98.5887
315123.025199.995166.2633.7356-76.9748
325340.795333.95290.7443.15996.89342
335526.355464.725416.6248.106261.6259
345557.945591.575552.738.8707-33.6295
355708.635746.965694.2852.6839-38.3335
365823.65880.795840.340.4903-57.1857
376049.466001.35984.5416.759848.1644
386019.636067.086120.06-52.9845-47.4459
396243.26NANA-37.4369NA
406382.25NANA-78.2163NA
416501.27NANA-71.61NA
426700.19NANA-33.5588NA
436799.1NANA33.7356NA
446917.3NANA43.1599NA



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')