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*The author of this computation has been verified*
R Software Module: /rwasp_decomposeloess.wasp (opens new window with default values)
Title produced by software: Decomposition by Loess
Date of computation: Tue, 21 Dec 2010 11:55:29 +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/21/t1292932569hwl0ofupag9tfx9.htm/, Retrieved Tue, 21 Dec 2010 12:56:10 +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/21/t1292932569hwl0ofupag9tfx9.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 «
9,4 9,4 9,5 9,5 9,4 9,4 9,3 9,4 9,4 9,2 9,1 9,1 9,1 9,0 9,0 8,9 8,8 8,7 8,5 8,3 8,1 7,9 7,8 7,6 7,4 7,2 7,0 7,0 6,8 6,8 6,7 6,8 6,7 6,7 6,7 6,5 6,3 6,3 6,3 6,5 6,6 6,5 6,3 6,3 6,5 7,0 7,1 7,3 7,3 7,4 7,4 7,3 7,4 7,5 7,7 7,7 7,7 7,7 7,7 7,8 8,0 8,1 8,1 8,2 8,2 8,2 8,1 8,1 8,2 8,3 8,3 8,4 8,5 8,5 8,4 8,0 7,9 8,1 8,5 8,8 8,8 8,6 8,3 8,3 8,3 8,4 8,4 8,5 8,6 8,6 8,6 8,6 8,6 8,5 8,4 8,4 8,4 8,5 8,5 8,6 8,6 8,4 8,2 8,0 8,0 8,0 8,0 7,9 7,9 7,8 7,8 8,0 7,8 7,4 7,2 7,0 7,0 7,2 7,2 7,2 7,0 6,9 6,8 6,8 6,8 6,9 7,2 7,2 7,2 7,1 7,2 7,3 7,5 7,6 7,7 7,7 7,7 7,8 8,0 8,1 8,1 8,0 8,1 8,2 8,3 8,4 8,4 8,4 8,5 8,5 8,6 8,6 8,5 8,5
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk


Seasonal Decomposition by Loess - Parameters
ComponentWindowDegreeJump
Seasonal15410155
Trend1912
Low-pass1312


Seasonal Decomposition by Loess - Time Series Components
tObservedFittedSeasonalTrendRemainder
19.49.2956907160481-0.002178494527250089.50648777847915-0.104309283951904
29.49.308365648009750.01424063414549319.47739371784476-0.0916343519902547
39.59.544117561717320.007582781072308749.448299657210370.0441175617173233
49.59.560241421941540.02240618734568729.417352390712770.0602414219415408
59.49.40713449693430.006460378850532249.386405124215180.00713449693429169
69.49.45855819100064-0.01267075539589019.354112564395250.0585581910006354
79.39.27921262940789-0.001032633983221539.32182000457533-0.0207873705921084
89.49.510544341574570.001034440920800569.288421217504630.110544341574565
99.49.54956829920892-0.004590729642857289.255022430433940.149568299208921
109.29.19781785237337-0.009098193866039869.21128034149266-0.00218214762662505
119.19.05122121242022-0.01875946497161589.1675382525514-0.0487787875797778
129.19.09731050200334-0.003394167943364369.10608366594003-0.00268949799666274
139.19.1575494151986-0.002178494527250089.044629079328660.0575494151985918
1499.024615745431920.01424063414549318.961143620422580.0246157454319249
1599.114759057411180.007582781072308748.87765816151650.114759057411185
168.99.006076818884170.02240618734568728.771516993770150.106076818884167
178.88.928163795125680.006460378850532248.665375826023790.128163795125683
188.78.87583551587184-0.01267075539589018.536835239524050.175835515871842
198.58.59273798095891-0.001032633983221538.408294653024310.0927379809589137
208.38.343231607353930.001034440920800568.255733951725270.0432316073539312
218.18.10141747921663-0.004590729642857288.103173250426230.00141747921662549
227.97.87093941632534-0.009098193866039867.9381587775407-0.02906058367466
237.87.84561516031645-0.01875946497161587.773144304655170.0456151603164479
247.67.58823296414816-0.003394167943364367.6151612037952-0.0117670358518414
257.47.34500039159201-0.002178494527250087.45717810293524-0.054999608407992
267.27.062255342645830.01424063414549317.32350402320868-0.137744657354173
2776.802587275445580.007582781072308747.18982994348212-0.197412724554423
2876.892640120066460.02240618734568727.08495369258785-0.107359879933538
296.86.613462179455880.006460378850532246.98007744169359-0.186537820544118
306.86.71690216621815-0.01267075539589016.89576858917774-0.083097833781852
316.76.58957289732133-0.001032633983221536.8114597366619-0.110427102678674
326.86.85464289530590.001034440920800566.74432266377330.0546428953058973
336.76.72740513875815-0.004590729642857286.677185590884710.0274051387581498
346.76.77786867939785-0.009098193866039866.631229514468190.0778686793978478
356.76.83348602691994-0.01875946497161586.585273438051680.13348602691994
366.56.4512315119991-0.003394167943364366.55216265594427-0.0487684880009063
376.36.08312662069039-0.002178494527250086.51905187383686-0.216873379309614
386.36.090430265376260.01424063414549316.49532910047825-0.209569734623741
396.36.120810891808060.007582781072308746.47160632711963-0.179189108191938
406.56.494996150779270.02240618734568726.48259766187504-0.00500384922072961
416.66.699950624519010.006460378850532246.493588996630450.099950624519014
426.56.46008679858714-0.01267075539589016.55258395680875-0.0399132014128618
436.35.98945371699617-0.001032633983221536.61157891698705-0.310546283003828
446.35.90117659961410.001034440920800566.6977889594651-0.398823400385895
456.56.22059172769972-0.004590729642857286.78399900194314-0.279408272300281
4677.1361388631909-0.009098193866039866.872959330675140.136138863190899
477.17.25683980556447-0.01875946497161586.961919659407140.156839805564474
487.37.54588117840212-0.003394167943364367.057512989541240.24588117840212
497.37.4490721748519-0.002178494527250087.153106319675350.149072174851902
507.47.538563430588880.01424063414549317.247195935265630.138563430588878
517.47.451131668071780.007582781072308747.341285550855910.0511316680717817
527.37.168208692790950.02240618734568727.40938511986336-0.131791307209047
537.47.316054932278660.006460378850532247.47748468887081-0.0839450677213405
547.57.48282235087855-0.01267075539589017.52984840451734-0.0171776491214501
557.77.81882051381935-0.001032633983221537.582212120163870.118820513819352
567.77.75838460454130.001034440920800567.64058095453790.0583846045413035
577.77.70564094073094-0.004590729642857287.698949788911920.00564094073093724
587.77.64644819460715-0.009098193866039867.76264999925889-0.0535518053928508
597.77.59240925536576-0.01875946497161587.82635020960586-0.107590744634245
607.87.72175474377436-0.003394167943364367.881639424169-0.078245256225638
6188.0652498557951-0.002178494527250087.936928638732140.0652498557951064
628.18.203732943336960.01424063414549317.982026422517550.103732943336958
638.18.165293012624740.007582781072308748.027124206302960.0652930126247355
648.28.306879362891940.02240618734568728.070714449762370.106879362891942
658.28.279234927927680.006460378850532248.114304693221780.0792349279276827
668.28.25743305053321-0.01267075539589018.155237704862680.0574330505332092
678.18.00486191747965-0.001032633983221538.19617071650358-0.0951380825203536
688.17.973743524673950.001034440920800568.22522203440525-0.126256475326054
698.28.15031737733593-0.004590729642857288.25427335230693-0.0496826226640739
708.38.34724597262893-0.009098193866039868.261852221237110.0472459726289269
718.38.34932837480432-0.01875946497161588.26943109016730.0493283748043218
728.48.52883632823838-0.003394167943364368.274557839704990.128836328238377
738.58.72249390528457-0.002178494527250088.279684589242680.222493905284569
748.58.681829782544430.01424063414549318.303929583310080.181829782544431
758.48.464242641550220.007582781072308748.328174577377470.0642426415502229
7687.626790215701920.02240618734568728.3508035969524-0.373209784298083
777.97.420107004622150.006460378850532248.37343261652732-0.479892995377854
788.17.83329222710701-0.01267075539589018.37937852828888-0.266707772892989
798.58.61570819393279-0.001032633983221538.385324440050430.11570819393279
808.89.206006065122860.001034440920800568.392959493956340.406006065122856
818.89.2039961817806-0.004590729642857288.400594547862260.403996181780601
828.68.7853881332106-0.009098193866039868.423710060655440.185388133210594
838.38.17193389152298-0.01875946497161588.44682557344863-0.128066108477016
848.38.13927312843916-0.003394167943364368.46412103950421-0.160726871560842
858.38.12076198896747-0.002178494527250088.48141650555978-0.179238011032528
868.48.30349314715340.01424063414549318.4822662187011-0.0965068528465949
878.48.309301287085260.007582781072308748.48311593184243-0.0906987129147367
888.58.490746372034340.02240618734568728.48684744061998-0.00925362796566453
898.68.702960671751940.006460378850532248.490578949397530.102960671751942
908.68.71310662675737-0.01267075539589018.499564128638520.113106626757366
918.68.6924833261037-0.001032633983221538.508549307879520.0924833261037001
928.68.686371655107870.001034440920800568.512593903971330.0863716551078735
938.68.68795222957973-0.004590729642857288.516638500063130.0879522295797255
948.58.49448289434816-0.009098193866039868.51461529951788-0.00551710565184393
958.48.30616736599898-0.01875946497161588.51259209897264-0.0938326340010196
968.48.30655316559951-0.003394167943364368.49684100234385-0.0934468344004884
978.48.32108858881218-0.002178494527250088.48108990571507-0.0789114111878195
988.58.537734423382690.01424063414549318.448024942471820.0377344233826875
998.58.577457239699120.007582781072308748.414959979228570.0774572396991218
1008.68.804298149799880.02240618734568728.373295662854440.204298149799877
1018.68.861908274669170.006460378850532248.33163134648030.261908274669166
1028.48.52863010050707-0.01267075539589018.284040654888830.128630100507065
1038.28.16458267068587-0.001032633983221538.23644996329735-0.0354173293141269
10487.820075229709260.001034440920800568.17889032936994-0.179924770290745
10587.88326003420032-0.004590729642857288.12133069544254-0.116739965799683
10687.94883916659534-0.009098193866039868.0602590272707-0.0511608334046603
10788.01957210587276-0.01875946497161587.999187359098860.0195721058727578
1087.97.87082639229931-0.003394167943364367.93256777564405-0.0291736077006899
1097.97.936230302338-0.002178494527250087.865948192189250.0362303023380006
1107.87.7959897847590.01424063414549317.7897695810955-0.00401021524099221
1117.87.878826248925940.007582781072308747.713590970001750.0788262489259433
11288.342409112769260.02240618734568727.635184699885060.342409112769257
1137.88.03676119138110.006460378850532247.556778429768360.236761191381106
1147.47.33136813428096-0.01267075539589017.48130262111493-0.0686318657190395
1157.26.99520582152172-0.001032633983221537.4058268124615-0.204794178478276
11676.672724798204340.001034440920800567.32624076087486-0.327275201795659
11776.75793602035464-0.004590729642857287.24665470928822-0.242063979645359
1187.27.23779323198578-0.009098193866039867.171304961880260.0377932319857779
1197.27.3228042504993-0.01875946497161587.09595521447230.122804250499309
1207.27.34852080462959-0.003394167943364367.054873363313780.148520804629588
12176.988386982372-0.002178494527250087.01379151215524-0.0116130176279947
1226.96.778195596193930.01424063414549317.00756376966057-0.121804403806068
1236.86.591081191761790.007582781072308747.0013360271659-0.208918808238213
1246.86.570637160547620.02240618734568727.00695665210669-0.229362839452381
1256.86.580962344101990.006460378850532247.01257727704748-0.219037655898013
1266.96.77554978434622-0.01267075539589017.03712097104967-0.124450215653784
1277.27.33936796893135-0.001032633983221537.061664665051870.139367968931354
1287.27.281117326777080.001034440920800567.117848232302120.08111732677708
1297.27.23055893009049-0.004590729642857287.174031799552370.0305589300904874
1307.16.96335506260602-0.009098193866039867.24574313126002-0.13664493739398
1317.27.10130500200395-0.01875946497161587.31745446296767-0.0986949979960521
1327.37.2131920151143-0.003394167943364367.39020215282906-0.0868079848856924
1337.57.5392286518368-0.002178494527250087.462949842690440.0392286518368063
1347.67.647638588157580.01424063414549317.538120777696930.0476385881575778
1357.77.779125506224280.007582781072308747.613291712703410.0791255062242788
1367.77.687495232251770.02240618734568727.69009858040254-0.0125047677482319
1377.77.626634173047790.006460378850532247.76690544810168-0.073365826952208
1387.87.77481947040055-0.01267075539589017.83785128499533-0.0251805295994449
13988.09223551209423-0.001032633983221537.9087971218890.092235512094228
1408.18.225400132803420.001034440920800567.973565426275780.125400132803421
1418.18.1662569989803-0.004590729642857288.038333730662560.0662569989802932
14287.91000738176733-0.009098193866039868.09909081209871-0.0899926182326691
1438.18.05891157143676-0.01875946497161588.15984789353486-0.0410884285632402
1448.28.18872116949574-0.003394167943364368.21467299844763-0.0112788305042617
1458.38.33268039116686-0.002178494527250088.26949810336040.0326803911668545
1468.48.473612082567780.01424063414549318.312147283286730.0736120825677808
1478.48.437620755714640.007582781072308748.354796463213060.0376207557146362
1488.48.383162991647230.02240618734568728.39443082100709-0.0168370083527751
1498.58.559474442348350.006460378850532248.434065178801120.059474442348348
1508.58.5394404231252-0.01267075539589018.473230332270690.0394404231251979
1518.68.68863714824296-0.001032633983221538.512395485740260.0886371482429595
1528.68.648276900956510.001034440920800568.550688658122690.0482769009565107
1538.58.41560889913774-0.004590729642857288.58898183050511-0.0843911008622573
1548.58.38300116063706-0.009098193866039868.62609703322898-0.116998839362944
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932569hwl0ofupag9tfx9/1mzd91292932523.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932569hwl0ofupag9tfx9/1mzd91292932523.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932569hwl0ofupag9tfx9/2x8uc1292932523.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932569hwl0ofupag9tfx9/2x8uc1292932523.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932569hwl0ofupag9tfx9/3x8uc1292932523.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932569hwl0ofupag9tfx9/3x8uc1292932523.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932569hwl0ofupag9tfx9/4q0ux1292932523.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292932569hwl0ofupag9tfx9/4q0ux1292932523.ps (open in new window)


 
Parameters (Session):
par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;
 
Parameters (R input):
par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;
 
R code (references can be found in the software module):
par1 <- as.numeric(par1) #seasonal period
if (par2 != 'periodic') par2 <- as.numeric(par2) #s.window
par3 <- as.numeric(par3) #s.degree
if (par4 == '') par4 <- NULL else par4 <- as.numeric(par4)#t.window
par5 <- as.numeric(par5)#t.degree
if (par6 != '') par6 <- as.numeric(par6)#l.window
par7 <- as.numeric(par7)#l.degree
if (par8 == 'FALSE') par8 <- FALSE else par9 <- TRUE #robust
nx <- length(x)
x <- ts(x,frequency=par1)
if (par6 != '') {
m <- stl(x,s.window=par2, s.degree=par3, t.window=par4, t.degre=par5, l.window=par6, l.degree=par7, robust=par8)
} else {
m <- stl(x,s.window=par2, s.degree=par3, t.window=par4, t.degre=par5, l.degree=par7, robust=par8)
}
m$time.series
m$win
m$deg
m$jump
m$inner
m$outer
bitmap(file='test1.png')
plot(m,main=main)
dev.off()
mylagmax <- nx/2
bitmap(file='test2.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(x),lag.max = mylagmax,main='Observed')
acf(as.numeric(m$time.series[,'trend']),na.action=na.pass,lag.max = mylagmax,main='Trend')
acf(as.numeric(m$time.series[,'seasonal']),na.action=na.pass,lag.max = mylagmax,main='Seasonal')
acf(as.numeric(m$time.series[,'remainder']),na.action=na.pass,lag.max = mylagmax,main='Remainder')
par(op)
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
spectrum(as.numeric(x),main='Observed')
spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'trend']),'trend']),main='Trend')
spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'seasonal']),'seasonal']),main='Seasonal')
spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'remainder']),'remainder']),main='Remainder')
par(op)
dev.off()
bitmap(file='test4.png')
op <- par(mfrow = c(2,2))
cpgram(as.numeric(x),main='Observed')
cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'trend']),'trend']),main='Trend')
cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'seasonal']),'seasonal']),main='Seasonal')
cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'remainder']),'remainder']),main='Remainder')
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Seasonal Decomposition by Loess - Parameters',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Component',header=TRUE)
a<-table.element(a,'Window',header=TRUE)
a<-table.element(a,'Degree',header=TRUE)
a<-table.element(a,'Jump',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Seasonal',header=TRUE)
a<-table.element(a,m$win['s'])
a<-table.element(a,m$deg['s'])
a<-table.element(a,m$jump['s'])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Trend',header=TRUE)
a<-table.element(a,m$win['t'])
a<-table.element(a,m$deg['t'])
a<-table.element(a,m$jump['t'])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Low-pass',header=TRUE)
a<-table.element(a,m$win['l'])
a<-table.element(a,m$deg['l'])
a<-table.element(a,m$jump['l'])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Seasonal Decomposition by Loess - Time Series Components',6,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Seasonal',header=TRUE)
a<-table.element(a,'Trend',header=TRUE)
a<-table.element(a,'Remainder',header=TRUE)
a<-table.row.end(a)
for (i in 1:nx) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]+m$time.series[i,'remainder'])
a<-table.element(a,m$time.series[i,'seasonal'])
a<-table.element(a,m$time.series[i,'trend'])
a<-table.element(a,m$time.series[i,'remainder'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
 





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Software written by Ed van Stee & Patrick Wessa


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