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Paper: analyse (18t/m24) 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: Tue, 28 Dec 2010 19:11:36 +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/28/t1293563396s17dqnk6u25zu1b.htm/, Retrieved Tue, 28 Dec 2010 20:10:01 +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/28/t1293563396s17dqnk6u25zu1b.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 «
49915 47469 45652 43492 41087 42931 67256 72316 65624 59450 52851 51214 44092 43752 40320 40551 38329 39530 59648 61031 55560 43877 38510 36085 35994 32617 30001 27894 26083 28817 48742 49915 40264 34276 30426 30793 29855 28081 26820 25782 22654 27373 43675 45096 38145 34017 31537 33814 36531 36935 36497 35110 33137 37407 53963 56602 49694 43957 41723 45599 42503 42153 39098 37449 34748 36548 53639 55289 47774 42156 38019
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'George Udny Yule' @ 72.249.76.132


Seasonal Decomposition by Loess - Parameters
ComponentWindowDegreeJump
Seasonal711072
Trend1912
Low-pass1312


Seasonal Decomposition by Loess - Time Series Components
tObservedFittedSeasonalTrendRemainder
14991550676.769197431-2735.8067548853451889.0375574544761.769197430956
24746946737.0109408704-3863.2955429859552064.2846021156-731.98905912965
34565244844.5853834577-5780.1170302344852239.5316467768-807.414616542344
44349241578.2156038576-6937.6738494808552343.4582456233-1913.78439614244
54108738843.5126958719-9116.8975403416952447.3848444698-2243.48730412807
64293139624.0764107556-6218.4838210894852456.4074103339-3306.9235892444
76725669075.142464189112971.427559612952465.4299761981819.14246418913
87231676910.293356681115298.745932341452422.96071097744594.29335668113
96562470660.4436227918207.0649314521852380.49144575685036.44362279099
105945064926.31508137921800.0130585074152173.67186011345476.31508137923
115285155898.6854584694-2163.5377329392651966.85227446993047.68545846936
125121452543.108408941-1461.4430158174951346.33460687651329.10840894101
134409240193.9898156023-2735.8067548853450725.8169392831-3898.01018439772
144375241538.285179155-3863.2955429859549829.010363831-2213.71482084503
154032037487.9132418556-5780.1170302344848932.2037883789-2832.08675814442
164055140106.806675642-6937.6738494808547932.8671738388-444.193324357955
173832938841.366981043-9116.8975403416946933.5305592987512.366981042971
183953039285.1830528128-6218.4838210894845993.3007682767-244.816947187195
195964861271.501463132512971.427559612945053.07097725461623.50146313250
206103162642.809710099515298.745932341444120.4443575591611.80971009952
215556059725.11733068448207.0649314521843187.81773786344165.11733068441
224387743798.35649494411800.0130585074142155.6304465485-78.6435050558939
233851038060.0945777057-2163.5377329392641123.4431552336-449.905422294294
243608533556.5757576067-1461.4430158174940074.8672582108-2528.42424239327
253599435697.5153936974-2735.8067548853439026.291361188-296.484606302634
263261731045.4688375994-3863.2955429859538051.8267053865-1571.53116240056
273000128704.7549806494-5780.1170302344837077.3620495850-1296.24501935056
282789426437.3368016021-6937.6738494808536288.3370478788-1456.66319839790
292608325783.5854941692-9116.8975403416935499.3120461725-299.414505830777
302881728896.6261042698-6218.4838210894834955.857716819779.6261042698025
314874250100.169052920212971.427559612934412.40338746691358.16905292023
324991550498.405440721615298.745932341434032.8486269369583.405440721603
334026438667.64120214088207.0649314521833653.293866407-1596.35879785918
343427633376.0795387391800.0130585074133375.9074027536-899.920461260979
353042629917.0167938391-2163.5377329392633098.5209391001-508.983206160883
363079330196.4195624940-1461.4430158174932851.0234533235-596.580437506025
372985529842.2807873385-2735.8067548853432603.5259675469-12.7192126615410
382808127646.3790658403-3863.2955429859532378.9164771456-434.620934159666
392682027265.8100434901-5780.1170302344832154.3069867443445.810043490139
402578226420.5998303424-6937.6738494808532081.0740191385638.599830342362
412265422417.0564888090-9116.8975403416932007.8410515326-236.943511190952
422737328736.7992590849-6218.4838210894832227.68456200461363.79925908486
434367541931.044367910512971.427559612932447.5280724766-1743.95563208947
444509641852.743606613815298.745932341433040.5104610447-3243.25639338619
453814534449.44221893498207.0649314521833633.4928496129-3695.55778106505
463401731731.21804981631800.0130585074134502.7688916763-2285.78195018367
473153729865.4927991996-2163.5377329392635372.0449337396-1671.50720080039
483381432707.0262462828-1461.4430158174936382.4167695347-1106.97375371720
493653138405.0181495556-2735.8067548853437392.78860532971874.01814955562
503693539346.0095996253-3863.2955429859538387.28594336062411.0095996253
513649739392.3337488429-5780.1170302344839381.78328139162895.3337488429
523511036939.6931737391-6937.6738494808540217.98067574171829.69317373913
533313734336.7194702498-9116.8975403416941054.17807009191199.71947024982
543740739346.1630118732-6218.4838210894841686.32080921631939.16301187318
555396352636.108892046412971.427559612942318.4635483407-1326.89110795360
565660255170.674718443215298.745932341442734.5793492153-1431.32528155675
574969448030.2399184588207.0649314521843150.6951500899-1663.76008154205
584395742712.11233789641800.0130585074143401.8746035962-1244.88766210363
594172341956.4836758367-2163.5377329392643653.0540571026233.483675836695
604559948906.607562454-1461.4430158174943752.83545336353307.60756245403
614250343889.189905261-2735.8067548853443852.61684962431386.18990526099
624215344533.1719694339-3863.2955429859543636.12357355212380.17196943389
633909840556.4867327547-5780.1170302344843419.63029747981458.48673275471
643744938800.5084267526-6937.6738494808543035.16542272821351.50842675265
653474835962.1969923651-9116.8975403416942650.70054797661214.19699236505
663654837078.0215792735-6218.4838210894842236.4622418159530.02157927354
675363952484.348504731912971.427559612941822.2239356552-1154.65149526812
685528953922.460315312915298.745932341441356.7937523456-1366.53968468708
694777446449.57149951188207.0649314521840891.363569036-1324.42850048819
704215642127.51383605451800.0130585074140384.4731054381-28.4861639454903
713801938323.9550910991-2163.5377329392639877.5826418402304.955091099102
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/28/t1293563396s17dqnk6u25zu1b/1xxfp1293563490.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/28/t1293563396s17dqnk6u25zu1b/1xxfp1293563490.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/28/t1293563396s17dqnk6u25zu1b/286xa1293563490.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/28/t1293563396s17dqnk6u25zu1b/286xa1293563490.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/28/t1293563396s17dqnk6u25zu1b/386xa1293563490.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/28/t1293563396s17dqnk6u25zu1b/386xa1293563490.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/28/t1293563396s17dqnk6u25zu1b/4ifev1293563490.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/28/t1293563396s17dqnk6u25zu1b/4ifev1293563490.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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