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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, 07 Dec 2016 10:58:03 +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/07/t148110521382rwc60cc7jh0w5.htm/, Retrieved Tue, 07 May 2024 16:53:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297949, Retrieved Tue, 07 May 2024 16:53:55 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Classical Decomposition] [Voorbeeld Classic...] [2016-12-07 09:58:03] [fc6d28d208bad0c833791fcb11cb4db1] [Current]
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Dataseries X:
2157.07
2267.88
2375.38
2803.62
2367.53
2439.08
2533.76
2956.28
2484.24
2588.49
2668.42
3085.62
2595.93
2686.64
2779.43
3221.13
2752.7
2886.58
2958.05
3444.61
2939.78
3088.73
3161.34
3672.39
3092.36
3228.05
3311.16
3801.93
3246.26
3309.22
3458.64
4005.04
3477.65
3524.42
3699.5
4247.68
3697.6
3746.72
3950.67
4566.86
3967.9
4059.35
4215.38
4856.13




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=297949&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=297949&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297949&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
12157.07NANA-187.913NA
22267.88NANA-145.816NA
32375.38NANA-68.7269NA
42803.62NANA357.314NA
52367.53NANA-195.716NA
62439.08NANA-142.986NA
72533.762513.872578.9-65.029919.8899
82956.282992.832614.63378.194-36.5486
92484.242483.272648.92-165.6440.966134
102588.492571.132683.15-112.02317.3629
112668.422667.062716.59-49.53271.35808
123085.623149.172751.29397.88-63.5487
132595.932599.72787.61-187.913-3.77039
142686.642679.822825.64-145.8166.81641
152779.432796.242864.97-68.7269-16.8106
163221.133262.112904.79357.314-40.9752
172752.72750.462946.17-195.7162.24252
182886.582848.172991.16-142.98638.4059
192958.052971.263036.29-65.0299-13.2139
203444.613457.733079.54378.194-13.1215
212939.782958.613124.25-165.644-18.8272
223088.733058.583170.61-112.02330.1459
233161.343165.843215.37-49.5327-4.499
243672.393651.433253.55397.8820.9638
253092.363104.13292.01-187.913-11.7412
263228.053190.413336.22-145.81637.6422
273311.163313.263381.99-68.7269-2.09935
283801.933779.863422.55357.31422.0652
293246.263267.413463.13-195.716-21.1525
303309.223366.543509.52-142.986-57.3158
313458.643493.683558.71-65.0299-35.0409
324005.043983.733605.54378.19421.3052
333477.653488.153653.8-165.644-10.5039
343524.423600.293712.32-112.023-75.8737
353699.53724.723774.26-49.5327-25.224
364247.684233.463835.58397.8814.22
373697.63710.453898.37-187.913-12.8533
383746.723819.543965.36-145.816-72.8236
393950.67NANA-68.7269NA
404566.86NANA357.314NA
413967.9NANA-195.716NA
424059.35NANA-142.986NA
434215.38NANA-65.0299NA
444856.13NANA378.194NA

\begin{tabular}{lllllllll}
\hline
Classical Decomposition by Moving Averages \tabularnewline
t & Observations & Fit & Trend & Seasonal & Random \tabularnewline
1 & 2157.07 & NA & NA & -187.913 & NA \tabularnewline
2 & 2267.88 & NA & NA & -145.816 & NA \tabularnewline
3 & 2375.38 & NA & NA & -68.7269 & NA \tabularnewline
4 & 2803.62 & NA & NA & 357.314 & NA \tabularnewline
5 & 2367.53 & NA & NA & -195.716 & NA \tabularnewline
6 & 2439.08 & NA & NA & -142.986 & NA \tabularnewline
7 & 2533.76 & 2513.87 & 2578.9 & -65.0299 & 19.8899 \tabularnewline
8 & 2956.28 & 2992.83 & 2614.63 & 378.194 & -36.5486 \tabularnewline
9 & 2484.24 & 2483.27 & 2648.92 & -165.644 & 0.966134 \tabularnewline
10 & 2588.49 & 2571.13 & 2683.15 & -112.023 & 17.3629 \tabularnewline
11 & 2668.42 & 2667.06 & 2716.59 & -49.5327 & 1.35808 \tabularnewline
12 & 3085.62 & 3149.17 & 2751.29 & 397.88 & -63.5487 \tabularnewline
13 & 2595.93 & 2599.7 & 2787.61 & -187.913 & -3.77039 \tabularnewline
14 & 2686.64 & 2679.82 & 2825.64 & -145.816 & 6.81641 \tabularnewline
15 & 2779.43 & 2796.24 & 2864.97 & -68.7269 & -16.8106 \tabularnewline
16 & 3221.13 & 3262.11 & 2904.79 & 357.314 & -40.9752 \tabularnewline
17 & 2752.7 & 2750.46 & 2946.17 & -195.716 & 2.24252 \tabularnewline
18 & 2886.58 & 2848.17 & 2991.16 & -142.986 & 38.4059 \tabularnewline
19 & 2958.05 & 2971.26 & 3036.29 & -65.0299 & -13.2139 \tabularnewline
20 & 3444.61 & 3457.73 & 3079.54 & 378.194 & -13.1215 \tabularnewline
21 & 2939.78 & 2958.61 & 3124.25 & -165.644 & -18.8272 \tabularnewline
22 & 3088.73 & 3058.58 & 3170.61 & -112.023 & 30.1459 \tabularnewline
23 & 3161.34 & 3165.84 & 3215.37 & -49.5327 & -4.499 \tabularnewline
24 & 3672.39 & 3651.43 & 3253.55 & 397.88 & 20.9638 \tabularnewline
25 & 3092.36 & 3104.1 & 3292.01 & -187.913 & -11.7412 \tabularnewline
26 & 3228.05 & 3190.41 & 3336.22 & -145.816 & 37.6422 \tabularnewline
27 & 3311.16 & 3313.26 & 3381.99 & -68.7269 & -2.09935 \tabularnewline
28 & 3801.93 & 3779.86 & 3422.55 & 357.314 & 22.0652 \tabularnewline
29 & 3246.26 & 3267.41 & 3463.13 & -195.716 & -21.1525 \tabularnewline
30 & 3309.22 & 3366.54 & 3509.52 & -142.986 & -57.3158 \tabularnewline
31 & 3458.64 & 3493.68 & 3558.71 & -65.0299 & -35.0409 \tabularnewline
32 & 4005.04 & 3983.73 & 3605.54 & 378.194 & 21.3052 \tabularnewline
33 & 3477.65 & 3488.15 & 3653.8 & -165.644 & -10.5039 \tabularnewline
34 & 3524.42 & 3600.29 & 3712.32 & -112.023 & -75.8737 \tabularnewline
35 & 3699.5 & 3724.72 & 3774.26 & -49.5327 & -25.224 \tabularnewline
36 & 4247.68 & 4233.46 & 3835.58 & 397.88 & 14.22 \tabularnewline
37 & 3697.6 & 3710.45 & 3898.37 & -187.913 & -12.8533 \tabularnewline
38 & 3746.72 & 3819.54 & 3965.36 & -145.816 & -72.8236 \tabularnewline
39 & 3950.67 & NA & NA & -68.7269 & NA \tabularnewline
40 & 4566.86 & NA & NA & 357.314 & NA \tabularnewline
41 & 3967.9 & NA & NA & -195.716 & NA \tabularnewline
42 & 4059.35 & NA & NA & -142.986 & NA \tabularnewline
43 & 4215.38 & NA & NA & -65.0299 & NA \tabularnewline
44 & 4856.13 & NA & NA & 378.194 & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297949&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]2157.07[/C][C]NA[/C][C]NA[/C][C]-187.913[/C][C]NA[/C][/ROW]
[ROW][C]2[/C][C]2267.88[/C][C]NA[/C][C]NA[/C][C]-145.816[/C][C]NA[/C][/ROW]
[ROW][C]3[/C][C]2375.38[/C][C]NA[/C][C]NA[/C][C]-68.7269[/C][C]NA[/C][/ROW]
[ROW][C]4[/C][C]2803.62[/C][C]NA[/C][C]NA[/C][C]357.314[/C][C]NA[/C][/ROW]
[ROW][C]5[/C][C]2367.53[/C][C]NA[/C][C]NA[/C][C]-195.716[/C][C]NA[/C][/ROW]
[ROW][C]6[/C][C]2439.08[/C][C]NA[/C][C]NA[/C][C]-142.986[/C][C]NA[/C][/ROW]
[ROW][C]7[/C][C]2533.76[/C][C]2513.87[/C][C]2578.9[/C][C]-65.0299[/C][C]19.8899[/C][/ROW]
[ROW][C]8[/C][C]2956.28[/C][C]2992.83[/C][C]2614.63[/C][C]378.194[/C][C]-36.5486[/C][/ROW]
[ROW][C]9[/C][C]2484.24[/C][C]2483.27[/C][C]2648.92[/C][C]-165.644[/C][C]0.966134[/C][/ROW]
[ROW][C]10[/C][C]2588.49[/C][C]2571.13[/C][C]2683.15[/C][C]-112.023[/C][C]17.3629[/C][/ROW]
[ROW][C]11[/C][C]2668.42[/C][C]2667.06[/C][C]2716.59[/C][C]-49.5327[/C][C]1.35808[/C][/ROW]
[ROW][C]12[/C][C]3085.62[/C][C]3149.17[/C][C]2751.29[/C][C]397.88[/C][C]-63.5487[/C][/ROW]
[ROW][C]13[/C][C]2595.93[/C][C]2599.7[/C][C]2787.61[/C][C]-187.913[/C][C]-3.77039[/C][/ROW]
[ROW][C]14[/C][C]2686.64[/C][C]2679.82[/C][C]2825.64[/C][C]-145.816[/C][C]6.81641[/C][/ROW]
[ROW][C]15[/C][C]2779.43[/C][C]2796.24[/C][C]2864.97[/C][C]-68.7269[/C][C]-16.8106[/C][/ROW]
[ROW][C]16[/C][C]3221.13[/C][C]3262.11[/C][C]2904.79[/C][C]357.314[/C][C]-40.9752[/C][/ROW]
[ROW][C]17[/C][C]2752.7[/C][C]2750.46[/C][C]2946.17[/C][C]-195.716[/C][C]2.24252[/C][/ROW]
[ROW][C]18[/C][C]2886.58[/C][C]2848.17[/C][C]2991.16[/C][C]-142.986[/C][C]38.4059[/C][/ROW]
[ROW][C]19[/C][C]2958.05[/C][C]2971.26[/C][C]3036.29[/C][C]-65.0299[/C][C]-13.2139[/C][/ROW]
[ROW][C]20[/C][C]3444.61[/C][C]3457.73[/C][C]3079.54[/C][C]378.194[/C][C]-13.1215[/C][/ROW]
[ROW][C]21[/C][C]2939.78[/C][C]2958.61[/C][C]3124.25[/C][C]-165.644[/C][C]-18.8272[/C][/ROW]
[ROW][C]22[/C][C]3088.73[/C][C]3058.58[/C][C]3170.61[/C][C]-112.023[/C][C]30.1459[/C][/ROW]
[ROW][C]23[/C][C]3161.34[/C][C]3165.84[/C][C]3215.37[/C][C]-49.5327[/C][C]-4.499[/C][/ROW]
[ROW][C]24[/C][C]3672.39[/C][C]3651.43[/C][C]3253.55[/C][C]397.88[/C][C]20.9638[/C][/ROW]
[ROW][C]25[/C][C]3092.36[/C][C]3104.1[/C][C]3292.01[/C][C]-187.913[/C][C]-11.7412[/C][/ROW]
[ROW][C]26[/C][C]3228.05[/C][C]3190.41[/C][C]3336.22[/C][C]-145.816[/C][C]37.6422[/C][/ROW]
[ROW][C]27[/C][C]3311.16[/C][C]3313.26[/C][C]3381.99[/C][C]-68.7269[/C][C]-2.09935[/C][/ROW]
[ROW][C]28[/C][C]3801.93[/C][C]3779.86[/C][C]3422.55[/C][C]357.314[/C][C]22.0652[/C][/ROW]
[ROW][C]29[/C][C]3246.26[/C][C]3267.41[/C][C]3463.13[/C][C]-195.716[/C][C]-21.1525[/C][/ROW]
[ROW][C]30[/C][C]3309.22[/C][C]3366.54[/C][C]3509.52[/C][C]-142.986[/C][C]-57.3158[/C][/ROW]
[ROW][C]31[/C][C]3458.64[/C][C]3493.68[/C][C]3558.71[/C][C]-65.0299[/C][C]-35.0409[/C][/ROW]
[ROW][C]32[/C][C]4005.04[/C][C]3983.73[/C][C]3605.54[/C][C]378.194[/C][C]21.3052[/C][/ROW]
[ROW][C]33[/C][C]3477.65[/C][C]3488.15[/C][C]3653.8[/C][C]-165.644[/C][C]-10.5039[/C][/ROW]
[ROW][C]34[/C][C]3524.42[/C][C]3600.29[/C][C]3712.32[/C][C]-112.023[/C][C]-75.8737[/C][/ROW]
[ROW][C]35[/C][C]3699.5[/C][C]3724.72[/C][C]3774.26[/C][C]-49.5327[/C][C]-25.224[/C][/ROW]
[ROW][C]36[/C][C]4247.68[/C][C]4233.46[/C][C]3835.58[/C][C]397.88[/C][C]14.22[/C][/ROW]
[ROW][C]37[/C][C]3697.6[/C][C]3710.45[/C][C]3898.37[/C][C]-187.913[/C][C]-12.8533[/C][/ROW]
[ROW][C]38[/C][C]3746.72[/C][C]3819.54[/C][C]3965.36[/C][C]-145.816[/C][C]-72.8236[/C][/ROW]
[ROW][C]39[/C][C]3950.67[/C][C]NA[/C][C]NA[/C][C]-68.7269[/C][C]NA[/C][/ROW]
[ROW][C]40[/C][C]4566.86[/C][C]NA[/C][C]NA[/C][C]357.314[/C][C]NA[/C][/ROW]
[ROW][C]41[/C][C]3967.9[/C][C]NA[/C][C]NA[/C][C]-195.716[/C][C]NA[/C][/ROW]
[ROW][C]42[/C][C]4059.35[/C][C]NA[/C][C]NA[/C][C]-142.986[/C][C]NA[/C][/ROW]
[ROW][C]43[/C][C]4215.38[/C][C]NA[/C][C]NA[/C][C]-65.0299[/C][C]NA[/C][/ROW]
[ROW][C]44[/C][C]4856.13[/C][C]NA[/C][C]NA[/C][C]378.194[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297949&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297949&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
12157.07NANA-187.913NA
22267.88NANA-145.816NA
32375.38NANA-68.7269NA
42803.62NANA357.314NA
52367.53NANA-195.716NA
62439.08NANA-142.986NA
72533.762513.872578.9-65.029919.8899
82956.282992.832614.63378.194-36.5486
92484.242483.272648.92-165.6440.966134
102588.492571.132683.15-112.02317.3629
112668.422667.062716.59-49.53271.35808
123085.623149.172751.29397.88-63.5487
132595.932599.72787.61-187.913-3.77039
142686.642679.822825.64-145.8166.81641
152779.432796.242864.97-68.7269-16.8106
163221.133262.112904.79357.314-40.9752
172752.72750.462946.17-195.7162.24252
182886.582848.172991.16-142.98638.4059
192958.052971.263036.29-65.0299-13.2139
203444.613457.733079.54378.194-13.1215
212939.782958.613124.25-165.644-18.8272
223088.733058.583170.61-112.02330.1459
233161.343165.843215.37-49.5327-4.499
243672.393651.433253.55397.8820.9638
253092.363104.13292.01-187.913-11.7412
263228.053190.413336.22-145.81637.6422
273311.163313.263381.99-68.7269-2.09935
283801.933779.863422.55357.31422.0652
293246.263267.413463.13-195.716-21.1525
303309.223366.543509.52-142.986-57.3158
313458.643493.683558.71-65.0299-35.0409
324005.043983.733605.54378.19421.3052
333477.653488.153653.8-165.644-10.5039
343524.423600.293712.32-112.023-75.8737
353699.53724.723774.26-49.5327-25.224
364247.684233.463835.58397.8814.22
373697.63710.453898.37-187.913-12.8533
383746.723819.543965.36-145.816-72.8236
393950.67NANA-68.7269NA
404566.86NANA357.314NA
413967.9NANA-195.716NA
424059.35NANA-142.986NA
434215.38NANA-65.0299NA
444856.13NANA378.194NA



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')