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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: Wed, 29 Dec 2010 15:16:02 +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/29/t1293635662bmymcs9ibowbimq.htm/, Retrieved Wed, 29 Dec 2010 16:14:27 +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/29/t1293635662bmymcs9ibowbimq.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 «
315.42 316.32 316.49 317.56 318.13 318.00 316.39 314.66 313.68 313.18 314.66 315.43 316.27 316.81 317.42 318.87 319.87 319.43 318.01 315.75 314.00 313.68 314.84 316.03 316.73 317.54 318.38 319.31 320.42 319.61 318.42 316.64 314.83 315.15 315.95 316.85 317.78 318.40 319.53 320.41 320.85 320.45 319.44 317.25 316.12 315.27 316.53 317.53 318.58 318.92 319.70 321.22 322.08 321.31 319.58 317.61 316.05 315.83 316.91 318.20 319.41 320.07 320.74 321.40 322.06 321.73 320.27 318.54 316.54 316.71 317.53 318.55 319.27 320.28 320.73 321.97 322.00 321.71 321.05 318.71 317.65 317.14 318.71 319.25 320.46 321.43 322.22 323.54 323.91 323.59 322.26 320.21 318.48 317.94 319.63 320.87 322.17 322.34 322.88 324.25 324.83 323.93 322.39 320.76 319.10 319.23 320.56 321.80 322.40 322.99 323.73 324.86 325.41 325.19 323.97 321.92 320.10 319.96 320.97 322.48 323.52 323.89 325.04 326.01 326.67 325.96 325.13 322.90 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time10 seconds
R Server'George Udny Yule' @ 72.249.76.132


Seasonal Decomposition by Loess - Parameters
ComponentWindowDegreeJump
Seasonal38410385
Trend1912
Low-pass1312


Seasonal Decomposition by Loess - Time Series Components
tObservedFittedSeasonalTrendRemainder
1315.42315.683821819114-0.0801751031857762315.2363532840720.263821819113673
2316.32316.7404590038980.563090582017656315.3364504140840.420459003897918
3316.49316.2686585583221.27479389758093315.436547544097-0.221341441677623
4317.56317.1903512511042.39344119163746315.536207557258-0.369648748895713
5318.13317.7332940077432.89083842183715315.63586757042-0.396705992256955
6318317.9789571122222.29014173617620315.730901151602-0.0210428877780942
7316.39316.1024326820370.851632585179337315.825934732784-0.287567317963294
8314.66314.556275944943-1.15437333592829315.918097390986-0.103724055057455
9313.68314.277306822825-2.92756687201237316.0102600491880.597306822824748
10313.18313.407100765093-3.16492775386903316.1178269887760.227100765092871
11314.66315.095644767087-2.00103869545191316.2253939283650.435644767087126
12315.43315.464264693645-0.935856696119192316.3315920024740.0342646936447863
13316.27316.182385026602-0.0801751031857762316.437790076584-0.0876149733982743
14316.81316.5388863945060.563090582017656316.518023023476-0.271113605493838
15317.42316.9669501320511.27479389758093316.598255970368-0.453049867949346
16318.87318.6973499487362.39344119163746316.649208859626-0.172650051263872
17319.87320.1489998292782.89083842183715316.7001617488840.278999829278462
18319.43319.8209449381632.29014173617620316.7489133256600.390944938163443
19318.01318.3707025123840.851632585179337316.7976649024360.360702512384364
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25316.73316.504285979245-0.0801751031857762317.035889123941-0.225714020754879
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28319.31318.9691977169722.39344119163746317.257361091391-0.340802283028268
29320.42320.5982370289642.89083842183715317.3509245491990.178237028964190
30319.61319.4836381601162.29014173617620317.446220103707-0.126361839883657
31318.42318.4468517566040.851632585179337317.5415156582160.0268517566044579
32316.64316.806409705409-1.15437333592829317.6279636305190.166409705409137
33314.83314.87315526919-2.92756687201237317.7144116028220.0431552691902084
34315.15315.678893704085-3.16492775386903317.7860340497840.528893704085249
35315.95316.043382198707-2.00103869545191317.8576564967450.0933821987065357
36316.85316.718173154173-0.935856696119192317.917683541946-0.131826845826708
37317.78317.662464516039-0.0801751031857762317.977710587146-0.117535483960751
38318.4318.1989986543170.563090582017656318.037910763665-0.201001345683153
39319.53319.6870951622351.27479389758093318.0981109401840.157095162234555
40320.41320.2682386881042.39344119163746318.158320120258-0.141761311895834
41320.85320.5906322778312.89083842183715318.218529300332-0.259367722169429
42320.45320.332139147882.29014173617620318.277719115943-0.117860852119691
43319.44319.6914584832660.851632585179337318.3369089315550.251458483265992
44317.25317.26647597963-1.15437333592829318.3878973562980.0164759796302860
45316.12316.728681090971-2.92756687201237318.4388857810410.608681090970947
46315.27315.213256865742-3.16492775386903318.491670888127-0.0567431342577152
47316.53316.51658270024-2.00103869545191318.544455995212-0.0134172997601922
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50318.92318.6062100952730.563090582017656318.670699322709-0.313789904726718
51319.7319.4232569708931.27479389758093318.701949131526-0.276743029106569
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53322.08322.4989232945322.89083842183715318.7702382836300.418923294532476
54321.31321.5037271322162.29014173617620318.8261311316080.193727132216168
55319.58319.4263434352360.851632585179337318.882023979585-0.153656564764219
56317.61317.428743128063-1.15437333592829318.945630207865-0.181256871936853
57316.05316.018330435867-2.92756687201237319.009236436145-0.0316695641330398
58315.83315.769502587224-3.16492775386903319.055425166645-0.0604974127757032
59316.91316.719424798308-2.00103869545191319.101613897144-0.190575201692127
60318.2318.193946943795-0.935856696119192319.141909752324-0.00605305620513263
61319.41319.717969495681-0.0801751031857762319.1822056075050.307969495681220
62320.07320.3404622677910.563090582017656319.2364471501910.27046226779089
63320.74320.9145174095411.27479389758093319.2906886928780.174517409540783
64321.4321.0654745497162.39344119163746319.341084258647-0.334525450284275
65322.06321.8376817537482.89083842183715319.391479824415-0.222318246252428
66321.73321.7484295354442.29014173617620319.421428728380.0184295354439428
67320.27320.2369897824760.851632585179337319.451377632344-0.0330102175237244
68318.54318.764868010603-1.15437333592829319.4695053253250.224868010603245
69316.54316.519933853707-2.92756687201237319.487633018306-0.0200661462934022
70316.71317.082685154100-3.16492775386903319.5022425997690.372685154099543
71317.53317.544186514219-2.00103869545191319.5168521812330.0141865142187498
72318.55318.505087058492-0.935856696119192319.530769637627-0.0449129415078460
73319.27319.075488009165-0.0801751031857762319.544687094021-0.194511990835281
74320.28320.4190340113120.563090582017656319.577875406670.139034011312162
75320.73320.57414238311.27479389758093319.611063719319-0.155857616900221
76321.97321.8696703186782.39344119163746319.676888489685-0.100329681321966
77322321.3664483181132.89083842183715319.74271326005-0.633551681886843
78321.71321.2981446304802.29014173617620319.831713633343-0.411855369519515
79321.05321.3276534081840.851632585179337319.9207140066370.277653408183824
80318.71318.540208427719-1.15437333592829320.034164908209-0.169791572280872
81317.65318.079951062231-2.92756687201237320.1476158097810.429951062230941
82317.14317.163628995732-3.16492775386903320.2812987581370.0236289957319968
83318.71319.006056988959-2.00103869545191320.4149817064930.296056988959208
84319.25318.889848798045-0.935856696119192320.546007898074-0.360151201954864
85320.46320.32314101353-0.0801751031857762320.677034089655-0.13685898646969
86321.43321.5153815971870.563090582017656320.7815278207950.0853815971872791
87322.22322.2791845504841.27479389758093320.8860215519350.0591845504843604
88323.54323.7086567983132.39344119163746320.9779020100490.168656798313236
89323.91323.8593791099992.89083842183715321.069782468164-0.0506208900010847
90323.59323.7202767324412.29014173617620321.1695815313830.130276732441018
91322.26322.3989868202190.851632585179337321.2693805946020.138986820219088
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93318.48318.439316718942-2.92756687201237321.44825015307-0.0406832810577953
94317.94317.53027919456-3.16492775386903321.514648559309-0.409720805440145
95319.63319.679991729904-2.00103869545191321.5810469655480.0499917299036952
96320.87321.048688429135-0.935856696119192321.6271682669840.178688429134695
97322.17322.746885534765-0.0801751031857762321.6732895684210.576885534764983
98322.34322.3999613112150.563090582017656321.7169481067670.0599613112150905
99322.88322.7245994573051.27479389758093321.760606645114-0.155400542694622
100324.25324.2887241671702.39344119163746321.8178346411930.0387241671697325
101324.83324.8940989408912.89083842183715321.8750626372720.0640989408909718
102323.93323.6325200978592.29014173617620321.937338165964-0.297479902140651
103322.39321.9287537201640.851632585179337321.999613694657-0.461246279836303
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105319.1319.000413500134-2.92756687201237322.127153371879-0.0995864998664615
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108321.8322.177764068063-0.935856696119192322.3580926280560.377764068063243
109322.4322.435705502296-0.0801751031857762322.444469600890.0357055022956843
110322.99322.8865421549010.563090582017656322.530367263081-0.103457845099115
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113325.41325.1810617283622.89083842183715322.748099849801-0.228938271637730
114325.19325.2729201049972.29014173617620322.8169381588270.0829201049971857
115323.97324.2025909469680.851632585179337322.8857764678530.232590946968116
116321.92322.019910805257-1.15437333592829322.9744625306710.0999108052572524
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119320.97320.693007757348-2.00103869545191323.248030938104-0.276992242652398
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128322.9322.876556805681-1.15437333592829324.077816530247-0.0234431943187019
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140324.42324.562581052019-1.15437333592829325.4317922839090.142581052019352
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174331.9332.0453737843582.29014173617620329.4644844794660.145373784358185
175330.7330.9590755649080.851632585179337329.5892918499120.259075564908244
176329.15329.778062330352-1.15437333592829329.6763110055760.628062330351895
177327.34327.844236710772-2.92756687201237329.763330161240.504236710771977
178327.02327.383924452007-3.16492775386903329.8210033018620.36392445200687
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183331.32331.4187678854241.27479389758093329.9464382169950.098767885424195
184332.48332.5874592373292.39344119163746329.9790995710330.107459237329351
185332.92332.9374006530912.89083842183715330.0117609250710.0174006530913857
186332.08331.8007526421232.29014173617620330.069105621701-0.279247357877068
187331.02331.0619170964900.851632585179337330.126450318330.0419170964904083
188329.24329.447878330447-1.15437333592829330.1864950054810.207878330447215
189327.28327.241027179380-2.92756687201237330.246539692632-0.0389728206196764
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316348.17348.4845520107352.39344119163746345.4620067976270.314552010735326
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329350.04350.3659451039422.89083842183715346.8232164742210.325945103941820
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341351.7351.9858409133582.89083842183715348.5233206648040.285840913358413
342351.11351.2139188598712.29014173617620348.7159394039530.103918859870532
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348348.82348.548316365629-0.935856696119192350.02754033049-0.271683634370902
349350.29350.407701469620-0.0801751031857762350.2524736335660.117701469619590
350351.58352.1295748577720.563090582017656350.467334560210.549574857772313
351352.08352.2030106155651.27479389758093350.6821954868540.123010615565136
352353.45353.6299639431022.39344119163746350.8765948652600.179963943102166
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358348.74348.798194331347-3.16492775386903351.8467334225220.0581943313466127
359349.93349.880504617059-2.00103869545191351.980534078393-0.0494953829409042
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362352.93352.9631875864450.563090582017656352.3337218315370.0331875864454787
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378355.99355.8274576815122.29014173617620353.862400582312-0.162542318487965
379354.58354.3502380759380.851632585179337353.958129338882-0.229761924061677
380352.68352.464583347172-1.15437333592829354.049789988756-0.215416652827969
381350.72350.226116233382-2.92756687201237354.141450638630-0.493883766617898
382350.92350.773950615944-3.16492775386903354.230977137925-0.146049384055743
383352.55352.780535058233-2.00103869545191354.3205036372190.230535058232533
384353.91354.344411555908-0.935856696119192354.4114451402110.4344115559079
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293635662bmymcs9ibowbimq/177v61293635751.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293635662bmymcs9ibowbimq/177v61293635751.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293635662bmymcs9ibowbimq/2igcr1293635751.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293635662bmymcs9ibowbimq/2igcr1293635751.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293635662bmymcs9ibowbimq/3igcr1293635751.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293635662bmymcs9ibowbimq/3igcr1293635751.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293635662bmymcs9ibowbimq/4b7bc1293635751.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293635662bmymcs9ibowbimq/4b7bc1293635751.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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