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workshop 5 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: Thu, 09 Dec 2010 21:06:26 +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/09/t12919287678xr88iynk2rj40d.htm/, Retrieved Thu, 09 Dec 2010 22:06:12 +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/09/t12919287678xr88iynk2rj40d.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 «
235.1 280.7 264.6 240.7 201.4 240.8 241.1 223.8 206.1 174.7 203.3 220.5 299.5 347.4 338.3 327.7 351.6 396.6 438.8 395.6 363.5 378.8 357 369 464.8 479.1 431.3 366.5 326.3 355.1 331.6 261.3 249 205.5 235.6 240.9 264.9 253.8 232.3 193.8 177 213.2 207.2 180.6 188.6 175.4 199 179.6 225.8 234 200.2 183.6 178.2 203.2 208.5 191.8 172.8 148 159.4 154.5 213.2 196.4 182.8 176.4 153.6 173.2 171 151.2 161.9 157.2 201.7 236.4 356.1 398.3 403.7 384.6 365.8 368.1 367.9 347 343.3 292.9 311.5 300.9 366.9 356.9 329.7 316.2 269 289.3 266.2 253.6 233.8 228.4 253.6 260.1 306.6 309.2 309.5 271 279.9 317.9 298.4 246.7 227.3 209.1 259.9 266 320.6 308.5 282.2 262.7 263.5 313.1 284.3 252.6 250.3 246.5 312.7 333.2 446.4 511.6 515.5 506.4 483.2 522.3 509.8 460.7 405.8 375 378.5 406.8 467.8 469.8 429.8 355.8 332.7 378 360.5 334.7 319.5 323.1 363.6 352.1 411.9 388.6 416.4 360.7 338 417.2 388. etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time12 seconds
R Server'George Udny Yule' @ 72.249.76.132


Seasonal Decomposition by Loess - Parameters
ComponentWindowDegreeJump
Seasonal37210373
Trend1912
Low-pass1312


Seasonal Decomposition by Loess - Time Series Components
tObservedFittedSeasonalTrendRemainder
1235.1214.82909453061945.7272473679813209.643658101400-20.2709054693809
2280.7293.79906118565654.3836745318679213.21726428247613.0990611856561
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6240.8211.24207795285141.0692991453643229.288622901785-29.5579220471488
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8223.8223.647314722719-14.5248380372195238.477523314501-0.152685277281023
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198445.3469.69518597935741.0692991453643379.83551487527824.3951859793573
199367.5341.51919192003817.4217692376093376.059038842353-25.9808080799619
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205394.1385.260779698845.7272473679813357.211972933219-8.83922030120016
206417.2425.63332454445254.3836745318679354.3830009236808.4333245444517
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212316.5320.461945683398-14.5248380372195327.0628923538213.96194568339848
213284.2280.437319602534-32.4327455262893320.395425923755-3.76268039746623
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232266.4251.232088456701-9.14411997212568290.712031515424-15.1679115432987
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234362.8388.1301124410941.0692991453643296.40058841354625.3301124410898
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270466.9491.15663152615641.0692991453643401.5740693284824.2566315261560
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273429.2444.425808560584-32.4327455262893446.40693696570615.2258085605835
274425.9444.072916637118-48.7799560450432456.50703940792518.1729166371179
275460.7482.407126237528-27.6142680876733466.60714185014521.7071262375284
276463.6479.828155289703-26.2016910964050473.57353580670216.2281552897028
277541.4556.53282286875945.7272473679813480.53992976325915.1328228687594
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289544.7546.3624339943945.7272473679813497.3103186376291.66243399439003
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292469.7456.638818458819-9.14411997212568491.905301513306-13.0611815411805
293434.4409.649710277813-30.7799655797835489.930255301971-24.7502897221873
294542.6557.8870815167441.0692991453643486.24361933789615.2870815167401
295517.3534.6212473885717.4217692376093482.5569833738217.3212473885702
296485.7508.482353032142-14.5248380372195477.44248500507722.7823530321421
297465.8491.704758889955-32.4327455262893472.32798663633425.9047588899550
298447476.283353657492-48.7799560450432466.49660238755129.2833536574925
299426.6420.149049948906-27.6142680876733460.665218138767-6.45095005109386
300411.6394.754195906014-26.2016910964050454.647495190391-16.8458040939860
301467.5440.64298039000445.7272473679813448.629772242015-26.8570196099959
302484.5471.16993125320754.3836745318679443.446394214925-13.3300687467930
303451.2433.26138905299730.8755947591673438.263016187835-17.9386109470027
304417.4408.588920891701-9.14411997212568435.355199080424-8.81107910829854
305379.9358.132583606770-30.7799655797835432.447381973013-21.7674163932295
306484.7495.79391952252041.0692991453643432.53678133211611.0939195225195
307455459.95205007117117.4217692376093432.6261806912194.95205007117124
308420.8421.629786515983-14.5248380372195434.4950515212360.829786515983187
309416.5429.068823175036-32.4327455262893436.36392235125312.5688231750361
310376.3362.737391673690-48.7799560450432438.642564371353-13.5626083263096
311405.6397.893061696221-27.6142680876733440.921206391453-7.70693830377922
312405.8393.205936461850-26.2016910964050444.595754634555-12.5940635381496
313500.8507.60244975436245.7272473679813448.2703028776566.80244975436233
314514518.7520696954254.3836745318679454.8642557727124.75206969541961
315475.5458.66619657306430.8755947591673461.458208667769-16.8338034269358
316430.1396.985507890066-9.14411997212568472.35861208206-33.1144921099344
317414.4376.320950083432-30.7799655797835483.259015496352-38.0790499165681
318538533.60938039926141.0692991453643501.321320455375-4.39061960073889
319526515.19460534799317.4217692376093519.383625414398-10.8053946520070
320488.5445.929816598915-14.5248380372195545.595021438304-42.5701834010845
321520.2501.026328064079-32.4327455262893571.80641746221-19.173671935921
322504.4455.492843514319-48.7799560450432602.087112530724-48.9071564856807
323568.5532.246460488436-27.6142680876733632.367807599237-36.253539511564
324610.6586.173699944291-26.2016910964050661.227991152114-24.4263000557088
325818900.18457792702945.7272473679813690.0881747049982.1845779270286
326830.9893.21468141787254.3836745318679714.2016440502662.314681417872
327835.9902.60929184530330.8755947591673738.3151133955366.7092918453028
328782818.767234243614-9.14411997212568754.37688572851136.7672342436143
329762.3784.94130751829-30.7799655797835770.43865806149322.6413075182905
330856.9896.47021830389741.0692991453643776.26048255073939.5702183038967
331820.9842.29592372240617.4217692376093782.08230703998521.3959237224055
332769.6774.491826208536-14.5248380372195779.2330118286844.89182620853569
333752.2760.449028908907-32.4327455262893776.3837166173838.24902890890678
334724.4728.719956043672-48.7799560450432768.8600000013714.31995604367216
335723.1712.477984702314-27.6142680876733761.336283385359-10.6220152976858
336719.5711.792069242997-26.2016910964050753.409621853408-7.70793075700328
337817.4843.58979231056145.7272473679813745.48296032145726.1897923105614
338803.3812.05615568618554.3836745318679740.1601697819478.75615568618468
339752.5739.28702599839530.8755947591673734.837379242437-13.2129740016046
340689655.172295290788-9.14411997212568731.971824681337-33.8277047092117
341630.4562.473695459546-30.7799655797835729.106270120238-67.9263045404541
342765.5761.99356103171541.0692991453643727.93713982292-3.50643896828478
343757.7771.21022123678717.4217692376093726.76800952560313.5102212367873
344732.2751.82654245377-14.5248380372195727.0982955834519.6265424537694
345702.6710.204163884992-32.4327455262893727.4285816412977.60416388499243
346683.3688.558515066544-48.7799560450432726.82144097855.25851506654385
347709.5720.399967771972-27.6142680876733726.21430031570210.8999677719717
348702.2707.766749750501-26.2016910964050722.8349413459045.566749750501
349784.8804.41717025591245.7272473679813719.45558237610619.6171702559125
350810.9853.30055489880854.3836745318679714.11577056932442.4005548988077
351755.6771.54844647829130.8755947591673708.77595876254215.9484464782906
352656.8620.197589074523-9.14411997212568702.546530897603-36.6024109254773
353615.1564.66286254712-30.7799655797835696.317103032664-50.4371374528804
354745.3761.07575859312141.0692991453643688.45494226151415.7757585931213
355694.1690.18544927202617.4217692376093680.592781490365-3.91455072797407
356675.7693.6588622882-14.5248380372195672.2659757490217.9588622882000
357643.7655.893575518615-32.4327455262893663.93917000767412.1935755186150
358622.1637.039310150027-48.7799560450432655.94064589501614.9393101500268
359634.6648.872146305315-27.6142680876733647.94212178235814.2721463053151
360588561.989746209275-26.2016910964050640.21194488713-26.0102537907248
361689.7701.19098464011845.7272473679813632.48176799190111.4909846401175
362673.9667.74424540596354.3836745318679625.672080062169-6.15575459403692
363647.9646.06201310839630.8755947591673618.862392132437-1.83798689160380
364568.8531.505368588922-9.14411997212568615.238751383204-37.2946314110781
365545.7510.564854945813-30.7799655797835611.615110633971-35.1351450541874
366632.6616.09556261465341.0692991453643608.035138239983-16.5044373853473
367643.8665.72306491639617.4217692376093604.45516584599521.9230649163957
368593.1599.40580716076-14.5248380372195601.319030876466.30580716075997
369579.7593.649849619365-32.4327455262893598.18289590692413.9498496193652
370546545.275613718932-48.7799560450432595.504342326111-0.724386281068064
371562.9560.588479342375-27.6142680876733592.825788745298-2.31152065762501
372572.5580.789109242778-26.2016910964050590.4125818536278.28910924277773
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/09/t12919287678xr88iynk2rj40d/10cpo1291928773.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t12919287678xr88iynk2rj40d/10cpo1291928773.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t12919287678xr88iynk2rj40d/20cpo1291928773.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t12919287678xr88iynk2rj40d/20cpo1291928773.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t12919287678xr88iynk2rj40d/3blpr1291928773.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t12919287678xr88iynk2rj40d/3blpr1291928773.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t12919287678xr88iynk2rj40d/4lu6b1291928773.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t12919287678xr88iynk2rj40d/4lu6b1291928773.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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