| WS 9 Classical Decomposition | | *The author of this computation has been verified* | | R Software Module: /rwasp_decompose.wasp (opens new window with default values) | | Title produced by software: Classical Decomposition | | Date of computation: Fri, 04 Dec 2009 07:05:31 -0700 | | | | Cite this page as follows: | | Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/04/t1259935669xerbhcbvm68fxna.htm/, Retrieved Fri, 04 Dec 2009 15:07:55 +0100 | | | | BibTeX entries for LaTeX users: | @Manual{KEY,
author = {{YOUR NAME}},
publisher = {Office for Research Development and Education},
title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Dec/04/t1259935669xerbhcbvm68fxna.htm/},
year = {2009},
}
@Manual{R,
title = {R: A Language and Environment for Statistical Computing},
author = {{R Development Core Team}},
organization = {R Foundation for Statistical Computing},
address = {Vienna, Austria},
year = {2009},
note = {{ISBN} 3-900051-07-0},
url = {http://www.R-project.org},
}
| | | | Original text written by user: | | | | | IsPrivate? | | No (this computation is public) | | | | User-defined keywords: | | | | | Dataseries X: | | » Textbox « » Textfile « » CSV « | | 98,8
100,5
110,4
96,4
101,9
106,2
81
94,7
101
109,4
102,3
90,7
96,2
96,1
106
103,1
102
104,7
86
92,1
106,9
112,6
101,7
92
97,4
97
105,4
102,7
98,1
104,5
87,4
89,9
109,8
111,7
98,6
96,9
95,1
97
112,7
102,9
97,4
111,4
87,4
96,8
114,1
110,3
103,9
101,6
94,6
95,9
104,7
102,8
98,1
113,9
80,9
95,7
113,2
105,9
108,8
102,3
99
100,7
115,5
100,7
109,9
114,6
85,4
100,5
114,8
116,5
112,9
102
106
105,3
118,8
106,1
109,3
117,2
92,5
104,2
112,5
122,4
113,3
100
110,7
112,8
109,8
117,3
109,1
115,9
96
99,8
116,8
115,7
99,4
94,3 | | | | Output produced by software: |
| Classical Decomposition by Moving Averages | | t | Observations | Fit | Trend | Seasonal | Random | | 1 | 98.8 | NA | NA | 0.964989564232974 | NA | | 2 | 100.5 | NA | NA | 0.971818484774287 | NA | | 3 | 110.4 | NA | NA | 1.06541920173552 | NA | | 4 | 96.4 | NA | NA | 1.01252753388232 | NA | | 5 | 101.9 | NA | NA | 0.995781731101289 | NA | | 6 | 106.2 | NA | NA | 1.07618654582335 | NA | | 7 | 81 | 83.0234774146545 | 99.3333333333333 | 0.835806819610616 | 0.975627648013966 | | 8 | 94.7 | 92.7097339006648 | 99.0416666666667 | 0.93606799058307 | 1.02146771450631 | | 9 | 101 | 105.839614235677 | 98.675 | 1.07260820102029 | 0.954274075254087 | | 10 | 109.4 | 108.061306039069 | 98.7708333333333 | 1.09406089219053 | 1.01238828226310 | | 11 | 102.3 | 101.662155014455 | 99.0541666666667 | 1.02632891109532 | 1.00627416353170 | | 12 | 90.7 | 93.888056587243 | 98.9958333333333 | 0.948404123950431 | 0.966044066698936 | | 13 | 96.2 | 95.6706737139975 | 99.1416666666667 | 0.964989564232974 | 1.00553279563584 | | 14 | 96.1 | 96.4448861264749 | 99.2416666666667 | 0.971818484774287 | 0.996424008152981 | | 15 | 106 | 105.880472419141 | 99.3791666666667 | 1.06541920173552 | 1.00112889164667 | | 16 | 103.1 | 101.008059234211 | 99.7583333333333 | 1.01252753388232 | 1.02071063221736 | | 17 | 102 | 99.4454022126487 | 99.8666666666667 | 0.995781731101289 | 1.02568844542344 | | 18 | 104.7 | 107.506551817146 | 99.8958333333333 | 1.07618654582335 | 0.97389413231373 | | 19 | 86 | 83.5806819610616 | 100 | 0.835806819610616 | 1.02894589972436 | | 20 | 92.1 | 93.6887050074829 | 100.0875 | 0.93606799058307 | 0.983042726363268 | | 21 | 106.9 | 107.368080922131 | 100.1 | 1.07260820102029 | 0.995640408973404 | | 22 | 112.6 | 109.469909437764 | 100.058333333333 | 1.09406089219053 | 1.02859315932855 | | 23 | 101.7 | 102.508876366108 | 99.8791666666667 | 1.02632891109532 | 0.992109206589881 | | 24 | 92 | 94.5637945255576 | 99.7083333333333 | 0.948404123950431 | 0.972888201679929 | | 25 | 97.4 | 96.265750611941 | 99.7583333333333 | 0.964989564232974 | 1.01178248110931 | | 26 | 97 | 96.9145983941158 | 99.725 | 0.971818484774287 | 1.00088120476481 | | 27 | 105.4 | 106.280004619792 | 99.7541666666667 | 1.06541920173552 | 0.991719941837228 | | 28 | 102.7 | 101.088217663976 | 99.8375 | 1.01252753388232 | 1.01594431451330 | | 29 | 98.1 | 99.2503949569747 | 99.6708333333333 | 0.995781731101289 | 0.98840916494616 | | 30 | 104.5 | 107.345123835272 | 99.7458333333333 | 1.07618654582335 | 0.97349554657333 | | 31 | 87.4 | 83.458793466535 | 99.8541666666667 | 0.835806819610616 | 1.04722338257916 | | 32 | 89.9 | 93.3805826272494 | 99.7583333333333 | 0.93606799058307 | 0.962726912498041 | | 33 | 109.8 | 107.327858114593 | 100.0625 | 1.07260820102029 | 1.02303355278709 | | 34 | 111.7 | 109.816362053624 | 100.375 | 1.09406089219053 | 1.01715261652408 | | 35 | 98.6 | 102.996382598879 | 100.354166666667 | 1.02632891109532 | 0.957315174689188 | | 36 | 96.9 | 95.4213099209628 | 100.6125 | 0.948404123950431 | 1.01549643449940 | | 37 | 95.1 | 97.3674470311071 | 100.9 | 0.964989564232974 | 0.976712473211065 | | 38 | 97 | 98.3358829280982 | 101.1875 | 0.971818484774287 | 0.986415102114098 | | 39 | 112.7 | 108.304301103089 | 101.654166666667 | 1.06541920173552 | 1.04058655890985 | | 40 | 102.9 | 103.049989760873 | 101.775 | 1.01252753388232 | 0.998544495140453 | | 41 | 97.4 | 101.507500214138 | 101.9375 | 0.995781731101289 | 0.959535007704135 | | 42 | 111.4 | 110.152177075628 | 102.354166666667 | 1.07618654582335 | 1.01132817305568 | | 43 | 87.4 | 85.6945767089934 | 102.529166666667 | 0.835806819610616 | 1.01990118110739 | | 44 | 96.8 | 95.9118664851177 | 102.4625 | 0.93606799058307 | 1.00925989189273 | | 45 | 114.1 | 109.495420520821 | 102.083333333333 | 1.07260820102029 | 1.04205271286486 | | 46 | 110.3 | 111.316137193335 | 101.745833333333 | 1.09406089219053 | 0.990871609283651 | | 47 | 103.9 | 104.450348556264 | 101.770833333333 | 1.02632891109532 | 0.99473100316207 | | 48 | 101.6 | 96.6463319143987 | 101.904166666667 | 0.948404123950431 | 1.05125562437267 | | 49 | 94.6 | 98.1756257911522 | 101.7375 | 0.964989564232974 | 0.963579292086627 | | 50 | 95.9 | 98.5626405745455 | 101.420833333333 | 0.971818484774287 | 0.972985295858306 | | 51 | 104.7 | 107.966918355873 | 101.3375 | 1.06541920173552 | 0.969741487433172 | | 52 | 102.8 | 102.383409134401 | 101.116666666667 | 1.01252753388232 | 1.00406892942051 | | 53 | 98.1 | 100.710874829257 | 101.1375 | 0.995781731101289 | 0.97407554215289 | | 54 | 113.9 | 109.093926972235 | 101.370833333333 | 1.07618654582335 | 1.04405445070273 | | 55 | 80.9 | 84.9040427587784 | 101.583333333333 | 0.835806819610616 | 0.952840375691482 | | 56 | 95.7 | 95.4477327731203 | 101.966666666667 | 0.93606799058307 | 1.00264298815226 | | 57 | 113.2 | 110.067478228032 | 102.616666666667 | 1.07260820102029 | 1.02846001218887 | | 58 | 105.9 | 112.665478960370 | 102.979166666667 | 1.09406089219053 | 0.939950737148597 | | 59 | 108.8 | 106.105303925405 | 103.383333333333 | 1.02632891109532 | 1.02539643142146 | | 60 | 102.3 | 98.5431401622996 | 103.904166666667 | 0.948404123950431 | 1.03812401179334 | | 61 | 99 | 100.475517585907 | 104.120833333333 | 0.964989564232974 | 0.985314655536401 | | 62 | 100.7 | 101.563130146286 | 104.508333333333 | 0.971818484774287 | 0.991501540519252 | | 63 | 115.5 | 111.629296861839 | 104.775 | 1.06541920173552 | 1.03467461721050 | | 64 | 100.7 | 106.602273858910 | 105.283333333333 | 1.01252753388232 | 0.944632758333822 | | 65 | 109.9 | 105.449136233080 | 105.895833333333 | 0.995781731101289 | 1.04220863181925 | | 66 | 114.6 | 114.134067295174 | 106.054166666667 | 1.07618654582335 | 1.00408232805391 | | 67 | 85.4 | 88.8741251519288 | 106.333333333333 | 0.835806819610616 | 0.960909599436396 | | 68 | 100.5 | 99.9876625274482 | 106.816666666667 | 0.93606799058307 | 1.00512400689846 | | 69 | 114.8 | 114.925499538486 | 107.145833333333 | 1.07260820102029 | 0.998907992229832 | | 70 | 116.5 | 117.620663084583 | 107.508333333333 | 1.09406089219053 | 0.990472226093662 | | 71 | 112.9 | 110.544176465892 | 107.708333333333 | 1.02632891109532 | 1.02131115007071 | | 72 | 102 | 102.230061194157 | 107.791666666667 | 0.948404123950431 | 0.99774957393677 | | 73 | 106 | 104.407850060157 | 108.195833333333 | 0.964989564232974 | 1.01524933172099 | | 74 | 105.3 | 105.584029127040 | 108.645833333333 | 0.971818484774287 | 0.99730992339099 | | 75 | 118.8 | 115.815506475324 | 108.704166666667 | 1.06541920173552 | 1.02576937765507 | | 76 | 106.1 | 110.217840927815 | 108.854166666667 | 1.01252753388232 | 0.962639071014718 | | 77 | 109.3 | 108.656383225336 | 109.116666666667 | 0.995781731101289 | 1.00592341430443 | | 78 | 117.2 | 117.358142822037 | 109.05 | 1.07618654582335 | 0.998652476784022 | | 79 | 92.5 | 91.2387619457438 | 109.1625 | 0.835806819610616 | 1.01382348935210 | | 80 | 104.2 | 102.659356583904 | 109.670833333333 | 0.93606799058307 | 1.01500733559378 | | 81 | 112.5 | 117.566797233499 | 109.608333333333 | 1.07260820102029 | 0.956902821606718 | | 82 | 122.4 | 120.018479873301 | 109.7 | 1.09406089219053 | 1.01984294526321 | | 83 | 113.3 | 113.058682298076 | 110.158333333333 | 1.02632891109532 | 1.00213444643984 | | 84 | 100 | 104.415342363093 | 110.095833333333 | 0.948404123950431 | 0.957713662923799 | | 85 | 110.7 | 106.329787608921 | 110.1875 | 0.964989564232974 | 1.04110054660461 | | 86 | 112.8 | 107.045806097888 | 110.15 | 0.971818484774287 | 1.05375450110442 | | 87 | 109.8 | 117.351485824493 | 110.145833333333 | 1.06541920173552 | 0.935650701212366 | | 88 | 117.3 | 111.424436239025 | 110.045833333333 | 1.01252753388232 | 1.05273137526468 | | 89 | 109.1 | 108.726917764622 | 109.1875 | 0.995781731101289 | 1.00343136955455 | | 90 | 115.9 | 116.627232792998 | 108.370833333333 | 1.07618654582335 | 0.99376446842146 | | 91 | 96 | NA | NA | 0.835806819610616 | NA | | 92 | 99.8 | NA | NA | 0.93606799058307 | NA | | 93 | 116.8 | NA | NA | 1.07260820102029 | NA | | 94 | 115.7 | NA | NA | 1.09406089219053 | NA | | 95 | 99.4 | NA | NA | 1.02632891109532 | NA | | 96 | 94.3 | NA | NA | 0.948404123950431 | NA |
| | | Charts produced by software: |  | | http://www.freestatistics.org/blog/date/2009/Dec/04/t1259935669xerbhcbvm68fxna/1zq5f1259935529.png (open in new window) | | http://www.freestatistics.org/blog/date/2009/Dec/04/t1259935669xerbhcbvm68fxna/1zq5f1259935529.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2009/Dec/04/t1259935669xerbhcbvm68fxna/2b3js1259935529.png (open in new window) | | http://www.freestatistics.org/blog/date/2009/Dec/04/t1259935669xerbhcbvm68fxna/2b3js1259935529.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2009/Dec/04/t1259935669xerbhcbvm68fxna/3cv5k1259935529.png (open in new window) | | http://www.freestatistics.org/blog/date/2009/Dec/04/t1259935669xerbhcbvm68fxna/3cv5k1259935529.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2009/Dec/04/t1259935669xerbhcbvm68fxna/4gbx71259935529.png (open in new window) | | http://www.freestatistics.org/blog/date/2009/Dec/04/t1259935669xerbhcbvm68fxna/4gbx71259935529.ps (open in new window) |
| | | | Parameters (Session): | | par1 = multiplicative ; par2 = 12 ; | | | | Parameters (R input): | | par1 = multiplicative ; 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$trend)) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
if (par1 == 'additive') a<-table.element(a,m$trend[i]+m$seasonal[i]) else a<-table.element(a,m$trend[i]*m$seasonal[i])
a<-table.element(a,m$trend[i])
a<-table.element(a,m$seasonal[i])
a<-table.element(a,m$random[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
| | |
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