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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 07:38:01 +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/t129360817914pnei8ufr7i825.htm/, Retrieved Wed, 29 Dec 2010 08:36:25 +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/t129360817914pnei8ufr7i825.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 «
11974 10106 12069 11412 11180 10508 11288 10928 10199 11030 11234 13747 13912 12376 12264 11675 11271 10672 10933 10379 10187 10747 10970 12175 14200 11676 11258 10872 11148 10690 10684 11658 10178 10981 10773 11665 11359 10716 12928 12317 11641 10459 10953 10703 10703 11101 11334 13268 13145 12334 13153 11289 11374 10914 11299 11284 10694 11077 11104 12820 14915 11773 11608 11468 11511 11200 11164 10960 10667 11556 11372 12333 13102 11115 12572 11557 12059 11420 11185 11113 10706 11523 11391 12634 13469 11735 13281 11968 11623 11084 11509 11134 10438 11530 11491 13093 13106 11305 13113 12203 11309 11088 11234 11619 10942 11445 11291 13281 13726 11300 11983 11092 11093 10692 10786 11166 10553 11103 10969 12090 12544 12264 13783 11214 11453 10883 10381 10348 10024 10805 10796 11907 12261 11377 12689 11474 10992 10764 12164 10409 10398 10349 10865 11630 12221 10884 12 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Seasonal Decomposition by Loess - Parameters
ComponentWindowDegreeJump
Seasonal18010181
Trend1912
Low-pass1312


Seasonal Decomposition by Loess - Time Series Components
tObservedFittedSeasonalTrendRemainder
11197411679.99310918701706.2263900632210561.7805007498-294.006890813038
2101069491.2865997757324.99562362930410695.7177765950-614.713400224275
31206912336.1132120904972.2317354694410829.6550524401267.113212090440
41141211864.22394546430.54235871096924610959.2336958247452.223945464311
51118011435.9343383155-164.74667752476811088.8123392093255.93433831545
61050810497.5591839124-697.97544410433811216.4162601919-10.4408160875992
71128811666.3843039766-434.40448515113311344.0201811746378.384303976576
81092811003.3605238831-614.29045059546111466.929926712475.3605238830587
9101999880.47029436249-1072.3099666127411589.8396722502-318.529705637511
101103010777.0739192735-372.67912522554111655.6052059521-252.92608072652
111123411116.1441549091-369.51489456292711721.3707396539-117.855845090948
121374714747.58007418651021.9249254622711724.49500035121000.58007418649
131391214390.15434888821706.2263900632211727.6192610486478.154348888182
141237613025.159597195724.99562362930411701.8447791750649.159597195718
151226411879.6979672292972.2317354694411676.0702973014-384.302032770791
161167511726.58855311310.54235871096924611622.869088176051.5885531130607
171127111137.0787984742-164.74667752476811569.6678790506-133.92120152582
181067210529.7777876096-697.97544410433811512.1976564948-142.222212390416
191093310845.6770512122-434.40448515113311454.7274339389-87.3229487877888
20103799961.745694545-614.29045059546111410.5447560505-417.254305455008
211018710079.9478884507-1072.3099666127411366.3620781620-107.052111549277
221074710530.5482328811-372.67912522554111336.1308923444-216.451767118861
231097011003.6151880361-369.51489456292711305.899706526833.6151880361376
241217512030.79343817241021.9249254622711297.2816363654-144.206561827623
251420015405.11004373291706.2263900632211288.66356620391205.11004373287
261167612018.543650703024.99562362930411308.4607256677342.543650702963
271125810215.510379399972.2317354694411328.2578851316-1042.48962060099
281087210414.74277839450.54235871096924611328.7148628945-457.257221605469
291114811131.5748368673-164.74667752476811329.1718406574-16.4251631326752
301069010802.3468954349-697.97544410433811275.6285486695112.346895434885
311068410580.3192284697-434.40448515113311222.0852566815-103.680771530331
321165812744.7127355784-614.29045059546111185.57771501711086.71273557841
331017810279.2397932601-1072.3099666127411149.0701733526101.239793260091
341098111158.9223349938-372.67912522554111175.7567902318177.922334993782
351077310713.0714874521-369.51489456292711202.4434071109-59.9285125479455
361166511088.38517894721021.9249254622711219.6898955905-576.614821052764
37113599774.837225866671706.2263900632211236.9363840701-1584.16277413333
381071610159.929505740824.99562362930411247.0748706299-556.070494259189
391292813626.5549073409972.2317354694411257.2133571897698.554907340904
401231713324.20816630360.54235871096924611309.24947498541007.20816630358
411164112085.4610847435-164.74667752476811361.2855927812444.461084743532
421045910164.5667307117-697.97544410433811451.4087133927-294.433269288342
431095310798.872651147-434.40448515113311541.5318340041-154.127348852993
441070310412.054851328-614.29045059546111608.2355992675-290.94514867201
451070310803.3706020819-1072.3099666127411674.9393645308100.370602081923
461110110887.4192455107-372.67912522554111687.2598797148-213.580754489309
471133411337.9344996640-369.51489456292711699.58039489893.93449966404114
481326813799.34757909951021.9249254622711714.7274954382531.347579099509
491314512853.89901395921706.2263900632211729.8745959776-291.100986040767
501233412897.775888248024.99562362930411745.2284881227563.775888247963
511315313573.1858842626972.2317354694411760.5823802679420.185884262646
521128910821.96964091960.54235871096924611755.4880003694-467.030359080385
531137411162.3530570539-164.74667752476811750.3936204709-211.646942946147
541091410774.3508966684-697.97544410433811751.6245474359-139.649103331592
551129911279.5490107502-434.40448515113311752.8554744009-19.4509892498118
561128411431.9637378786-614.29045059546111750.3267127169147.963737878566
571069410712.5120155799-1072.3099666127411747.797951032818.5120155798904
581107710787.6825797412-372.67912522554111738.9965454844-289.317420258849
591110410847.319754627-369.51489456292711730.1951399359-256.680245373007
601282012894.67272004871021.9249254622711723.402354489074.6727200487403
611491516407.16404089471706.2263900632211716.60956904201492.16404089474
621177311808.293004641424.99562362930411712.711371729335.2930046414112
631160810534.9550901140972.2317354694411708.8131744165-1073.04490988597
641146811233.96083162820.54235871096924611701.4968096609-234.039168371826
651151111492.5662326196-164.74667752476811694.1804449052-18.4337673804184
661120011432.2628793255-697.97544410433811665.7125647789232.262879325479
671116411125.1598004986-434.40448515113311637.2446846525-38.8401995013974
681096010922.3986171789-614.29045059546111611.8918334166-37.601382821118
691066710819.7709844321-1072.3099666127411586.5389821806152.770984432109
701155611888.5617882319-372.67912522554111596.1173369936332.561788231931
711137211507.8192027563-369.51489456292711605.6956918066135.819202756335
721233312025.54453146991021.9249254622711618.5305430678-307.455468530106
731310212866.40821560771706.2263900632211631.3653943291-235.591784392294
741111510560.740631291324.99562362930411644.2637450794-554.259368708663
751257212514.6061687009972.2317354694411657.1620958296-57.3938312990795
761155711440.66020596310.54235871096924611672.7974353259-116.339794036914
771205912594.3139027025-164.74667752476811688.4327748222535.313902702519
781142011822.5626648829-697.97544410433811715.4127792214402.562664882918
791118511062.0117015305-434.40448515113311742.3927836206-122.988298469460
801111311067.9377371198-614.29045059546111772.3527134756-45.0622628801866
811070610681.9973232820-1072.3099666127411802.3126433307-24.0026767179679
821152311603.3781068431-372.67912522554111815.301018382480.3781068431072
831139111323.2255011288-369.51489456292711828.2893934342-67.7744988712348
841263412416.19808330461021.9249254622711829.8769912331-217.80191669542
851346913400.30902090461706.2263900632211831.4645890321-68.6909790953505
861173511612.430477104724.99562362930411832.5738992660-122.569522895268
871328113756.0850550308972.2317354694411833.6832094998475.08505503077
881196812099.65392294600.54235871096924611835.803718343131.653922946025
891162311572.8224503385-164.74667752476811837.9242271862-50.1775496614518
901108411032.1980482599-697.97544410433811833.7773958445-51.8019517401208
911150911622.7739206484-434.40448515113311829.6305645027113.773920648437
921113411067.3052142561-614.29045059546111814.9852363394-66.6947857439045
931043810147.9700584367-1072.3099666127411800.3399081760-290.0299415633
941153011644.2371030427-372.67912522554111788.4420221828114.237103042737
951149111574.9707583734-369.51489456292711776.544136189683.9707583733525
961309313387.45394411791021.9249254622711776.6211304198294.453944117946
971310612729.07548528681706.2263900632211776.69812465-376.924514713208
981130510798.091290389024.99562362930411786.9130859817-506.908709611038
991311313456.6402172171972.2317354694411797.1280473135343.640217217086
1001220312594.28377680930.54235871096924611811.1738644798391.283776809267
1011130910957.5269958787-164.74667752476811825.2196816461-351.473004121284
1021108811034.9055589167-697.97544410433811839.0698851876-53.0944410832999
1031123411049.4843964219-434.40448515113311852.9200887292-184.515603578091
1041161912012.1695936763-614.29045059546111840.1208569192393.169593676288
1051094211128.9883415036-1072.3099666127411827.3216251091186.988341503615
1061144511484.8635320976-372.67912522554111777.815593128039.8635320975827
1071129111223.2053334161-369.51489456292711728.3095611468-67.7946665838663
1081328113865.36071410231021.9249254622711674.7143604354584.360714102309
1091372614124.65445021271706.2263900632211621.1191597240398.65445021274
1101130010999.758100073624.99562362930411575.2462762970-300.24189992635
1111198311464.3948716605972.2317354694411529.3733928700-518.605128339486
1121109210695.97944333280.54235871096924611487.4781979563-396.020556667219
1131109310905.1636744823-164.74667752476811445.5830030425-187.836325517686
1141069210669.9486607918-697.97544410433811412.0267833125-22.0513392082103
1151078610627.9339215685-434.40448515113311378.4705635826-158.066078431510
1161116611545.5520703672-614.29045059546111400.7383802283379.552070367175
1171055310755.3037697388-1072.3099666127411423.0061968739202.30376973881
1181110311107.1373939792-372.67912522554111471.54173124634.13739397924837
1191096910787.4376289443-369.51489456292711520.0772656187-181.56237105573
1201209011627.93778223881021.9249254622711530.1372922989-462.062217761168
1211254411841.57629095761706.2263900632211540.1973189791-702.42370904235
1221226412990.591881247624.99562362930411512.4124951231726.591881247557
1231378315109.1405932634972.2317354694411484.62767126711326.14059326342
1241121410974.93753453470.54235871096924611452.5201067543-239.062465465317
1251145311650.3341352832-164.74667752476811420.4125422416197.334135283216
1261088311089.8444694566-697.97544410433811374.1309746477206.844469456648
127103819868.5550780973-434.40448515113311327.8494070538-512.444921902694
1281034810039.7473906705-614.29045059546111270.543059925-308.252609329533
129100249907.07325381658-1072.3099666127411213.2367127962-116.926746183424
1301080510797.5736866322-372.67912522554111185.1054385934-7.4263133678487
1311079610804.5407301723-369.51489456292711156.97416439068.54073017230621
1321190711604.59252460281021.9249254622711187.4825499349-302.407475397211
1331226111597.78267445751706.2263900632211217.9909354793-663.217325542471
1341137711467.593949472024.99562362930411261.410426898790.5939494719787
1351268913100.9383462124972.2317354694411304.8299183182411.938346212384
1361147411624.32642690780.54235871096924611323.1312143813150.326426907777
1371099210807.3141670804-164.74667752476811341.4325104443-184.685832919560
1381076410901.3766129485-697.97544410433811324.5988311558137.376612948492
1391216413454.6393332838-434.40448515113311307.76515186741290.63933328377
1401040910167.9627723646-614.29045059546111264.3276782309-241.037227635436
1411039810647.4197620183-1072.3099666127411220.8902045944249.419762018308
142103499906.57666779037-372.67912522554111164.1024574352-442.423332209626
1431086510992.2001842870-369.51489456292711107.3147102759127.200184287021
1441163011182.12803889481021.9249254622711055.9470356429-447.871961105166
1451222111731.19424892691706.2263900632211004.5793610099-489.805751073096
1461088410766.815506690524.99562362930410976.1888696801-117.184493309453
1471201912117.9698861801972.2317354694410947.798378350498.9698861801444
1481102111068.20393197720.54235871096924610973.253709311947.2039319771538
1491079910764.0376372514-164.74667752476810998.7090402733-34.9623627485689
1501042310494.7728332791-697.97544410433811049.202610825371.7728332790557
1511048410302.7083037739-434.40448515113311099.6961813772-181.291696226093
1521045010372.4756526879-614.29045059546111141.8147979075-77.5243473120518
15399069700.37655217494-1072.3099666127411183.9334144378-205.623447825063
1541104911258.1637752747-372.67912522554111212.5153499508209.163775274719
1551128111690.4176090991-369.51489456292711241.0972854638409.417609099082
1561248512684.95880651231021.9249254622711263.1162680254199.958806512326
1571284912706.63835934981706.2263900632211285.1352505870-142.361640650177
1581138011443.919571316424.99562362930411291.084805054363.919571316379
1591207911888.7339050089972.2317354694411297.0343595217-190.266094991110
1601136611440.91064325870.54235871096924611290.546998030374.9106432587214
1611132811536.6870409858-164.74667752476811284.0596365389208.687040985822
1621044410285.4492627837-697.97544410433811300.5261813207-158.550737216316
1631085410825.4117590488-434.40448515113311316.9927261024-28.5882409512287
1641043410143.4349771434-614.29045059546111338.8554734521-290.565022856605
165101379985.59174581097-1072.3099666127411360.7182208018-151.408254189033
1661099211006.7284981273-372.67912522554111349.950627098314.7284981272733
1671090610842.3318611682-369.51489456292711339.1830333948-63.6681388318411
1681236712401.19798822531021.9249254622711310.877086312434.1979882253017
1691437115753.20247070671706.2263900632211282.57113923011382.2024707067
1701169512103.585422223224.99562362930411261.4189541475408.58542222315
1711154610879.5014954656972.2317354694411240.266769065-666.498504534446
1721092210626.46815372870.54235871096924611216.9894875603-295.531846271264
1731067010311.0344714692-164.74667752476811193.7122060556-358.965528530814
1741025410046.0762032863-697.97544410433811159.8992408180-207.923796713707
1751057310454.3182095706-434.40448515113311126.0862755805-118.681790429373
1761023910000.0023848218-614.29045059546111092.2880657736-238.997615178156
1771025310519.8201106460-1072.3099666127411058.4898559667266.820110646009
1781117611695.0124911386-372.67912522554111029.6666340870519.012491138581
1791071910806.6714823557-369.51489456292711000.843412207287.6714823557322
1801181711636.18024470781021.9249254622710975.8948298299-180.81975529215
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/29/t129360817914pnei8ufr7i825/18ibi1293608273.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t129360817914pnei8ufr7i825/18ibi1293608273.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t129360817914pnei8ufr7i825/28ibi1293608273.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t129360817914pnei8ufr7i825/28ibi1293608273.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t129360817914pnei8ufr7i825/3i9ak1293608273.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t129360817914pnei8ufr7i825/3i9ak1293608273.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t129360817914pnei8ufr7i825/4i9ak1293608273.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t129360817914pnei8ufr7i825/4i9ak1293608273.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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