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Author's title

Author*Unverified author*
R Software Modulerwasp_decompose.wasp
Title produced by softwareClassical Decomposition
Date of computationMon, 01 May 2017 11:57:26 +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/2017/May/01/t149363633705dy8a8vhpbjq3l.htm/, Retrieved Wed, 22 Apr 2026 18:47:51 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 22 Apr 2026 18:47:51 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
95.2
95.34
95.32
96.04
99.65
100.85
108.18
108.18
103.14
99.71
99.39
98.99
98.83
99.52
99.5
99.5
99.39
101.79
106.03
105.41
104.32
101.17
99.79
100.08
100.27
101.63
101.74
103.73
103.29
105.71
107.42
107.57
105.13
103.61
102.35
102.14
104.32
104.69
106.02
104.78
106.36
109.27
113.46
113.46
110.61
104.37
103.82
104.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Classical Decomposition by Moving Averages
tObservationsFitTrendSeasonalRandom
195.2NANA0.978558NA
295.34NANA0.98504NA
395.32NANA0.987845NA
496.04NANA0.988803NA
599.65NANA0.990737NA
6100.85NANA1.01419NA
7108.18105.371100.151.052121.02666
8108.18105.29100.4761.047921.02744
9103.14102.546100.8241.017071.0058
1099.7199.9267101.1420.9879790.997832
1199.3998.8828101.2760.9763711.00513
1298.9998.605101.3040.9733561.0039
1398.8399.0827101.2540.9785580.99745
1499.5299.5371101.0490.985040.999828
1599.599.7551100.9820.9878450.997443
1699.599.9605101.0920.9888030.995393
1799.39100.233101.170.9907370.991591
18101.79102.669101.2321.014190.991438
19106.03106.62101.3381.052120.99447
20105.41106.348101.4851.047920.991176
21104.32103.402101.6671.017071.00887
22101.17100.711101.9360.9879791.00456
2399.7999.8583102.2750.9763710.999316
24100.0899.8671102.6010.9733561.00213
25100.27100.617102.8220.9785580.996547
26101.63101.43102.970.985041.00198
27101.74101.841103.0940.9878450.999012
28103.73102.073103.2290.9888031.01623
29103.29102.479103.4370.9907371.00791
30105.71105.101103.631.014191.00579
31107.42109.299103.8851.052120.982805
32107.57109.173104.1811.047920.985317
33105.13106.271104.4871.017070.989267
34103.61103.45104.7090.9879791.00155
35102.35102.402104.880.9763710.999491
36102.14102.355105.1570.9733560.997901
37104.32103.293105.5570.9785581.00994
38104.69104.467106.0540.985041.00213
39106.02105.233106.5280.9878451.00748
40104.78105.592106.7870.9888030.992312
41106.36105.89106.880.9907371.00443
42109.27108.542107.0231.014191.0067
43113.46NANA1.05212NA
44113.46NANA1.04792NA
45110.61NANA1.01707NA
46104.37NANA0.987979NA
47103.82NANA0.976371NA
48104.1NANA0.973356NA

\begin{tabular}{lllllllll}
\hline
Classical Decomposition by Moving Averages \tabularnewline
t & Observations & Fit & Trend & Seasonal & Random \tabularnewline
1 & 95.2 & NA & NA & 0.978558 & NA \tabularnewline
2 & 95.34 & NA & NA & 0.98504 & NA \tabularnewline
3 & 95.32 & NA & NA & 0.987845 & NA \tabularnewline
4 & 96.04 & NA & NA & 0.988803 & NA \tabularnewline
5 & 99.65 & NA & NA & 0.990737 & NA \tabularnewline
6 & 100.85 & NA & NA & 1.01419 & NA \tabularnewline
7 & 108.18 & 105.371 & 100.15 & 1.05212 & 1.02666 \tabularnewline
8 & 108.18 & 105.29 & 100.476 & 1.04792 & 1.02744 \tabularnewline
9 & 103.14 & 102.546 & 100.824 & 1.01707 & 1.0058 \tabularnewline
10 & 99.71 & 99.9267 & 101.142 & 0.987979 & 0.997832 \tabularnewline
11 & 99.39 & 98.8828 & 101.276 & 0.976371 & 1.00513 \tabularnewline
12 & 98.99 & 98.605 & 101.304 & 0.973356 & 1.0039 \tabularnewline
13 & 98.83 & 99.0827 & 101.254 & 0.978558 & 0.99745 \tabularnewline
14 & 99.52 & 99.5371 & 101.049 & 0.98504 & 0.999828 \tabularnewline
15 & 99.5 & 99.7551 & 100.982 & 0.987845 & 0.997443 \tabularnewline
16 & 99.5 & 99.9605 & 101.092 & 0.988803 & 0.995393 \tabularnewline
17 & 99.39 & 100.233 & 101.17 & 0.990737 & 0.991591 \tabularnewline
18 & 101.79 & 102.669 & 101.232 & 1.01419 & 0.991438 \tabularnewline
19 & 106.03 & 106.62 & 101.338 & 1.05212 & 0.99447 \tabularnewline
20 & 105.41 & 106.348 & 101.485 & 1.04792 & 0.991176 \tabularnewline
21 & 104.32 & 103.402 & 101.667 & 1.01707 & 1.00887 \tabularnewline
22 & 101.17 & 100.711 & 101.936 & 0.987979 & 1.00456 \tabularnewline
23 & 99.79 & 99.8583 & 102.275 & 0.976371 & 0.999316 \tabularnewline
24 & 100.08 & 99.8671 & 102.601 & 0.973356 & 1.00213 \tabularnewline
25 & 100.27 & 100.617 & 102.822 & 0.978558 & 0.996547 \tabularnewline
26 & 101.63 & 101.43 & 102.97 & 0.98504 & 1.00198 \tabularnewline
27 & 101.74 & 101.841 & 103.094 & 0.987845 & 0.999012 \tabularnewline
28 & 103.73 & 102.073 & 103.229 & 0.988803 & 1.01623 \tabularnewline
29 & 103.29 & 102.479 & 103.437 & 0.990737 & 1.00791 \tabularnewline
30 & 105.71 & 105.101 & 103.63 & 1.01419 & 1.00579 \tabularnewline
31 & 107.42 & 109.299 & 103.885 & 1.05212 & 0.982805 \tabularnewline
32 & 107.57 & 109.173 & 104.181 & 1.04792 & 0.985317 \tabularnewline
33 & 105.13 & 106.271 & 104.487 & 1.01707 & 0.989267 \tabularnewline
34 & 103.61 & 103.45 & 104.709 & 0.987979 & 1.00155 \tabularnewline
35 & 102.35 & 102.402 & 104.88 & 0.976371 & 0.999491 \tabularnewline
36 & 102.14 & 102.355 & 105.157 & 0.973356 & 0.997901 \tabularnewline
37 & 104.32 & 103.293 & 105.557 & 0.978558 & 1.00994 \tabularnewline
38 & 104.69 & 104.467 & 106.054 & 0.98504 & 1.00213 \tabularnewline
39 & 106.02 & 105.233 & 106.528 & 0.987845 & 1.00748 \tabularnewline
40 & 104.78 & 105.592 & 106.787 & 0.988803 & 0.992312 \tabularnewline
41 & 106.36 & 105.89 & 106.88 & 0.990737 & 1.00443 \tabularnewline
42 & 109.27 & 108.542 & 107.023 & 1.01419 & 1.0067 \tabularnewline
43 & 113.46 & NA & NA & 1.05212 & NA \tabularnewline
44 & 113.46 & NA & NA & 1.04792 & NA \tabularnewline
45 & 110.61 & NA & NA & 1.01707 & NA \tabularnewline
46 & 104.37 & NA & NA & 0.987979 & NA \tabularnewline
47 & 103.82 & NA & NA & 0.976371 & NA \tabularnewline
48 & 104.1 & NA & NA & 0.973356 & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]95.2[/C][C]NA[/C][C]NA[/C][C]0.978558[/C][C]NA[/C][/ROW]
[ROW][C]2[/C][C]95.34[/C][C]NA[/C][C]NA[/C][C]0.98504[/C][C]NA[/C][/ROW]
[ROW][C]3[/C][C]95.32[/C][C]NA[/C][C]NA[/C][C]0.987845[/C][C]NA[/C][/ROW]
[ROW][C]4[/C][C]96.04[/C][C]NA[/C][C]NA[/C][C]0.988803[/C][C]NA[/C][/ROW]
[ROW][C]5[/C][C]99.65[/C][C]NA[/C][C]NA[/C][C]0.990737[/C][C]NA[/C][/ROW]
[ROW][C]6[/C][C]100.85[/C][C]NA[/C][C]NA[/C][C]1.01419[/C][C]NA[/C][/ROW]
[ROW][C]7[/C][C]108.18[/C][C]105.371[/C][C]100.15[/C][C]1.05212[/C][C]1.02666[/C][/ROW]
[ROW][C]8[/C][C]108.18[/C][C]105.29[/C][C]100.476[/C][C]1.04792[/C][C]1.02744[/C][/ROW]
[ROW][C]9[/C][C]103.14[/C][C]102.546[/C][C]100.824[/C][C]1.01707[/C][C]1.0058[/C][/ROW]
[ROW][C]10[/C][C]99.71[/C][C]99.9267[/C][C]101.142[/C][C]0.987979[/C][C]0.997832[/C][/ROW]
[ROW][C]11[/C][C]99.39[/C][C]98.8828[/C][C]101.276[/C][C]0.976371[/C][C]1.00513[/C][/ROW]
[ROW][C]12[/C][C]98.99[/C][C]98.605[/C][C]101.304[/C][C]0.973356[/C][C]1.0039[/C][/ROW]
[ROW][C]13[/C][C]98.83[/C][C]99.0827[/C][C]101.254[/C][C]0.978558[/C][C]0.99745[/C][/ROW]
[ROW][C]14[/C][C]99.52[/C][C]99.5371[/C][C]101.049[/C][C]0.98504[/C][C]0.999828[/C][/ROW]
[ROW][C]15[/C][C]99.5[/C][C]99.7551[/C][C]100.982[/C][C]0.987845[/C][C]0.997443[/C][/ROW]
[ROW][C]16[/C][C]99.5[/C][C]99.9605[/C][C]101.092[/C][C]0.988803[/C][C]0.995393[/C][/ROW]
[ROW][C]17[/C][C]99.39[/C][C]100.233[/C][C]101.17[/C][C]0.990737[/C][C]0.991591[/C][/ROW]
[ROW][C]18[/C][C]101.79[/C][C]102.669[/C][C]101.232[/C][C]1.01419[/C][C]0.991438[/C][/ROW]
[ROW][C]19[/C][C]106.03[/C][C]106.62[/C][C]101.338[/C][C]1.05212[/C][C]0.99447[/C][/ROW]
[ROW][C]20[/C][C]105.41[/C][C]106.348[/C][C]101.485[/C][C]1.04792[/C][C]0.991176[/C][/ROW]
[ROW][C]21[/C][C]104.32[/C][C]103.402[/C][C]101.667[/C][C]1.01707[/C][C]1.00887[/C][/ROW]
[ROW][C]22[/C][C]101.17[/C][C]100.711[/C][C]101.936[/C][C]0.987979[/C][C]1.00456[/C][/ROW]
[ROW][C]23[/C][C]99.79[/C][C]99.8583[/C][C]102.275[/C][C]0.976371[/C][C]0.999316[/C][/ROW]
[ROW][C]24[/C][C]100.08[/C][C]99.8671[/C][C]102.601[/C][C]0.973356[/C][C]1.00213[/C][/ROW]
[ROW][C]25[/C][C]100.27[/C][C]100.617[/C][C]102.822[/C][C]0.978558[/C][C]0.996547[/C][/ROW]
[ROW][C]26[/C][C]101.63[/C][C]101.43[/C][C]102.97[/C][C]0.98504[/C][C]1.00198[/C][/ROW]
[ROW][C]27[/C][C]101.74[/C][C]101.841[/C][C]103.094[/C][C]0.987845[/C][C]0.999012[/C][/ROW]
[ROW][C]28[/C][C]103.73[/C][C]102.073[/C][C]103.229[/C][C]0.988803[/C][C]1.01623[/C][/ROW]
[ROW][C]29[/C][C]103.29[/C][C]102.479[/C][C]103.437[/C][C]0.990737[/C][C]1.00791[/C][/ROW]
[ROW][C]30[/C][C]105.71[/C][C]105.101[/C][C]103.63[/C][C]1.01419[/C][C]1.00579[/C][/ROW]
[ROW][C]31[/C][C]107.42[/C][C]109.299[/C][C]103.885[/C][C]1.05212[/C][C]0.982805[/C][/ROW]
[ROW][C]32[/C][C]107.57[/C][C]109.173[/C][C]104.181[/C][C]1.04792[/C][C]0.985317[/C][/ROW]
[ROW][C]33[/C][C]105.13[/C][C]106.271[/C][C]104.487[/C][C]1.01707[/C][C]0.989267[/C][/ROW]
[ROW][C]34[/C][C]103.61[/C][C]103.45[/C][C]104.709[/C][C]0.987979[/C][C]1.00155[/C][/ROW]
[ROW][C]35[/C][C]102.35[/C][C]102.402[/C][C]104.88[/C][C]0.976371[/C][C]0.999491[/C][/ROW]
[ROW][C]36[/C][C]102.14[/C][C]102.355[/C][C]105.157[/C][C]0.973356[/C][C]0.997901[/C][/ROW]
[ROW][C]37[/C][C]104.32[/C][C]103.293[/C][C]105.557[/C][C]0.978558[/C][C]1.00994[/C][/ROW]
[ROW][C]38[/C][C]104.69[/C][C]104.467[/C][C]106.054[/C][C]0.98504[/C][C]1.00213[/C][/ROW]
[ROW][C]39[/C][C]106.02[/C][C]105.233[/C][C]106.528[/C][C]0.987845[/C][C]1.00748[/C][/ROW]
[ROW][C]40[/C][C]104.78[/C][C]105.592[/C][C]106.787[/C][C]0.988803[/C][C]0.992312[/C][/ROW]
[ROW][C]41[/C][C]106.36[/C][C]105.89[/C][C]106.88[/C][C]0.990737[/C][C]1.00443[/C][/ROW]
[ROW][C]42[/C][C]109.27[/C][C]108.542[/C][C]107.023[/C][C]1.01419[/C][C]1.0067[/C][/ROW]
[ROW][C]43[/C][C]113.46[/C][C]NA[/C][C]NA[/C][C]1.05212[/C][C]NA[/C][/ROW]
[ROW][C]44[/C][C]113.46[/C][C]NA[/C][C]NA[/C][C]1.04792[/C][C]NA[/C][/ROW]
[ROW][C]45[/C][C]110.61[/C][C]NA[/C][C]NA[/C][C]1.01707[/C][C]NA[/C][/ROW]
[ROW][C]46[/C][C]104.37[/C][C]NA[/C][C]NA[/C][C]0.987979[/C][C]NA[/C][/ROW]
[ROW][C]47[/C][C]103.82[/C][C]NA[/C][C]NA[/C][C]0.976371[/C][C]NA[/C][/ROW]
[ROW][C]48[/C][C]104.1[/C][C]NA[/C][C]NA[/C][C]0.973356[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
195.2NANA0.978558NA
295.34NANA0.98504NA
395.32NANA0.987845NA
496.04NANA0.988803NA
599.65NANA0.990737NA
6100.85NANA1.01419NA
7108.18105.371100.151.052121.02666
8108.18105.29100.4761.047921.02744
9103.14102.546100.8241.017071.0058
1099.7199.9267101.1420.9879790.997832
1199.3998.8828101.2760.9763711.00513
1298.9998.605101.3040.9733561.0039
1398.8399.0827101.2540.9785580.99745
1499.5299.5371101.0490.985040.999828
1599.599.7551100.9820.9878450.997443
1699.599.9605101.0920.9888030.995393
1799.39100.233101.170.9907370.991591
18101.79102.669101.2321.014190.991438
19106.03106.62101.3381.052120.99447
20105.41106.348101.4851.047920.991176
21104.32103.402101.6671.017071.00887
22101.17100.711101.9360.9879791.00456
2399.7999.8583102.2750.9763710.999316
24100.0899.8671102.6010.9733561.00213
25100.27100.617102.8220.9785580.996547
26101.63101.43102.970.985041.00198
27101.74101.841103.0940.9878450.999012
28103.73102.073103.2290.9888031.01623
29103.29102.479103.4370.9907371.00791
30105.71105.101103.631.014191.00579
31107.42109.299103.8851.052120.982805
32107.57109.173104.1811.047920.985317
33105.13106.271104.4871.017070.989267
34103.61103.45104.7090.9879791.00155
35102.35102.402104.880.9763710.999491
36102.14102.355105.1570.9733560.997901
37104.32103.293105.5570.9785581.00994
38104.69104.467106.0540.985041.00213
39106.02105.233106.5280.9878451.00748
40104.78105.592106.7870.9888030.992312
41106.36105.89106.880.9907371.00443
42109.27108.542107.0231.014191.0067
43113.46NANA1.05212NA
44113.46NANA1.04792NA
45110.61NANA1.01707NA
46104.37NANA0.987979NA
47103.82NANA0.976371NA
48104.1NANA0.973356NA



Parameters (Session):
par1 = multiplicative ; par2 = 12 ;
Parameters (R input):
par1 = multiplicative ; par2 = 12 ;
R code (references can be found in the software module):
par2 <- '12'
par1 <- 'multiplicative'
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')