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paper - 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: Sun, 19 Dec 2010 21:08:11 +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/19/t12927927814x19lj1dht9lvew.htm/, Retrieved Sun, 19 Dec 2010 22:06:26 +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/19/t12927927814x19lj1dht9lvew.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 «
631 923 654 294 671 833 586 840 600 969 625 568 558 110 630 577 628 654 603 184 656 255 600 730 670 326 678 423 641 502 625 311 628 177 589 767 582 471 636 248 599 885 621 694 637 406 595 994 696 308 674 201 648 861 649 605 672 392 598 396 613 177 638 104 615 632 634 465 638 686 604 243 706 669 677 185 644 328 644 825 605 707 600 136 612 166 599 659 634 210 618 234 613 576 627 200 668 973 651 479 619 661 644 260 579 936 601 752 595 376 588 902 634 341 594 305 606 200 610 926 633 685 639 696 659 451 593 248 606 677 599 434 569 578 629 873 613 438 604 172 658 328 612 633 707 372 739 770 777 535 685 030 730 234 714 154 630 872 719 492 677 023 679 272 718 317 645 672
 
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'George Udny Yule' @ 72.249.76.132


Seasonal Decomposition by Loess - Parameters
ComponentWindowDegreeJump
Seasonal841085
Trend1912
Low-pass1312


Seasonal Decomposition by Loess - Time Series Components
tObservedFittedSeasonalTrendRemainder
1631923616034.02038092642765.5880950509605046.391524023-15888.9796190744
2654294659394.5228359641422.3490083471607771.1281556935100.52283596003
3671833700472.31451337932697.8206992584610495.86478736228639.3145133792
4586840561919.646890477-1346.46386559658613106.81697512-24920.3531095234
5600969588893.200771647-2672.96993452455615717.769162878-12075.7992283531
6625568650017.198208185-17022.9684511532618141.77024296824449.1982081853
7558110537394.570785143-41740.3421082012620565.771323058-20715.4292148568
8630577641211.162334035-2797.38162240198622740.21928836710634.1623340354
9628654642072.976956634-9679.64421030965624914.66725367513418.9769566344
10603184598106.259224822-17977.6621642822626239.40293946-5077.7407751783
11656255679607.4200120635338.44136269107627564.13862524623352.420012063
12600730602709.057206246-28986.7774605308627737.7202542851979.05720624619
13670326669975.11002162642765.5880950509627911.301883323-350.889978374005
14678423687979.74909229441422.3490083471627443.9018993589556.74909229449
15641502623329.67738534832697.8206992584626976.501915394-18172.3226146523
16625311625525.46842721-1346.46386559658626442.995438387214.468427209766
17628177633117.480973145-2672.96993452455625909.488961384940.48097314488
18589767570458.854099481-17022.9684511532626098.114351672-19308.145900519
19582471580395.602366237-41740.3421082012626286.739741965-2075.39763376350
20636248648078.589987552-2797.38162240198627214.7916348511830.5899875520
21599885581306.800682574-9679.64421030965628142.843527735-18578.1993174256
22621694631453.089027544-17977.6621642822629912.5731367399759.08902754355
23637406637791.2558915675338.44136269107631682.302745742385.255891566863
24595994587370.516706921-28986.7774605308633604.26075361-8623.48329307872
25696308714324.19314347242765.5880950509635526.21876147718016.1931434721
26674201670053.88350893641422.3490083471636925.767482717-4147.11649106385
27648861626698.86309678532697.8206992584638325.316203956-22162.1369032149
28649605661462.211381555-1346.46386559658639094.25248404211857.2113815546
29672392707593.781170397-2672.96993452455639863.18876412835201.7811703969
30598396573399.957420206-17022.9684511532640415.011030948-24996.0425797944
31613177627127.508810434-41740.3421082012640966.83329776813950.5088104337
32638104638120.804145917-2797.38162240198640884.57747648516.8041459174128
33615632600141.322555108-9679.64421030965640802.321655202-15490.677444892
34634465647302.273026206-17977.6621642822639605.38913807612837.2730262062
35638686633625.1020163585338.44136269107638408.45662095-5060.8979836416
36604243600673.758841075-28986.7774605308636799.018619456-3569.24115892535
37706669735382.83128698742765.5880950509635189.58061796228713.8312869873
38677185678893.80417825841422.3490083471634053.8468133951708.80417825829
39644328623040.06629191432697.8206992584632918.113008827-21287.9337080858
40644825659065.482261348-1346.46386559658631930.98160424914240.4822613476
41605707583143.119734854-2672.96993452455630943.85019967-22563.8802651461
42600136587261.397530341-17022.9684511532630033.570920812-12874.6024696591
43612166636949.050466247-41740.3421082012629123.29164195424783.0504662474
44599659574156.297282446-2797.38162240198627959.084339956-25502.7027175536
45634210651304.767172352-9679.64421030965626794.87703795717094.7671723523
46618234628865.942906415-17977.6621642822625579.71925786710631.9429064153
47613576597448.9971595335338.44136269107624364.561477776-16127.0028404675
48627200660296.901063941-28986.7774605308623089.8763965933096.9010639411
49668973673365.22058954642765.5880950509621815.1913154034392.22058954625
50651479640909.56938123441422.3490083471620626.081610419-10569.4306187663
51619661587187.20739530632697.8206992584619436.971905436-32473.7926046943
52644260671543.434539549-1346.46386559658618323.02932604827283.4345395488
53579936545335.883187865-2672.96993452455617209.086746659-34600.116812135
54601752604281.540631462-17022.9684511532616245.4278196912529.54063146177
55595376617210.573215478-41740.3421082012615281.76889272321834.5732154781
56588902565835.820031414-2797.38162240198614765.561590988-23066.1799685857
57634341664112.289921057-9679.64421030965614249.35428925229771.2899210574
58594305592734.948428397-17977.6621642822613852.713735885-1570.05157160282
59606200593605.4854547915338.44136269107613456.073182518-12594.5145452088
60610926637791.728203606-28986.7774605308613047.04925692526865.7282036056
61633685611966.38657361742765.5880950509612638.025331333-21718.6134263835
62639696625270.88564763441422.3490083471612698.765344019-14425.1143523661
63659451673444.67394403632697.8206992584612759.50535670613993.6739440361
64593248573761.87624545-1346.46386559658614080.587620147-19486.1237545502
65606677600625.300050936-2672.96993452455615401.669883588-6051.69994906359
66599434596978.087047192-17022.9684511532618912.881403961-2455.91295280785
67569578558472.249183867-41740.3421082012622424.092924334-11105.7508161325
68629873633260.315339528-2797.38162240198629283.0662828743387.31533952779
69613438600413.604568895-9679.64421030965636142.039641415-13024.3954311050
70604172581066.190997333-17977.6621642822645255.47116695-23105.8090026674
71658328656948.6559448245338.44136269107654368.902692485-1379.34405517566
72612633590759.78798165-28986.7774605308663492.989478881-21873.2120183498
73707372699361.33563967242765.5880950509672617.076265277-8010.66436032753
74739770758000.88188841941422.3490083471680116.76910323418230.8818884187
75777535834755.7173595532697.8206992584687616.46194119257220.7173595497
76685030680687.985605624-1346.46386559658690718.478259973-4342.01439437619
77730234769320.475355771-2672.96993452455693820.49457875439086.4753557709
78714154748975.883954368-17022.9684511532696355.08449678534821.8839543684
79630872604594.667693385-41740.3421082012698889.674414816-26277.3323066146
80719492740947.429858847-2797.38162240198700833.95176355521455.4298588473
81677023660947.415098016-9679.64421030965702778.229112294-16075.5849019841
82679272672472.890576317-17977.6621642822704048.771587965-6799.10942368314
83718317725976.2445736725338.44136269107705319.3140636377659.24457367195
84645672614221.114487474-28986.7774605308706109.662973057-31450.8855125265
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/19/t12927927814x19lj1dht9lvew/1875d1292792886.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/19/t12927927814x19lj1dht9lvew/1875d1292792886.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/19/t12927927814x19lj1dht9lvew/2875d1292792886.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/19/t12927927814x19lj1dht9lvew/2875d1292792886.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/19/t12927927814x19lj1dht9lvew/3tqpb1292792887.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/19/t12927927814x19lj1dht9lvew/3tqpb1292792887.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/19/t12927927814x19lj1dht9lvew/4tqpb1292792887.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/19/t12927927814x19lj1dht9lvew/4tqpb1292792887.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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