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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 11:38:11 +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/t1481711992bp3bus9oquuimdq.htm/, Retrieved Fri, 03 May 2024 19:08:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299291, Retrieved Fri, 03 May 2024 19:08:19 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Classical Decomposition] [1] [2016-12-14 10:38:11] [b7f10b15eba379294ac5bdad7f2e1205] [Current]
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Dataseries X:
2973.66
3100.21
2997.06
2848.63
2778
2906.69
2842.44
2731.06
2807.5
2961.31
2834.46
2487.13
2372.74
2618.44
2564.18
2379.94
2556.62
2800.82
2718.07
2622.63
4315.77
4582.99
4656.31
4572.72
4793.4
5109.75
5277.5
5332.15
5470.3
5615.8
5616.25
5824.7
5811.4
5974.85
6037.55
5722.8
6080.4




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=299291&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=299291&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299291&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
12973.66NANA20.7183NA
23100.213022.073042.78-20.718378.1433
32997.063006.462985.7420.7183-9.39826
42848.632847.362868.08-20.71831.26826
527782848.552827.8320.7183-70.5483
62906.692837.742858.46-20.718368.9533
72842.442851.382830.6620.7183-8.93576
82731.062757.32778.02-20.7183-26.2367
92807.52847.562826.8420.7183-40.0608
102961.312870.432891.14-20.718390.8833
112834.462800.062779.3420.718334.4017
122487.132524.652545.36-20.7183-37.5167
132372.742483.482462.7620.7183-110.741
142618.442522.732543.45-20.718395.7083
152564.182552.42531.6820.718311.7767
162379.942449.452470.17-20.7183-69.5117
172556.622594.222573.520.7183-37.5983
182800.822698.362719.08-20.7183102.456
192718.072735.622714.920.7183-17.5458
202622.633049.063069.78-20.7183-426.427
214315.773980.013959.2920.7183335.762
224582.994513.84534.52-20.718369.1933
234656.314637.84617.0820.718318.5092
244572.724628.074648.79-20.7183-55.3492
254793.44838.044817.3220.7183-44.6358
265109.755051.885072.6-20.718357.8683
275277.55269.945249.2220.71837.55674
285332.155332.315353.02-20.7183-0.15674
295470.35492.865472.1420.7183-22.5558
305615.85558.825579.54-20.718356.9808
315616.255688.975668.2520.7183-72.7183
325824.75748.545769.26-20.718376.1558
335811.45876.315855.5920.7183-64.9058
345974.855928.945949.66-20.718345.9058
356037.555963.915943.1920.718373.6442
365722.85870.175890.89-20.7183-147.369
376080.4NANA20.7183NA

\begin{tabular}{lllllllll}
\hline
Classical Decomposition by Moving Averages \tabularnewline
t & Observations & Fit & Trend & Seasonal & Random \tabularnewline
1 & 2973.66 & NA & NA & 20.7183 & NA \tabularnewline
2 & 3100.21 & 3022.07 & 3042.78 & -20.7183 & 78.1433 \tabularnewline
3 & 2997.06 & 3006.46 & 2985.74 & 20.7183 & -9.39826 \tabularnewline
4 & 2848.63 & 2847.36 & 2868.08 & -20.7183 & 1.26826 \tabularnewline
5 & 2778 & 2848.55 & 2827.83 & 20.7183 & -70.5483 \tabularnewline
6 & 2906.69 & 2837.74 & 2858.46 & -20.7183 & 68.9533 \tabularnewline
7 & 2842.44 & 2851.38 & 2830.66 & 20.7183 & -8.93576 \tabularnewline
8 & 2731.06 & 2757.3 & 2778.02 & -20.7183 & -26.2367 \tabularnewline
9 & 2807.5 & 2847.56 & 2826.84 & 20.7183 & -40.0608 \tabularnewline
10 & 2961.31 & 2870.43 & 2891.14 & -20.7183 & 90.8833 \tabularnewline
11 & 2834.46 & 2800.06 & 2779.34 & 20.7183 & 34.4017 \tabularnewline
12 & 2487.13 & 2524.65 & 2545.36 & -20.7183 & -37.5167 \tabularnewline
13 & 2372.74 & 2483.48 & 2462.76 & 20.7183 & -110.741 \tabularnewline
14 & 2618.44 & 2522.73 & 2543.45 & -20.7183 & 95.7083 \tabularnewline
15 & 2564.18 & 2552.4 & 2531.68 & 20.7183 & 11.7767 \tabularnewline
16 & 2379.94 & 2449.45 & 2470.17 & -20.7183 & -69.5117 \tabularnewline
17 & 2556.62 & 2594.22 & 2573.5 & 20.7183 & -37.5983 \tabularnewline
18 & 2800.82 & 2698.36 & 2719.08 & -20.7183 & 102.456 \tabularnewline
19 & 2718.07 & 2735.62 & 2714.9 & 20.7183 & -17.5458 \tabularnewline
20 & 2622.63 & 3049.06 & 3069.78 & -20.7183 & -426.427 \tabularnewline
21 & 4315.77 & 3980.01 & 3959.29 & 20.7183 & 335.762 \tabularnewline
22 & 4582.99 & 4513.8 & 4534.52 & -20.7183 & 69.1933 \tabularnewline
23 & 4656.31 & 4637.8 & 4617.08 & 20.7183 & 18.5092 \tabularnewline
24 & 4572.72 & 4628.07 & 4648.79 & -20.7183 & -55.3492 \tabularnewline
25 & 4793.4 & 4838.04 & 4817.32 & 20.7183 & -44.6358 \tabularnewline
26 & 5109.75 & 5051.88 & 5072.6 & -20.7183 & 57.8683 \tabularnewline
27 & 5277.5 & 5269.94 & 5249.22 & 20.7183 & 7.55674 \tabularnewline
28 & 5332.15 & 5332.31 & 5353.02 & -20.7183 & -0.15674 \tabularnewline
29 & 5470.3 & 5492.86 & 5472.14 & 20.7183 & -22.5558 \tabularnewline
30 & 5615.8 & 5558.82 & 5579.54 & -20.7183 & 56.9808 \tabularnewline
31 & 5616.25 & 5688.97 & 5668.25 & 20.7183 & -72.7183 \tabularnewline
32 & 5824.7 & 5748.54 & 5769.26 & -20.7183 & 76.1558 \tabularnewline
33 & 5811.4 & 5876.31 & 5855.59 & 20.7183 & -64.9058 \tabularnewline
34 & 5974.85 & 5928.94 & 5949.66 & -20.7183 & 45.9058 \tabularnewline
35 & 6037.55 & 5963.91 & 5943.19 & 20.7183 & 73.6442 \tabularnewline
36 & 5722.8 & 5870.17 & 5890.89 & -20.7183 & -147.369 \tabularnewline
37 & 6080.4 & NA & NA & 20.7183 & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299291&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]2973.66[/C][C]NA[/C][C]NA[/C][C]20.7183[/C][C]NA[/C][/ROW]
[ROW][C]2[/C][C]3100.21[/C][C]3022.07[/C][C]3042.78[/C][C]-20.7183[/C][C]78.1433[/C][/ROW]
[ROW][C]3[/C][C]2997.06[/C][C]3006.46[/C][C]2985.74[/C][C]20.7183[/C][C]-9.39826[/C][/ROW]
[ROW][C]4[/C][C]2848.63[/C][C]2847.36[/C][C]2868.08[/C][C]-20.7183[/C][C]1.26826[/C][/ROW]
[ROW][C]5[/C][C]2778[/C][C]2848.55[/C][C]2827.83[/C][C]20.7183[/C][C]-70.5483[/C][/ROW]
[ROW][C]6[/C][C]2906.69[/C][C]2837.74[/C][C]2858.46[/C][C]-20.7183[/C][C]68.9533[/C][/ROW]
[ROW][C]7[/C][C]2842.44[/C][C]2851.38[/C][C]2830.66[/C][C]20.7183[/C][C]-8.93576[/C][/ROW]
[ROW][C]8[/C][C]2731.06[/C][C]2757.3[/C][C]2778.02[/C][C]-20.7183[/C][C]-26.2367[/C][/ROW]
[ROW][C]9[/C][C]2807.5[/C][C]2847.56[/C][C]2826.84[/C][C]20.7183[/C][C]-40.0608[/C][/ROW]
[ROW][C]10[/C][C]2961.31[/C][C]2870.43[/C][C]2891.14[/C][C]-20.7183[/C][C]90.8833[/C][/ROW]
[ROW][C]11[/C][C]2834.46[/C][C]2800.06[/C][C]2779.34[/C][C]20.7183[/C][C]34.4017[/C][/ROW]
[ROW][C]12[/C][C]2487.13[/C][C]2524.65[/C][C]2545.36[/C][C]-20.7183[/C][C]-37.5167[/C][/ROW]
[ROW][C]13[/C][C]2372.74[/C][C]2483.48[/C][C]2462.76[/C][C]20.7183[/C][C]-110.741[/C][/ROW]
[ROW][C]14[/C][C]2618.44[/C][C]2522.73[/C][C]2543.45[/C][C]-20.7183[/C][C]95.7083[/C][/ROW]
[ROW][C]15[/C][C]2564.18[/C][C]2552.4[/C][C]2531.68[/C][C]20.7183[/C][C]11.7767[/C][/ROW]
[ROW][C]16[/C][C]2379.94[/C][C]2449.45[/C][C]2470.17[/C][C]-20.7183[/C][C]-69.5117[/C][/ROW]
[ROW][C]17[/C][C]2556.62[/C][C]2594.22[/C][C]2573.5[/C][C]20.7183[/C][C]-37.5983[/C][/ROW]
[ROW][C]18[/C][C]2800.82[/C][C]2698.36[/C][C]2719.08[/C][C]-20.7183[/C][C]102.456[/C][/ROW]
[ROW][C]19[/C][C]2718.07[/C][C]2735.62[/C][C]2714.9[/C][C]20.7183[/C][C]-17.5458[/C][/ROW]
[ROW][C]20[/C][C]2622.63[/C][C]3049.06[/C][C]3069.78[/C][C]-20.7183[/C][C]-426.427[/C][/ROW]
[ROW][C]21[/C][C]4315.77[/C][C]3980.01[/C][C]3959.29[/C][C]20.7183[/C][C]335.762[/C][/ROW]
[ROW][C]22[/C][C]4582.99[/C][C]4513.8[/C][C]4534.52[/C][C]-20.7183[/C][C]69.1933[/C][/ROW]
[ROW][C]23[/C][C]4656.31[/C][C]4637.8[/C][C]4617.08[/C][C]20.7183[/C][C]18.5092[/C][/ROW]
[ROW][C]24[/C][C]4572.72[/C][C]4628.07[/C][C]4648.79[/C][C]-20.7183[/C][C]-55.3492[/C][/ROW]
[ROW][C]25[/C][C]4793.4[/C][C]4838.04[/C][C]4817.32[/C][C]20.7183[/C][C]-44.6358[/C][/ROW]
[ROW][C]26[/C][C]5109.75[/C][C]5051.88[/C][C]5072.6[/C][C]-20.7183[/C][C]57.8683[/C][/ROW]
[ROW][C]27[/C][C]5277.5[/C][C]5269.94[/C][C]5249.22[/C][C]20.7183[/C][C]7.55674[/C][/ROW]
[ROW][C]28[/C][C]5332.15[/C][C]5332.31[/C][C]5353.02[/C][C]-20.7183[/C][C]-0.15674[/C][/ROW]
[ROW][C]29[/C][C]5470.3[/C][C]5492.86[/C][C]5472.14[/C][C]20.7183[/C][C]-22.5558[/C][/ROW]
[ROW][C]30[/C][C]5615.8[/C][C]5558.82[/C][C]5579.54[/C][C]-20.7183[/C][C]56.9808[/C][/ROW]
[ROW][C]31[/C][C]5616.25[/C][C]5688.97[/C][C]5668.25[/C][C]20.7183[/C][C]-72.7183[/C][/ROW]
[ROW][C]32[/C][C]5824.7[/C][C]5748.54[/C][C]5769.26[/C][C]-20.7183[/C][C]76.1558[/C][/ROW]
[ROW][C]33[/C][C]5811.4[/C][C]5876.31[/C][C]5855.59[/C][C]20.7183[/C][C]-64.9058[/C][/ROW]
[ROW][C]34[/C][C]5974.85[/C][C]5928.94[/C][C]5949.66[/C][C]-20.7183[/C][C]45.9058[/C][/ROW]
[ROW][C]35[/C][C]6037.55[/C][C]5963.91[/C][C]5943.19[/C][C]20.7183[/C][C]73.6442[/C][/ROW]
[ROW][C]36[/C][C]5722.8[/C][C]5870.17[/C][C]5890.89[/C][C]-20.7183[/C][C]-147.369[/C][/ROW]
[ROW][C]37[/C][C]6080.4[/C][C]NA[/C][C]NA[/C][C]20.7183[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299291&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299291&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
12973.66NANA20.7183NA
23100.213022.073042.78-20.718378.1433
32997.063006.462985.7420.7183-9.39826
42848.632847.362868.08-20.71831.26826
527782848.552827.8320.7183-70.5483
62906.692837.742858.46-20.718368.9533
72842.442851.382830.6620.7183-8.93576
82731.062757.32778.02-20.7183-26.2367
92807.52847.562826.8420.7183-40.0608
102961.312870.432891.14-20.718390.8833
112834.462800.062779.3420.718334.4017
122487.132524.652545.36-20.7183-37.5167
132372.742483.482462.7620.7183-110.741
142618.442522.732543.45-20.718395.7083
152564.182552.42531.6820.718311.7767
162379.942449.452470.17-20.7183-69.5117
172556.622594.222573.520.7183-37.5983
182800.822698.362719.08-20.7183102.456
192718.072735.622714.920.7183-17.5458
202622.633049.063069.78-20.7183-426.427
214315.773980.013959.2920.7183335.762
224582.994513.84534.52-20.718369.1933
234656.314637.84617.0820.718318.5092
244572.724628.074648.79-20.7183-55.3492
254793.44838.044817.3220.7183-44.6358
265109.755051.885072.6-20.718357.8683
275277.55269.945249.2220.71837.55674
285332.155332.315353.02-20.7183-0.15674
295470.35492.865472.1420.7183-22.5558
305615.85558.825579.54-20.718356.9808
315616.255688.975668.2520.7183-72.7183
325824.75748.545769.26-20.718376.1558
335811.45876.315855.5920.7183-64.9058
345974.855928.945949.66-20.718345.9058
356037.555963.915943.1920.718373.6442
365722.85870.175890.89-20.7183-147.369
376080.4NANA20.7183NA



Parameters (Session):
par1 = additive ; par2 = 2 ;
Parameters (R input):
par1 = additive ; par2 = 2 ;
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')