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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 computationSat, 17 Dec 2016 12:29:18 +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/17/t1481974190imr2nhwni3g2rll.htm/, Retrieved Thu, 02 May 2024 00:48:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300710, Retrieved Thu, 02 May 2024 00:48:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact39
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Classical Decomposition] [] [2016-12-17 11:29:18] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Dataseries X:
9290
6160
8320
8310
6750
8710
6300
5710
5740
6710
7310
7240
8650
8330
7810
8260
6680
5580
6340
4490
5000
7030
6100
9740
7940
7740
7820
7820
5380
7070
6970
4080
4930
4820
6220
6360
7630
5130
6960
5350
6290
4630
5130
3620
3980
3120
4310
4250
5730
3630
5680




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=300710&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=300710&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300710&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
19290NANA1492.01NA
26160NANA530.616NA
38320NANA1047.42NA
48310NANA735.061NA
56750NANA-200.078NA
68710NANA-473.55NA
763006951.387185.83-234.453-651.38
857105368.577249.58-1881.02341.432
957405929.097318.75-1389.66-189.089
1067106717.287295.42-578.134-7.28299
1173107116.457290.42-173.967193.55
1272408282.847157.081125.76-1042.84
1386508520.347028.331492.01129.661
1483307509.786979.17530.616820.217
1578107944.926897.51047.42-134.922
1682607615.066880735.061644.939
1766806642.846842.92-200.07837.1615
1855806423.126896.67-473.55-843.116
1963406736.86971.25-234.453-396.797
2044905036.076917.08-1881.02-546.068
2150005503.266892.92-1389.66-503.255
2270306296.876875-578.134733.134
2361006628.536802.5-173.967-528.533
2497407936.176810.421125.761803.83
2579408390.766898.751492.01-450.755
2677407438.536907.92530.616301.467
2778207935.346887.921047.42-115.339
2878207527.986792.92735.061292.023
2953806505.766705.83-200.078-1125.76
3070706096.456570-473.55973.55
3169706181.86416.25-234.453788.203
3240804413.576294.58-1881.02-333.568
3349304760.346150-1389.66169.661
3448205433.126011.25-578.134-613.116
3562205772.285946.25-173.967447.717
3663607008.265882.51125.76-648.255
3776307196.175704.171492.01433.828
3851306138.955608.33530.616-1008.95
3969606597.015549.581047.42362.995
4053506174.235439.17735.061-824.227
4162905088.675288.75-200.0781201.33
4246304647.75121.25-473.55-17.6997
4351304719.714954.17-234.453410.286
4436202931.484812.5-1881.02688.516
4539803307.014696.67-1389.66672.995
463120NANA-578.134NA
474310NANA-173.967NA
484250NANA1125.76NA
495730NANA1492.01NA
503630NANA530.616NA
515680NANA1047.42NA

\begin{tabular}{lllllllll}
\hline
Classical Decomposition by Moving Averages \tabularnewline
t & Observations & Fit & Trend & Seasonal & Random \tabularnewline
1 & 9290 & NA & NA & 1492.01 & NA \tabularnewline
2 & 6160 & NA & NA & 530.616 & NA \tabularnewline
3 & 8320 & NA & NA & 1047.42 & NA \tabularnewline
4 & 8310 & NA & NA & 735.061 & NA \tabularnewline
5 & 6750 & NA & NA & -200.078 & NA \tabularnewline
6 & 8710 & NA & NA & -473.55 & NA \tabularnewline
7 & 6300 & 6951.38 & 7185.83 & -234.453 & -651.38 \tabularnewline
8 & 5710 & 5368.57 & 7249.58 & -1881.02 & 341.432 \tabularnewline
9 & 5740 & 5929.09 & 7318.75 & -1389.66 & -189.089 \tabularnewline
10 & 6710 & 6717.28 & 7295.42 & -578.134 & -7.28299 \tabularnewline
11 & 7310 & 7116.45 & 7290.42 & -173.967 & 193.55 \tabularnewline
12 & 7240 & 8282.84 & 7157.08 & 1125.76 & -1042.84 \tabularnewline
13 & 8650 & 8520.34 & 7028.33 & 1492.01 & 129.661 \tabularnewline
14 & 8330 & 7509.78 & 6979.17 & 530.616 & 820.217 \tabularnewline
15 & 7810 & 7944.92 & 6897.5 & 1047.42 & -134.922 \tabularnewline
16 & 8260 & 7615.06 & 6880 & 735.061 & 644.939 \tabularnewline
17 & 6680 & 6642.84 & 6842.92 & -200.078 & 37.1615 \tabularnewline
18 & 5580 & 6423.12 & 6896.67 & -473.55 & -843.116 \tabularnewline
19 & 6340 & 6736.8 & 6971.25 & -234.453 & -396.797 \tabularnewline
20 & 4490 & 5036.07 & 6917.08 & -1881.02 & -546.068 \tabularnewline
21 & 5000 & 5503.26 & 6892.92 & -1389.66 & -503.255 \tabularnewline
22 & 7030 & 6296.87 & 6875 & -578.134 & 733.134 \tabularnewline
23 & 6100 & 6628.53 & 6802.5 & -173.967 & -528.533 \tabularnewline
24 & 9740 & 7936.17 & 6810.42 & 1125.76 & 1803.83 \tabularnewline
25 & 7940 & 8390.76 & 6898.75 & 1492.01 & -450.755 \tabularnewline
26 & 7740 & 7438.53 & 6907.92 & 530.616 & 301.467 \tabularnewline
27 & 7820 & 7935.34 & 6887.92 & 1047.42 & -115.339 \tabularnewline
28 & 7820 & 7527.98 & 6792.92 & 735.061 & 292.023 \tabularnewline
29 & 5380 & 6505.76 & 6705.83 & -200.078 & -1125.76 \tabularnewline
30 & 7070 & 6096.45 & 6570 & -473.55 & 973.55 \tabularnewline
31 & 6970 & 6181.8 & 6416.25 & -234.453 & 788.203 \tabularnewline
32 & 4080 & 4413.57 & 6294.58 & -1881.02 & -333.568 \tabularnewline
33 & 4930 & 4760.34 & 6150 & -1389.66 & 169.661 \tabularnewline
34 & 4820 & 5433.12 & 6011.25 & -578.134 & -613.116 \tabularnewline
35 & 6220 & 5772.28 & 5946.25 & -173.967 & 447.717 \tabularnewline
36 & 6360 & 7008.26 & 5882.5 & 1125.76 & -648.255 \tabularnewline
37 & 7630 & 7196.17 & 5704.17 & 1492.01 & 433.828 \tabularnewline
38 & 5130 & 6138.95 & 5608.33 & 530.616 & -1008.95 \tabularnewline
39 & 6960 & 6597.01 & 5549.58 & 1047.42 & 362.995 \tabularnewline
40 & 5350 & 6174.23 & 5439.17 & 735.061 & -824.227 \tabularnewline
41 & 6290 & 5088.67 & 5288.75 & -200.078 & 1201.33 \tabularnewline
42 & 4630 & 4647.7 & 5121.25 & -473.55 & -17.6997 \tabularnewline
43 & 5130 & 4719.71 & 4954.17 & -234.453 & 410.286 \tabularnewline
44 & 3620 & 2931.48 & 4812.5 & -1881.02 & 688.516 \tabularnewline
45 & 3980 & 3307.01 & 4696.67 & -1389.66 & 672.995 \tabularnewline
46 & 3120 & NA & NA & -578.134 & NA \tabularnewline
47 & 4310 & NA & NA & -173.967 & NA \tabularnewline
48 & 4250 & NA & NA & 1125.76 & NA \tabularnewline
49 & 5730 & NA & NA & 1492.01 & NA \tabularnewline
50 & 3630 & NA & NA & 530.616 & NA \tabularnewline
51 & 5680 & NA & NA & 1047.42 & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300710&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]9290[/C][C]NA[/C][C]NA[/C][C]1492.01[/C][C]NA[/C][/ROW]
[ROW][C]2[/C][C]6160[/C][C]NA[/C][C]NA[/C][C]530.616[/C][C]NA[/C][/ROW]
[ROW][C]3[/C][C]8320[/C][C]NA[/C][C]NA[/C][C]1047.42[/C][C]NA[/C][/ROW]
[ROW][C]4[/C][C]8310[/C][C]NA[/C][C]NA[/C][C]735.061[/C][C]NA[/C][/ROW]
[ROW][C]5[/C][C]6750[/C][C]NA[/C][C]NA[/C][C]-200.078[/C][C]NA[/C][/ROW]
[ROW][C]6[/C][C]8710[/C][C]NA[/C][C]NA[/C][C]-473.55[/C][C]NA[/C][/ROW]
[ROW][C]7[/C][C]6300[/C][C]6951.38[/C][C]7185.83[/C][C]-234.453[/C][C]-651.38[/C][/ROW]
[ROW][C]8[/C][C]5710[/C][C]5368.57[/C][C]7249.58[/C][C]-1881.02[/C][C]341.432[/C][/ROW]
[ROW][C]9[/C][C]5740[/C][C]5929.09[/C][C]7318.75[/C][C]-1389.66[/C][C]-189.089[/C][/ROW]
[ROW][C]10[/C][C]6710[/C][C]6717.28[/C][C]7295.42[/C][C]-578.134[/C][C]-7.28299[/C][/ROW]
[ROW][C]11[/C][C]7310[/C][C]7116.45[/C][C]7290.42[/C][C]-173.967[/C][C]193.55[/C][/ROW]
[ROW][C]12[/C][C]7240[/C][C]8282.84[/C][C]7157.08[/C][C]1125.76[/C][C]-1042.84[/C][/ROW]
[ROW][C]13[/C][C]8650[/C][C]8520.34[/C][C]7028.33[/C][C]1492.01[/C][C]129.661[/C][/ROW]
[ROW][C]14[/C][C]8330[/C][C]7509.78[/C][C]6979.17[/C][C]530.616[/C][C]820.217[/C][/ROW]
[ROW][C]15[/C][C]7810[/C][C]7944.92[/C][C]6897.5[/C][C]1047.42[/C][C]-134.922[/C][/ROW]
[ROW][C]16[/C][C]8260[/C][C]7615.06[/C][C]6880[/C][C]735.061[/C][C]644.939[/C][/ROW]
[ROW][C]17[/C][C]6680[/C][C]6642.84[/C][C]6842.92[/C][C]-200.078[/C][C]37.1615[/C][/ROW]
[ROW][C]18[/C][C]5580[/C][C]6423.12[/C][C]6896.67[/C][C]-473.55[/C][C]-843.116[/C][/ROW]
[ROW][C]19[/C][C]6340[/C][C]6736.8[/C][C]6971.25[/C][C]-234.453[/C][C]-396.797[/C][/ROW]
[ROW][C]20[/C][C]4490[/C][C]5036.07[/C][C]6917.08[/C][C]-1881.02[/C][C]-546.068[/C][/ROW]
[ROW][C]21[/C][C]5000[/C][C]5503.26[/C][C]6892.92[/C][C]-1389.66[/C][C]-503.255[/C][/ROW]
[ROW][C]22[/C][C]7030[/C][C]6296.87[/C][C]6875[/C][C]-578.134[/C][C]733.134[/C][/ROW]
[ROW][C]23[/C][C]6100[/C][C]6628.53[/C][C]6802.5[/C][C]-173.967[/C][C]-528.533[/C][/ROW]
[ROW][C]24[/C][C]9740[/C][C]7936.17[/C][C]6810.42[/C][C]1125.76[/C][C]1803.83[/C][/ROW]
[ROW][C]25[/C][C]7940[/C][C]8390.76[/C][C]6898.75[/C][C]1492.01[/C][C]-450.755[/C][/ROW]
[ROW][C]26[/C][C]7740[/C][C]7438.53[/C][C]6907.92[/C][C]530.616[/C][C]301.467[/C][/ROW]
[ROW][C]27[/C][C]7820[/C][C]7935.34[/C][C]6887.92[/C][C]1047.42[/C][C]-115.339[/C][/ROW]
[ROW][C]28[/C][C]7820[/C][C]7527.98[/C][C]6792.92[/C][C]735.061[/C][C]292.023[/C][/ROW]
[ROW][C]29[/C][C]5380[/C][C]6505.76[/C][C]6705.83[/C][C]-200.078[/C][C]-1125.76[/C][/ROW]
[ROW][C]30[/C][C]7070[/C][C]6096.45[/C][C]6570[/C][C]-473.55[/C][C]973.55[/C][/ROW]
[ROW][C]31[/C][C]6970[/C][C]6181.8[/C][C]6416.25[/C][C]-234.453[/C][C]788.203[/C][/ROW]
[ROW][C]32[/C][C]4080[/C][C]4413.57[/C][C]6294.58[/C][C]-1881.02[/C][C]-333.568[/C][/ROW]
[ROW][C]33[/C][C]4930[/C][C]4760.34[/C][C]6150[/C][C]-1389.66[/C][C]169.661[/C][/ROW]
[ROW][C]34[/C][C]4820[/C][C]5433.12[/C][C]6011.25[/C][C]-578.134[/C][C]-613.116[/C][/ROW]
[ROW][C]35[/C][C]6220[/C][C]5772.28[/C][C]5946.25[/C][C]-173.967[/C][C]447.717[/C][/ROW]
[ROW][C]36[/C][C]6360[/C][C]7008.26[/C][C]5882.5[/C][C]1125.76[/C][C]-648.255[/C][/ROW]
[ROW][C]37[/C][C]7630[/C][C]7196.17[/C][C]5704.17[/C][C]1492.01[/C][C]433.828[/C][/ROW]
[ROW][C]38[/C][C]5130[/C][C]6138.95[/C][C]5608.33[/C][C]530.616[/C][C]-1008.95[/C][/ROW]
[ROW][C]39[/C][C]6960[/C][C]6597.01[/C][C]5549.58[/C][C]1047.42[/C][C]362.995[/C][/ROW]
[ROW][C]40[/C][C]5350[/C][C]6174.23[/C][C]5439.17[/C][C]735.061[/C][C]-824.227[/C][/ROW]
[ROW][C]41[/C][C]6290[/C][C]5088.67[/C][C]5288.75[/C][C]-200.078[/C][C]1201.33[/C][/ROW]
[ROW][C]42[/C][C]4630[/C][C]4647.7[/C][C]5121.25[/C][C]-473.55[/C][C]-17.6997[/C][/ROW]
[ROW][C]43[/C][C]5130[/C][C]4719.71[/C][C]4954.17[/C][C]-234.453[/C][C]410.286[/C][/ROW]
[ROW][C]44[/C][C]3620[/C][C]2931.48[/C][C]4812.5[/C][C]-1881.02[/C][C]688.516[/C][/ROW]
[ROW][C]45[/C][C]3980[/C][C]3307.01[/C][C]4696.67[/C][C]-1389.66[/C][C]672.995[/C][/ROW]
[ROW][C]46[/C][C]3120[/C][C]NA[/C][C]NA[/C][C]-578.134[/C][C]NA[/C][/ROW]
[ROW][C]47[/C][C]4310[/C][C]NA[/C][C]NA[/C][C]-173.967[/C][C]NA[/C][/ROW]
[ROW][C]48[/C][C]4250[/C][C]NA[/C][C]NA[/C][C]1125.76[/C][C]NA[/C][/ROW]
[ROW][C]49[/C][C]5730[/C][C]NA[/C][C]NA[/C][C]1492.01[/C][C]NA[/C][/ROW]
[ROW][C]50[/C][C]3630[/C][C]NA[/C][C]NA[/C][C]530.616[/C][C]NA[/C][/ROW]
[ROW][C]51[/C][C]5680[/C][C]NA[/C][C]NA[/C][C]1047.42[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300710&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300710&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
19290NANA1492.01NA
26160NANA530.616NA
38320NANA1047.42NA
48310NANA735.061NA
56750NANA-200.078NA
68710NANA-473.55NA
763006951.387185.83-234.453-651.38
857105368.577249.58-1881.02341.432
957405929.097318.75-1389.66-189.089
1067106717.287295.42-578.134-7.28299
1173107116.457290.42-173.967193.55
1272408282.847157.081125.76-1042.84
1386508520.347028.331492.01129.661
1483307509.786979.17530.616820.217
1578107944.926897.51047.42-134.922
1682607615.066880735.061644.939
1766806642.846842.92-200.07837.1615
1855806423.126896.67-473.55-843.116
1963406736.86971.25-234.453-396.797
2044905036.076917.08-1881.02-546.068
2150005503.266892.92-1389.66-503.255
2270306296.876875-578.134733.134
2361006628.536802.5-173.967-528.533
2497407936.176810.421125.761803.83
2579408390.766898.751492.01-450.755
2677407438.536907.92530.616301.467
2778207935.346887.921047.42-115.339
2878207527.986792.92735.061292.023
2953806505.766705.83-200.078-1125.76
3070706096.456570-473.55973.55
3169706181.86416.25-234.453788.203
3240804413.576294.58-1881.02-333.568
3349304760.346150-1389.66169.661
3448205433.126011.25-578.134-613.116
3562205772.285946.25-173.967447.717
3663607008.265882.51125.76-648.255
3776307196.175704.171492.01433.828
3851306138.955608.33530.616-1008.95
3969606597.015549.581047.42362.995
4053506174.235439.17735.061-824.227
4162905088.675288.75-200.0781201.33
4246304647.75121.25-473.55-17.6997
4351304719.714954.17-234.453410.286
4436202931.484812.5-1881.02688.516
4539803307.014696.67-1389.66672.995
463120NANA-578.134NA
474310NANA-173.967NA
484250NANA1125.76NA
495730NANA1492.01NA
503630NANA530.616NA
515680NANA1047.42NA



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 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')