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Classical Decomposition Paper

*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, 24 Dec 2010 14:34:05 +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/24/t1293201143a2m0fjha86pbnys.htm/, Retrieved Fri, 24 Dec 2010 15:32:23 +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/24/t1293201143a2m0fjha86pbnys.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 «
44164 40399 36763 37903 35532 35533 32110 33374 35462 33508 36080 34560 38737 38144 37594 36424 36843 37246 38661 40454 44928 48441 48140 45998 47369 49554 47510 44873 45344 42413 36912 43452 42142 44382 43636 44167 44423 42868 43908 42013 38846 35087 33026 34646 37135 37985 43121 43722 43630 42234 39351 39327 35704 30466 28155 29257 29998 32529 34787 33855 34556 31348 30805 28353 24514 21106 21346 23335 24379 26290 30084 29429 30632 27349 27264 27474 24482 21453 18788 19282 19713 21917 23812 23785 24696 24562 23580 24939 23899 21454 19761 19815 20780 23462 25005 24725 26198 27543 26471 26558 25317 22896
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Classical Decomposition by Moving Averages
tObservationsFitTrendSeasonalRandom
144164NANA3515.85565476190NA
240399NANA2529.49851190476NA
336763NANA1833.74255952381NA
437903NANA1036.79017857143NA
535532NANA-804.775297619049NA
635533NANA-3595.59672619048NA
73211030797.2187536056.2083333333-5258.989583333331312.78125000001
83337432556.587797619035736.125-3179.53720238095817.412202380961
93546233888.563988095235676.7916666667-1788.227678571431573.43601190476
103350836262.355654761935649.7916666667612.56398809524-2754.3556547619
113608038322.546130952435642.79166666672679.75446428571-2242.54613095237
123456038187.712797619035768.79166666672418.92113095238-3627.71279761905
133873739628.980654761936113.1253515.85565476190-891.980654761908
143814439210.581845238136681.08333333332529.49851190476-1066.5818452381
153759439204.242559523837370.51833.74255952381-1610.24255952381
163642439423.915178571438387.1251036.79017857143-2999.91517857142
173684338707.058035714339511.8333333333-804.775297619049-1864.05803571429
183724636895.319940476240490.9166666667-3595.59672619048350.680059523809
193866136068.177083333341327.1666666667-5258.989583333332592.82291666667
204045438982.712797619142162.25-3179.537202380951471.28720238095
214492841262.605654761943050.8333333333-1788.227678571433665.39434523809
224844144428.605654761943816.0416666667612.563988095244012.3943452381
234814047202.046130952444522.29166666672679.75446428571937.953869047618
244599847510.71279761945091.79166666672418.92113095238-1512.71279761905
254736948750.063988095245234.20833333333515.85565476190-1381.06398809524
264955447815.748511904845286.252529.498511904761738.25148809524
274751047128.825892857145295.08333333331833.74255952381381.174107142862
284487346046.665178571445009.8751036.79017857143-1173.66517857142
294534443848.308035714344653.0833333333-804.7752976190491495.69196428571
304241340793.528273809544389.125-3595.596726190481619.47172619047
313691238931.0937544190.0833333333-5258.98958333333-2019.09375
324345240609.21279761943788.75-3179.537202380952842.78720238096
334214241571.855654761943360.0833333333-1788.22767857143570.144345238099
344438243703.397321428643090.8333333333612.56398809524678.602678571435
354363645380.671130952442700.91666666672679.75446428571-1744.67113095237
364416744543.837797619042124.91666666672418.92113095238-376.837797619046
374442345173.605654761941657.753515.85565476190-750.605654761908
384286843658.415178571441128.91666666672529.49851190476-790.415178571428
394390842387.117559523840553.3751833.742559523811520.88244047620
404201341114.998511904840078.20833333331036.79017857143898.001488095237
413884638985.433035714339790.2083333333-804.775297619049-139.433035714283
423508736154.611607142939750.2083333333-3595.59672619048-1067.61160714286
433302634439.635416666739698.625-5258.98958333333-1413.63541666667
443464636459.629464285739639.1666666667-3179.53720238095-1813.62946428571
453713537634.647321428639422.875-1788.22767857143-499.647321428572
463798539733.647321428639121.0833333333612.56398809524-1748.64732142857
474312141558.004464285738878.252679.754464285711562.99553571429
484372240973.712797619038554.79166666672418.921130952382748.28720238095
494363041675.147321428638159.29166666673515.855654761901954.85267857143
504223440261.290178571437731.79166666672529.498511904761972.70982142857
513935139043.617559523837209.8751833.74255952381307.382440476198
523932737721.956845238136685.16666666671036.790178571431605.04315476191
533570435305.808035714336110.5833333333-804.775297619049398.19196428571
543046631756.611607142935352.2083333333-3595.59672619048-1290.61160714286
552815529304.010416666734563-5258.98958333333-1149.01041666666
562925730551.796130952433731.3333333333-3179.53720238095-1294.79613095237
572999831133.438988095232921.6666666667-1788.22767857143-1135.43898809523
583252932720.897321428632108.3333333333612.56398809524-191.897321428569
593478733864.587797619031184.83333333332679.75446428571922.412202380958
603385532747.504464285730328.58333333332418.921130952381107.49553571429
613455633170.730654761929654.8753515.855654761901385.2693452381
623134831653.915178571429124.41666666672529.49851190476-305.915178571428
633080530477.284226190528643.54166666671833.74255952381327.715773809523
642835329186.248511904828149.45833333331036.79017857143-833.248511904763
652451426888.766369047627693.5416666667-804.775297619049-2374.76636904761
662110623717.569940476227313.1666666667-3595.59672619048-2611.56994047619
672134621706.260416666726965.25-5258.98958333333-360.260416666664
682333523455.587797619026635.125-3179.53720238095-120.587797619042
692437924532.730654761926320.9583333333-1788.22767857143-153.730654761905
702629026749.355654761926136.7916666667612.56398809524-459.355654761901
713008428778.587797619026098.83333333332679.754464285711305.41220238096
722942928530.879464285726111.95833333332418.92113095238898.12053571429
733063229535.688988095226019.83333333333515.855654761901096.31101190477
742734928273.873511904825744.3752529.49851190476-924.873511904756
752726427214.825892857125381.08333333331833.7425595238149.1741071428551
762747426041.248511904825004.45833333331036.790178571431432.75148809524
772448223756.141369047624560.9166666667-804.775297619049725.858630952382
782145320468.819940476224064.4166666667-3595.59672619048984.180059523813
791878818322.927083333323581.9166666667-5258.98958333333465.072916666668
801928220038.921130952423218.4583333333-3179.53720238095-756.921130952382
811971321160.605654761922948.8333333333-1788.22767857143-1447.60565476190
822191723302.272321428622689.7083333333612.56398809524-1385.27232142858
832381225239.546130952422559.79166666672679.75446428571-1427.54613095238
842378524954.462797619022535.54166666672418.92113095238-1169.46279761905
852469626091.980654761922576.1253515.85565476190-1395.98065476190
862456225168.373511904822638.8752529.49851190476-606.373511904763
872358024539.284226190522705.54166666671833.74255952381-959.284226190477
882493923851.165178571422814.3751036.790178571431087.83482142858
892389922123.683035714322928.4583333333-804.7752976190491775.31696428572
902145419421.736607142923017.3333333333-3595.596726190482032.26339285714
911976117860.0937523119.0833333333-5258.989583333331900.90625
921981520126.337797619023305.875-3179.53720238095-311.337797619046
932078021762.313988095223550.5416666667-1788.22767857143-982.313988095237
942346224351.022321428623738.4583333333612.56398809524-889.022321428569
952500526544.7544642857238652679.75446428571-1539.75446428571
962472526403.087797619023984.16666666672418.92113095238-1678.08779761905
9726198NANANANA
9827543NANANANA
9926471NANANANA
10026558NANANANA
10125317NANANANA
10222896NANANANA
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293201143a2m0fjha86pbnys/1ql121293201242.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293201143a2m0fjha86pbnys/1ql121293201242.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/24/t1293201143a2m0fjha86pbnys/2ql121293201242.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293201143a2m0fjha86pbnys/2ql121293201242.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/24/t1293201143a2m0fjha86pbnys/3jd051293201242.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293201143a2m0fjha86pbnys/3jd051293201242.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/24/t1293201143a2m0fjha86pbnys/4jd051293201242.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293201143a2m0fjha86pbnys/4jd051293201242.ps (open in new window)


 
Parameters (Session):
par1 = additive ; par2 = 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$trend)) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
a<-table.element(a,m$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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