| paper 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, 10 Dec 2010 11:47:05 +0000 | | | | Cite this page as follows: | | Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/10/t1291981509aet3kvnw5ysr4f3.htm/, Retrieved Fri, 10 Dec 2010 12:45:10 +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/2010/Dec/10/t1291981509aet3kvnw5ysr4f3.htm/},
year = {2010},
}
@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 = {2010},
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 « | | 1.579
2.146
2.462
3.695
4.831
5.134
6.250
5.760
6.249
2.917
1.741
2.359
1.511
2.059
2.635
2.867
4.403
5.720
4.502
5.749
5.627
2.846
1.762
2.429
1.169
2.154
2.249
2.687
4.359
5.382
4.459
6.398
4.596
3.024
1.887
2.070
1.351
2.218
2.461
3.028
4.784
4.975
4.607
6.249
4.809
3.157
1.910
2.228
1.594
2.467
2.222
3.607
4.685
4.962
5.770
5.480
5.000
3.228
1.993
2.288
1.580
2.111
2.192
3.601
4.665
4.876
5.813
5.589
5.331
3.075
2.002
2.306
1.507
1.992
2.487
3.490
4.647
5.594
5.611
5.788
6.204
3.013
1.931
2.549
1.504
2.090
2.702
2.939
4.500
6.208
6.415
5.657
5.964
3.163
1.997
2.422
1.376
2.202
2.683
3.303
5.202
5.231
4.880
7.998
4.977
3.531
2.025
2.205
1.442
2.238
2.179
3.218
5.139
4.990
4.914
6.084
5.672
3.548
1.793
2.086 | | | | Output produced by software: |
| Classical Decomposition by Moving Averages | | t | Observations | Fit | Trend | Seasonal | Random | | 1 | 1.579 | NA | NA | 0.40011901419982 | NA | | 2 | 2.146 | NA | NA | 0.601339586447101 | NA | | 3 | 2.462 | NA | NA | 0.670637515584853 | NA | | 4 | 3.695 | NA | NA | 0.883688483330432 | NA | | 5 | 4.831 | NA | NA | 1.30295056315214 | NA | | 6 | 5.134 | NA | NA | 1.47419090742475 | NA | | 7 | 6.25 | 5.54408387155024 | 3.75741666666667 | 1.47550414643489 | 1.12732782273952 | | 8 | 5.76 | 6.28136683996881 | 3.75095833333333 | 1.67460320317309 | 0.916997867939934 | | 9 | 6.249 | 5.59880344823213 | 3.75454166666667 | 1.49120823400072 | 1.1161313408802 | | 10 | 2.917 | 3.19498657864038 | 3.72725 | 0.857196747908077 | 0.912992880627788 | | 11 | 1.741 | 1.9440560915497 | 3.67491666666667 | 0.529006850463648 | 0.895550291767643 | | 12 | 2.359 | 2.35452080432194 | 3.6815 | 0.639554747880467 | 1.00190238101521 | | 13 | 1.511 | 1.45366572183913 | 3.63308333333333 | 0.40011901419982 | 1.03944117089611 | | 14 | 2.059 | 2.14064364867117 | 3.55979166666667 | 0.601339586447101 | 0.961860233616253 | | 15 | 2.635 | 2.36964177485945 | 3.53341666666667 | 0.670637515584853 | 1.11198242196599 | | 16 | 2.867 | 3.09692311018497 | 3.50454166666667 | 0.883688483330432 | 0.925757565814658 | | 17 | 4.403 | 4.56353005783356 | 3.50245833333333 | 1.30295056315214 | 0.964823271502726 | | 18 | 5.72 | 5.16888186915804 | 3.50625 | 1.47419090742475 | 1.10662231112891 | | 19 | 4.502 | 5.15676403311108 | 3.49491666666667 | 1.47550414643489 | 0.873028118233276 | | 20 | 5.749 | 5.83536418685704 | 3.484625 | 1.67460320317309 | 0.985199863437562 | | 21 | 5.627 | 5.17822059256751 | 3.4725 | 1.49120823400072 | 1.08666672255652 | | 22 | 2.846 | 2.95640015047263 | 3.44891666666667 | 0.857196747908077 | 0.962657236891636 | | 23 | 1.762 | 1.81956314607392 | 3.43958333333333 | 0.529006850463648 | 0.968364304257246 | | 24 | 2.429 | 2.18962227182676 | 3.42366666666667 | 0.639554747880467 | 1.10932375471936 | | 25 | 1.169 | 1.36352224226503 | 3.40779166666667 | 0.40011901419982 | 0.857338416466242 | | 26 | 2.154 | 2.064423856089 | 3.43304166666667 | 0.601339586447101 | 1.04339038402739 | | 27 | 2.249 | 2.29165222044289 | 3.417125 | 0.670637515584853 | 0.981388004662135 | | 28 | 2.687 | 2.9882662470888 | 3.38158333333333 | 0.883688483330432 | 0.899183599392357 | | 29 | 4.359 | 4.42248565937234 | 3.39420833333333 | 1.30295056315214 | 0.9856448015297 | | 30 | 5.382 | 4.98933770155794 | 3.38445833333333 | 1.47419090742475 | 1.07870028487337 | | 31 | 4.459 | 4.9829004611895 | 3.37708333333333 | 1.47550414643489 | 0.894860339822154 | | 32 | 6.398 | 5.672439250215 | 3.38733333333333 | 1.67460320317309 | 1.12790983169322 | | 33 | 4.596 | 5.06836825266279 | 3.39883333333333 | 1.49120823400072 | 0.906800723800086 | | 34 | 3.024 | 2.93322012174795 | 3.421875 | 0.857196747908077 | 1.0309488802354 | | 35 | 1.887 | 1.82707945174093 | 3.45379166666667 | 0.529006850463648 | 1.03279580874383 | | 36 | 2.07 | 2.20936852466757 | 3.45454166666667 | 0.639554747880467 | 0.936919294761593 | | 37 | 1.351 | 1.37790985515063 | 3.44375 | 0.40011901419982 | 0.980470525666071 | | 38 | 2.218 | 2.0708381450111 | 3.44370833333333 | 0.601339586447101 | 1.07106390972343 | | 39 | 2.461 | 2.31126836777375 | 3.446375 | 0.670637515584853 | 1.06478331738277 | | 40 | 3.028 | 3.05826173903927 | 3.46079166666667 | 0.883688483330432 | 0.990104921808042 | | 41 | 4.784 | 4.51770962969604 | 3.46729166666667 | 1.30295056315214 | 1.05894366662115 | | 42 | 4.975 | 5.12256770481645 | 3.47483333333333 | 1.47419090742475 | 0.971192629688877 | | 43 | 4.607 | 5.15178420661686 | 3.49154166666667 | 1.47550414643489 | 0.894253294631956 | | 44 | 6.249 | 5.88127622467737 | 3.51204166666667 | 1.67460320317309 | 1.06252448639968 | | 45 | 4.809 | 5.23780678825113 | 3.51245833333333 | 1.49120823400072 | 0.918132377617865 | | 46 | 3.157 | 3.02301148109132 | 3.526625 | 0.857196747908077 | 1.04432286140717 | | 47 | 1.91 | 1.87618892102564 | 3.546625 | 0.529006850463648 | 1.01802114840113 | | 48 | 2.228 | 2.26527626887812 | 3.54195833333333 | 0.639554747880467 | 0.983544493274288 | | 49 | 1.594 | 1.43637724610058 | 3.589875 | 0.40011901419982 | 1.10973632054346 | | 50 | 2.467 | 2.16860593944096 | 3.60629166666667 | 0.601339586447101 | 1.13759717942853 | | 51 | 2.222 | 2.40236329697402 | 3.58220833333333 | 0.670637515584853 | 0.924922555551358 | | 52 | 3.607 | 3.17520318166666 | 3.593125 | 0.883688483330432 | 1.13599029530661 | | 53 | 4.685 | 4.69002484167291 | 3.59954166666667 | 1.30295056315214 | 0.998928610861873 | | 54 | 4.962 | 5.31519531671995 | 3.6055 | 1.47419090742475 | 0.93354988938809 | | 55 | 5.77 | 5.322758249585 | 3.60741666666667 | 1.47550414643489 | 1.08402443422071 | | 56 | 5.48 | 6.01517470579775 | 3.592 | 1.67460320317309 | 0.911029233235417 | | 57 | 5 | 5.33243637743375 | 3.57591666666667 | 1.49120823400072 | 0.93765769455017 | | 58 | 3.228 | 3.06397834233509 | 3.57441666666667 | 0.857196747908077 | 1.05353225099493 | | 59 | 1.993 | 1.89031781232344 | 3.57333333333333 | 0.529006850463648 | 1.05432006565624 | | 60 | 2.288 | 2.2825175989564 | 3.56891666666667 | 0.639554747880467 | 1.00240190964841 | | 61 | 1.58 | 1.42727453852753 | 3.567125 | 0.40011901419982 | 1.10700496460199 | | 62 | 2.111 | 2.14886195635261 | 3.57345833333333 | 0.601339586447101 | 0.982380461322477 | | 63 | 2.192 | 2.40879023983171 | 3.59179166666667 | 0.670637515584853 | 0.910000366056424 | | 64 | 3.601 | 3.18057895327359 | 3.59920833333333 | 0.883688483330432 | 1.13218381084164 | | 65 | 4.665 | 4.68177282143962 | 3.59320833333333 | 1.30295056315214 | 0.996417420904575 | | 66 | 4.876 | 5.29873351825371 | 3.59433333333333 | 1.47419090742475 | 0.92021989466022 | | 67 | 5.813 | 5.30007237333356 | 3.59204166666667 | 1.47550414643489 | 1.09677747595432 | | 68 | 5.589 | 6.00184765530583 | 3.58404166666667 | 1.67460320317309 | 0.93121323981943 | | 69 | 5.331 | 5.35548797138435 | 3.591375 | 1.49120823400072 | 0.995427499507945 | | 70 | 3.075 | 3.08508681225233 | 3.59904166666667 | 0.857196747908077 | 0.9967304608051 | | 71 | 2.002 | 1.90107428494953 | 3.59366666666667 | 0.529006850463648 | 1.05308878030147 | | 72 | 2.306 | 2.31700025911295 | 3.62283333333333 | 0.639554747880467 | 0.995252370357022 | | 73 | 1.507 | 1.45816706074888 | 3.64433333333333 | 0.40011901419982 | 1.03348926235245 | | 74 | 1.992 | 2.19140673209375 | 3.64420833333333 | 0.601339586447101 | 0.909005147618933 | | 75 | 2.487 | 2.47389796530308 | 3.688875 | 0.670637515584853 | 1.0052961095731 | | 76 | 3.49 | 3.28967766061142 | 3.72266666666667 | 0.883688483330432 | 1.06089421519534 | | 77 | 4.647 | 4.84323011205689 | 3.717125 | 1.30295056315214 | 0.959483628174432 | | 78 | 5.594 | 5.49031691159778 | 3.72429166666667 | 1.47419090742475 | 1.01888471832713 | | 79 | 5.611 | 5.50996283816393 | 3.73429166666667 | 1.47550414643489 | 1.0183371766387 | | 80 | 5.788 | 6.26008542426182 | 3.73825 | 1.67460320317309 | 0.92458802200491 | | 81 | 6.204 | 5.59395702147163 | 3.75129166666667 | 1.49120823400072 | 1.10905392661881 | | 82 | 3.013 | 3.20359426265062 | 3.73729166666667 | 0.857196747908077 | 0.940506116872326 | | 83 | 1.931 | 1.96166761127972 | 3.70820833333333 | 0.529006850463648 | 0.984366560826421 | | 84 | 2.549 | 2.38404691518242 | 3.72766666666667 | 0.639554747880467 | 1.0691903685985 | | 85 | 1.504 | 1.51515067702117 | 3.78675 | 0.40011901419982 | 0.99264054909503 | | 86 | 2.09 | 2.29398524321518 | 3.81479166666667 | 0.601339586447101 | 0.911078223446076 | | 87 | 2.702 | 2.54797546754539 | 3.79933333333333 | 0.670637515584853 | 1.06044977057923 | | 88 | 2.939 | 3.3541132791876 | 3.79558333333333 | 0.883688483330432 | 0.876237549350705 | | 89 | 4.5 | 4.9571839967259 | 3.80458333333333 | 1.30295056315214 | 0.90777344616866 | | 90 | 6.208 | 5.60493525465006 | 3.80204166666667 | 1.47419090742475 | 1.1075953098387 | | 91 | 6.415 | 5.59425101252902 | 3.79141666666667 | 1.47550414643489 | 1.14671293541044 | | 92 | 5.657 | 6.3480020924284 | 3.79075 | 1.67460320317309 | 0.891146524155592 | | 93 | 5.964 | 5.658576044945 | 3.794625 | 1.49120823400072 | 1.05397540876522 | | 94 | 3.163 | 3.26506241278186 | 3.809 | 0.857196747908077 | 0.968741053040115 | | 95 | 1.997 | 2.03848381435746 | 3.85341666666667 | 0.529006850463648 | 0.979649671944764 | | 96 | 2.422 | 2.45714269324226 | 3.84195833333333 | 0.639554747880467 | 0.985697740168322 | | 97 | 1.376 | 1.49536145744387 | 3.73729166666667 | 0.40011901419982 | 0.920178859198428 | | 98 | 2.202 | 2.26757641304371 | 3.770875 | 0.601339586447101 | 0.971080836497285 | | 99 | 2.683 | 2.56672537475195 | 3.82729166666667 | 0.670637515584853 | 1.0453007658676 | | 100 | 3.303 | 3.35934176938064 | 3.8015 | 0.883688483330432 | 0.983228330652696 | | 101 | 5.202 | 4.97466525011486 | 3.818 | 1.30295056315214 | 1.04569850200069 | | 102 | 5.231 | 5.61685163115174 | 3.810125 | 1.47419090742475 | 0.931304642442083 | | 103 | 4.88 | 5.61257185568059 | 3.80383333333333 | 1.47550414643489 | 0.869476618826868 | | 104 | 7.998 | 6.37702854795007 | 3.80808333333333 | 1.67460320317309 | 1.25418914779219 | | 105 | 4.977 | 5.64956666186458 | 3.78858333333333 | 1.49120823400072 | 0.880952522181126 | | 106 | 3.531 | 3.22652427565716 | 3.76404166666667 | 0.857196747908077 | 1.09436647560348 | | 107 | 2.025 | 1.98794161818608 | 3.757875 | 0.529006850463648 | 1.01864158457919 | | 108 | 2.205 | 2.39526577138482 | 3.74520833333333 | 0.639554747880467 | 0.920565903935235 | | 109 | 1.442 | 1.49507803980881 | 3.73658333333333 | 0.40011901419982 | 0.964498147658165 | | 110 | 2.238 | 2.19985054212011 | 3.65825 | 0.601339586447101 | 1.01734184079757 | | 111 | 2.179 | 2.41929689424254 | 3.60745833333333 | 0.670637515584853 | 0.900674904839335 | | 112 | 3.218 | 3.2140854749332 | 3.637125 | 0.883688483330432 | 1.00121792811589 | | 113 | 5.139 | 4.72732180154314 | 3.62816666666667 | 1.30295056315214 | 1.08708486871414 | | 114 | 4.99 | 5.32705026860049 | 3.61354166666667 | 1.47419090742475 | 0.936728536130552 | | 115 | 4.914 | NA | NA | 1.47550414643489 | NA | | 116 | 6.084 | NA | NA | 1.67460320317309 | NA | | 117 | 5.672 | NA | NA | 1.49120823400072 | NA | | 118 | 3.548 | NA | NA | 0.857196747908077 | NA | | 119 | 1.793 | NA | NA | 0.529006850463648 | NA | | 120 | 2.086 | NA | NA | 0.639554747880467 | NA |
| | | | Charts produced by software: |  | | http://www.freestatistics.org/blog/date/2010/Dec/10/t1291981509aet3kvnw5ysr4f3/1tz5w1291981620.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/10/t1291981509aet3kvnw5ysr4f3/1tz5w1291981620.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/10/t1291981509aet3kvnw5ysr4f3/2tz5w1291981620.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/10/t1291981509aet3kvnw5ysr4f3/2tz5w1291981620.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/10/t1291981509aet3kvnw5ysr4f3/34rmh1291981620.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/10/t1291981509aet3kvnw5ysr4f3/34rmh1291981620.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2010/Dec/10/t1291981509aet3kvnw5ysr4f3/44rmh1291981620.png (open in new window) | | http://www.freestatistics.org/blog/date/2010/Dec/10/t1291981509aet3kvnw5ysr4f3/44rmh1291981620.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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