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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, 07 Dec 2010 14:23:13 +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/07/t12917316983os9f6xgk568b32.htm/, Retrieved Tue, 07 Dec 2010 15:21:39 +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/07/t12917316983os9f6xgk568b32.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 «
1145,11 1176,86 1206,41 1192,72 1214,82 1199,07 1157,47 1100,1 1095,63 1105,63 1137,79 1124,72 1152,6 1211,85 1239,62 1244,13 1198,42 1227,99 1304,92 1340,26 1307,32 1356,51 1383,29 1437,87 1494,56 1521,42 1498,76 1488,75 1524,62 1439,27 1423,11 1466,85 1425,83 1363,45 1389,18 1395,89 1368,43 1349,03 1299,88 1365,41 1451,04 1433,75 1464,65 1475,57 1471,16 1429,12 1452,46 1538,09 1631,59 1665,5 1690,6 1711,74 1734,1 1748,09 1703,45 1745,74 1751,01 1795,65 1852,13 1877,1 1989,31 2097,76 2154,87 2152,18 2250,27 2346,9 2525,56 2409,36 2394,36 2401,33 2354,32 2450,41 2504,67 2661,39 2880,4 3064,42 3141,12 3327,7 3564,95 3403,13 3149,9 3006,84 3230,66 3361,13 3484,74 3411,13 3288,18 3280,37 3173,95 3165,26 3092,71 3053,05 3181,96 2999,93 3249,57 3210,52 3030,29 2803,47 2767,63 2882,6 2863,36 2897,06 3012,61 3142,95 3032,93 3045,78 3110,52 3013,24 2987,1 2995,55 2833,18 2848,96 2794,83 2845,26 2915,02 2 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk


Seasonal Decomposition by Loess - Parameters
ComponentWindowDegreeJump
Seasonal21610217
Trend1912
Low-pass1312


Seasonal Decomposition by Loess - Time Series Components
tObservedFittedSeasonalTrendRemainder
11145.111120.035011898154.656820628700431165.52816747315-25.0749881018528
21176.861184.261181951175.669324889600481163.789493159237.40118195117157
31206.411273.81734312876-23.04816197406081162.050818845367.4073431287572
41192.721181.9291703564342.47292480032721161.03790484324-10.7908296435653
51214.821223.4887985612646.12621059756431160.024990841178.6687985612632
61199.071221.9400558548316.40019108477851159.799753060422.8700558548262
71157.471143.8268661954711.53861852491371159.57451527962-13.643133804532
81100.11030.902929443949.800863360732821159.49620719532-69.1970705560577
91095.631043.06514136844-11.22304047947151159.41789911103-52.5648586315599
101105.631102.92103793521-52.43927770518141160.77823976997-2.70896206478824
111137.791145.0774291753-31.63600960421161162.138580428917.28742917530371
121124.721098.08961303303-18.31845856967471169.66884553665-26.6303869669709
131152.61123.344068726924.656820628700431177.19911064438-29.2559312730841
141211.851226.584369752975.669324889600481191.4463053574314.73436975297
151239.621296.59466190359-23.04816197406081205.6935000704856.9746619035855
161244.131220.058635169142.47292480032721225.72844003057-24.0713648308952
171198.421104.9504094117846.12621059756431245.76337999066-93.4695905882247
181227.991169.632562392616.40019108477851269.94724652263-58.3574376074048
191304.921304.1702684204911.53861852491371294.13111305459-0.749731579505578
201340.261349.924941747499.800863360732821320.794194891789.66494174748527
211307.321278.4057637505-11.22304047947151347.45727672897-28.9142362495006
221356.511393.09460811605-52.43927770518141372.3646695891336.584608116051
231383.291400.94394715492-31.63600960421161397.2720624492917.6539471549229
241437.871478.34290447445-18.31845856967471415.7155540952340.4729044744465
251494.561550.304133630134.656820628700431434.1590457411755.7441336301322
261521.421593.75231959365.669324889600481443.418355516872.3323195935968
271498.761567.89049668162-23.04816197406081452.6776652924469.1304966816222
281488.751480.8026088045242.47292480032721454.22446639515-7.94739119548149
291524.621547.3425219045746.12621059756431455.7712674978722.7225219045656
301439.271412.2838480869216.40019108477851449.85596082831-26.9861519130843
311423.111390.7407273163411.53861852491371443.94065415874-32.3692726836553
321466.851491.16736007869.800863360732821432.7317765606624.3173600786047
331425.831441.36014151689-11.22304047947151421.5228989625815.5301415168879
341363.451367.87991556646-52.43927770518141411.459362138724.42991556645939
351389.181408.60018428935-31.63600960421161401.3958253148619.4201842893513
361395.891412.92532578788-18.31845856967471397.173132781817.0353257878764
371368.431339.252739122564.656820628700431392.95044024874-29.1772608774365
381349.031298.078622673485.669324889600481394.31205243692-50.9513773265155
391299.881227.13449734897-23.04816197406081395.67366462509-72.7455026510329
401365.411286.2364203853742.47292480032721402.1106548143-79.1735796146304
411451.041447.4061443989246.12621059756431408.54764500351-3.6338556010769
421433.751427.5076881416.40019108477851423.59212077523-6.24231186000384
431464.651479.1247849281511.53861852491371438.6365965469414.4747849281482
441475.571477.968817467119.800863360732821463.370319172162.39881746711148
451471.161465.4389986821-11.22304047947151488.10404179737-5.72100131790148
461429.121394.70968148215-52.43927770518141515.96959622303-34.4103185178508
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491631.591663.697723232254.656820628700431594.8254561390532.10772323225
501665.51705.841299856175.669324889600481619.4893752542340.341299856173
511690.61760.09486760466-23.04816197406081644.153294369469.494867604657
521711.741710.2740120823442.47292480032721670.73306311733-1.46598791765996
531734.11724.7609575371746.12621059756431697.31283186526-9.33904246282577
541748.091753.8396104241316.40019108477851725.940198491095.7496104241336
551703.451640.7938163581711.53861852491371754.56756511691-62.656183641828
561745.741693.508405860619.800863360732821788.17073077866-52.2315941393942
571751.011691.46914403906-11.22304047947151821.77389644041-59.540855960937
581795.651780.41651696445-52.43927770518141863.32276074073-15.2334830355455
591852.131831.02438456317-31.63600960421161904.87162504105-21.1056154368339
601877.11815.27304437211-18.31845856967471957.24541419756-61.8269556278876
611989.311964.343976017224.656820628700432009.61920335408-24.966023982779
622097.762122.881242580835.669324889600482066.9694325295725.1212425808267
632154.872208.46850026899-23.04816197406082124.3196617050753.5985002689927
642152.182084.8078080423342.47292480032722177.07926715734-67.3721919576683
652250.272224.5749167928246.12621059756432229.83887260961-25.6950832071784
662346.92401.5282263151316.40019108477852275.8715826000954.6282263151306
672525.562717.6770888845211.53861852491372321.90429259057192.117088884519
682409.362437.676201614119.800863360732822371.2429350251628.3162016141068
692394.362379.36146301972-11.22304047947152420.58157745975-14.998536980283
702401.332372.23585491848-52.43927770518142482.8634227867-29.0941450815221
712354.322195.13074149056-31.63600960421162545.14526811365-159.18925850944
722450.412295.64892352198-18.31845856967472623.48953504769-154.761076478018
732504.672302.849377389574.656820628700432701.83380198173-201.820622610434
742661.392532.253704055115.669324889600482784.85697105529-129.136295944891
752880.42915.96802184521-23.04816197406082867.8801401288535.5680218452148
763064.423141.0666018812542.47292480032722945.3004733184276.6466018812484
773141.123213.3929828944346.12621059756433022.72080650872.2729828944334
783327.73546.6169698400916.40019108477853092.38283907513218.916969840093
793564.953956.3165098328311.53861852491373162.04487164225391.366509832833
803403.133583.574571351389.800863360732823212.88456528789180.444571351378
813149.93047.29878154595-11.22304047947153263.72425893352-102.601218454053
823006.842785.23344677554-52.43927770518143280.88583092964-221.606553224456
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843361.133452.75951334264-18.31845856967473287.8189452270491.6295133426352
853484.743687.232691842974.656820628700433277.59048752833202.49269184297
863411.133555.734641738085.669324889600483260.85603337232144.604641738079
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883280.373286.4088936935242.47292480032723231.858181506156.03889369351919
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953249.573479.48699770452-31.63600960421163051.2890118997229.916997704515
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1012863.362711.3527097599446.12621059756432969.2410796425-152.007290240061
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1844591.274719.494031506842.47292480032724420.57304369288128.224031506795
1854696.964914.8563869298146.12621059756434432.93740247263217.896386929808
1864621.44815.526916989616.40019108477854410.87289192562194.126916989597
1874562.844725.3330000964711.53861852491374388.80838137862162.493000096465
1884202.524060.990048094329.800863360732824334.24908854495-141.529951905681
1894296.494324.5132447682-11.22304047947154279.6897957112828.0232447681965
1904435.234716.976270168-52.43927770518144205.92300753719281.746270167996
1914105.184109.83979024112-31.63600960421164132.15621936314.65979024111584
1924116.684211.77824802231-18.31845856967474039.9002105473695.0982480223129
1933844.493736.678977639674.656820628700433947.64420173163-107.811022360328
1943720.983602.985303034685.669324889600483833.30537207572-117.994696965318
1953674.43652.88161955425-23.04816197406083718.96654241981-21.5183804457479
1963857.624102.9910776981942.47292480032723569.77599750149245.371077698186
1973801.064135.4083368192746.12621059756433420.58545258317334.34833681927
1983504.373744.6318751323116.40019108477853247.70793378291240.26187513231
1993032.62978.8309664924311.53861852491373074.83041498266-53.7690335075695
2003047.033189.150626447579.800863360732822895.1085101917142.120626447571
2012962.343220.51643507874-11.22304047947152715.38660540074258.176435078735
2022197.821898.65616734056-52.43927770518142549.42311036463-299.163832659444
2032014.451677.0763942757-31.63600960421162383.45961532851-337.373605724302
2041862.831483.14719511812-18.31845856967472260.83126345155-379.68280488188
2051905.411667.960267796714.656820628700432138.20291157459-237.449732203294
2061810.991532.971132360725.669324889600482083.33954274968-278.018867639284
2071670.071334.71198804929-23.04816197406082028.47617392477-335.358011950713
2081864.441616.0894859306542.47292480032722070.31758926902-248.350514069351
2092052.021945.7547847891646.12621059756432112.15900461327-106.265215210839
2102029.61884.6671119847216.40019108477852158.1326969305-144.932888015281
2112070.831926.0149922273611.53861852491372204.10638924773-144.815007772645
2122293.412320.153381761099.800863360732822256.8657548781826.7433817610918
2132443.272588.13791997085-11.22304047947152309.62512050862144.867919970852
2142513.172709.14796474379-52.43927770518142369.63131296139195.977964743787
2152466.922535.83850419004-31.63600960421162429.6375054141768.9185041900423
2162502.662529.51793849938-18.31845856967472494.1205200702926.8579384993809
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/07/t12917316983os9f6xgk568b32/1k9zc1291731787.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/07/t12917316983os9f6xgk568b32/1k9zc1291731787.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/07/t12917316983os9f6xgk568b32/2k9zc1291731787.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/07/t12917316983os9f6xgk568b32/2k9zc1291731787.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/07/t12917316983os9f6xgk568b32/3v0yf1291731787.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/07/t12917316983os9f6xgk568b32/3v0yf1291731787.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/07/t12917316983os9f6xgk568b32/4v0yf1291731787.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/07/t12917316983os9f6xgk568b32/4v0yf1291731787.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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