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LOESS

*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 17:16:51 +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/t12936428753kjcx6bn48df6mf.htm/, Retrieved Wed, 29 Dec 2010 18:14:36 +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/t12936428753kjcx6bn48df6mf.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 «
347553 353245 347966 364343 341713 361162 354400 345183 341807 348712 349011 416259 360289 367557 364611 378688 351763 377765 373212 365819 364686 363333 362536 428803 375361 377205 381266 390516 366117 393928 387784 385656 385320 389053 390595 462440 402532 409070 421329 428841 404864 432633 416886 414893 417914 417518 423137 506710 436264 443712 452849 453009 437876 460041 450426 447873 444955 452043 480877 546696 483668 489627 490007 496590 480846 497677 492795 488495 486769 494455 498054 558648 506424 512528 512866 529324 508431 523026 521355 514103 513885 522150 527384 654047 543115 543200 571201 568892 537223 553186 550954 543433 557195 565522 571691 633972 575265 572364 586744 600389 578540 610778 596577 590558 597294 602384 614190 690042 639497 649304 678762 691885 667973 682032 672651 671865 671463 675917 680952 754718 694413 699390 710573 714217 702996 712370 708445 707083 etc...
 
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
Seasonal21510216
Trend1912
Low-pass1312


Seasonal Decomposition by Loess - Time Series Components
tObservedFittedSeasonalTrendRemainder
1347553348027.451370448-4063.15246568874351141.701095241474.451370447583
2353245357454.429745036-3040.20500239953352075.7752573634209.42974503606
3347966341118.8991282461803.25145226837353009.849419486-6847.10087175411
4364343364026.71675130110710.1015384793353949.181710219-316.283248698688
5341713341103.47551642-12565.989517373354888.514000953-609.524483579968
6361162365887.581753262586.097910133774355850.3203366044725.58175326174
7354400357719.022460799-5731.14913305476356812.1266722563319.02246079867
8345183343803.466161068-11264.9008528425357827.434691774-1379.53383893153
9341807337972.686324109-13201.4290354014358842.742711292-3834.31367589056
10348712348059.999394623-10596.8289107607359960.829516137-652.000605376728
11349011344967.587138496-8024.50345947902361078.916320983-4043.41286150384
12416259414719.21233505655388.7079138832362410.079751061-1539.78766494425
13360289360899.90928455-4063.15246568874363741.243181139610.909284549649
14367557372750.591925222-3040.20500239953365403.6130771785193.59192522196
15364611360352.7655745161803.25145226837367065.982973216-4258.23442548438
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40428841429533.72308751910710.1015384793417438.175374001692.723087519174
41404864402136.263729789-12565.989517373420157.725787584-2727.73627021105
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199763910763070.587608357-5731.14913305476770480.561524697-839.412391642574
200761677764162.364107419-11264.9008528425770456.5367454242485.36410741892
201759173761114.917069252-13201.4290354014770432.511966151941.91706925165
202762486764831.897861349-10596.8289107607770736.9310494122345.89786134858
203762690762363.153326805-8024.50345947902771041.350132674-326.846673195367
204809542792117.30468408955388.7079138832771577.987402028-17424.695315911
205769041770030.527794308-4063.15246568874772114.624671381989.52779430768
206770889771737.177953819-3040.20500239953773081.02704858848.17795381893
207773527771203.3191219511803.25145226837774047.42942578-2323.68087804853
208789890793733.76142947310710.1015384793775336.1370320483843.76142947283
209768325772591.144879058-12565.989517373776624.8446383154266.14487905754
210772712766871.609075198586.097910133774777966.293014668-5840.39092480158
211772944772311.407742035-5731.14913305476779307.74139102-632.592257965473
212769637769862.170750144-11264.9008528425780676.730102698225.170750144287
213768546768247.710221025-13201.4290354014782045.718814376-298.289778974722
214775013777184.482292629-10596.8289107607783438.3466181322171.48229262908
215776635776463.529037592-8024.50345947902784830.974421887-171.470962407999
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/29/t12936428753kjcx6bn48df6mf/1e5601293643005.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t12936428753kjcx6bn48df6mf/1e5601293643005.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t12936428753kjcx6bn48df6mf/2e5601293643005.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t12936428753kjcx6bn48df6mf/2e5601293643005.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t12936428753kjcx6bn48df6mf/36w531293643005.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t12936428753kjcx6bn48df6mf/36w531293643005.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t12936428753kjcx6bn48df6mf/4h6mo1293643005.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t12936428753kjcx6bn48df6mf/4h6mo1293643005.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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