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*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 22:28:52 +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/t12936616919bikiulwnyrnxaq.htm/, Retrieved Wed, 29 Dec 2010 23:28:15 +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/t12936616919bikiulwnyrnxaq.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 «
206010 198112 194519 185705 180173 176142 203401 221902 197378 185001 176356 180449 180144 173666 165688 161570 156145 153730 182698 200765 176512 166618 158644 159585 163095 159044 155511 153745 150569 150605 179612 194690 189917 184128 175335 179566 181140 177876 175041 169292 166070 166972 206348 215706 202108 195411 193111 195198 198770 194163 190420 189733 186029 191531 232571 243477 227247 217859 208679 213188 216234 213586 209465 204045 200237 203666 241476 260307 243324 244460 233575 237217 235243 230354 227184 221678 217142 219452 256446 265845 248624 241114 229245 231805 219277 219313 212610 214771 211142 211457 240048 240636 230580 208795 197922 194596 194581 185686 178106 172608 167302 168053 202300 202388 182516 173476 166444 171297 169701 164182 161914 159612 151001 158114 186530 187069 174330 169362 166827 178037 186413 189226 191563 188906 186005 195309 223532 226899 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ www.wessa.org


Seasonal Decomposition by Loess - Parameters
ComponentWindowDegreeJump
Seasonal14310144
Trend1912
Low-pass1312


Seasonal Decomposition by Loess - Time Series Components
tObservedFittedSeasonalTrendRemainder
1206010207466.67020455-278.167016693425204831.4968121441456.67020454953
2198112197788.980184734-4093.16961067612202528.189425942-323.019815265812
3194519196956.873667936-8143.75570767551200224.882039742437.87366793552
4185705185176.525741265-11724.450699345197957.92495808-528.474258734786
5180173180989.178167715-16334.146044135195690.96787642816.17816771532
6176142172992.538082139-14155.6645696925193447.126487553-3149.4619178607
7203401197205.06121080618393.6536905069191203.285098687-6195.93878919352
8221902227689.60679031227148.947749881188965.4454598075787.60679031172
9197378196773.39926355411254.9949155186186727.605820928-604.600736446358
10185001182588.1549674932771.38997611625184642.455056391-2412.84503250709
11176356174907.246004056-4752.55029590942182557.304291854-1448.75399594445
12180449180322.124943311-87.0840112223662180662.959067911-126.875056688761
13180144181797.553172725-278.167016693425178768.6138439681653.55317272508
14173666174404.670375606-4093.16961067612177020.49923507738.670375606336
15165688164247.371081504-8143.75570767551175272.384626171-1440.62891849573
16161570161224.159464909-11724.450699345173640.291234436-345.840535091178
17156145156615.948201434-16334.146044135172008.197842701470.948201433755
18153730151116.353631337-14155.6645696925170499.310938355-2613.64636866277
19182698178011.92227548418393.6536905069168990.424034009-4686.07772451613
20200765206597.83361848627148.947749881167783.2186316335832.83361848575
21176512175192.99185522411254.9949155186166576.013229257-1319.0081447757
22166618164599.5745810432771.38997611625165865.035442841-2018.42541895696
23158644156886.492639485-4752.55029590942165154.057656424-1757.50736051492
24159585154470.238820171-87.0840112223662164786.845191051-5114.76117982893
25163095162048.534291015-278.167016693425164419.632725678-1046.46570898479
26159044157557.678723512-4093.16961067612164623.490887164-1486.32127648807
27155511154338.406659025-8143.75570767551164827.34904865-1172.59334097468
28153745153324.816630088-11724.450699345165889.634069257-420.183369912265
29150569150520.226954271-16334.146044135166951.919089864-48.7730457294674
30150605146815.506467788-14155.6645696925168550.158101905-3789.49353221231
31179612170681.94919554818393.6536905069170148.397113945-8930.05080445198
32194690190408.03029890127148.947749881171823.021951218-4281.96970109915
33189917195081.3582959911254.9949155186173497.6467884915164.35829599033
34184128190371.0460351692771.38997611625175113.5639887156243.04603516863
35175335178693.06910697-4752.55029590942176729.4811889393358.06910697027
36179566180957.136367289-87.0840112223662178261.9476439331391.13636728906
37181140182763.752917766-278.167016693425179794.4140989271623.75291776596
38177876178718.257423676-4093.16961067612181126.912187842.257423675648
39175041175766.345432602-8143.75570767551182459.410275073725.345432602015
40169292166668.018241632-11724.450699345183640.432457713-2623.9817583682
41166070163652.691403782-16334.146044135184821.454640353-2417.308596218
42166972161911.043992117-14155.6645696925186188.620577576-5060.95600788333
43206348206746.55979469518393.6536905069187555.786514799398.559794694505
44215706215179.03835647327148.947749881189084.013893646-526.961643526593
45202108202348.76381198911254.9949155186190612.241272492240.763811988989
46195411195778.5109917542771.38997611625192272.09903213367.510991753603
47193111197042.593504142-4752.55029590942193931.9567917683931.59350414155
48195198194679.486309874-87.0840112223662195803.597701348-518.513690125983
49198770200142.928405765-278.167016693425197675.2386109291372.92840576463
50194163192731.08554041-4093.16961067612199688.084070266-1431.91445959028
51190420187282.826178072-8143.75570767551201700.929529604-3137.17382192847
52189733187596.222054355-11724.450699345203594.22864499-2136.77794564533
53186029182904.618283758-16334.146044135205487.527760377-3124.38171624174
54191531190054.630355666-14155.6645696925207163.034214027-1476.36964433431
55232571237909.80564181618393.6536905069208838.5406676775338.80564181629
56243477249420.1486766227148.947749881210384.9035734995943.1486766203
57227247231307.73860516111254.9949155186211931.266479324060.73860516094
58217859219786.7776142052771.38997611625213159.8324096791927.777614205
59208679207722.151955872-4752.55029590942214388.398340037-956.848044127604
60213188211168.790521504-87.0840112223662215294.293489719-2019.20947849617
61216234216545.978377293-278.167016693425216200.1886394311.978377293417
62213586213918.824633782-4093.16961067612217346.344976895332.824633781594
63209465208581.254393286-8143.75570767551218492.501314389-883.74560671355
64204045199521.627831967-11724.450699345220292.822867378-4523.37216803321
65200237194715.001623768-16334.146044135222093.144420367-5521.99837623248
66203666197361.138860848-14155.6645696925224126.525708845-6304.86113915205
67241476238398.43931217218393.6536905069226159.906997322-3077.56068782843
68260307265469.12069579727148.947749881227995.9315543225162.12069579665
69243324245561.04897315811254.9949155186229831.9561113232237.04897315841
70244460254791.4906100722771.38997611625231357.11941381210331.4906100719
71233575239020.267579609-4752.55029590942232882.2827163015445.26757960866
72237217240598.562147116-87.0840112223662233922.5218641073381.56214711574
73235243235801.406004781-278.167016693425234962.761011912558.406004780962
74230354229413.365899866-4093.16961067612235387.803710811-940.634100134455
75227184226698.909297967-8143.75570767551235812.846409709-485.090702033194
76221678219297.740997635-11724.450699345235782.70970171-2380.25900236546
77217142214865.573050423-16334.146044135235752.572993712-2276.42694957732
78219452217766.87833946-14155.6645696925235292.786230232-1685.12166053994
79256446259665.34684274118393.6536905069234832.9994667533219.3468427406
80265845270556.84234427627148.947749881233984.2099058434711.8423442757
81248624252857.58473954711254.9949155186233135.4203449344233.58473954746
82241114247295.9882642292771.38997611625232160.6217596556181.98826422874
83229245232056.727121533-4752.55029590942231185.8231743762811.72712153336
84231805233678.56145647-87.0840112223662230018.5225547531873.56145646982
85219277209980.945081564-278.167016693425228851.221935129-9296.05491843558
86219313215499.736373526-4093.16961067612227219.43323715-3813.26362647431
87212610207776.111168504-8143.75570767551225587.644539172-4833.88883149633
88214771217769.088466773-11724.450699345223497.3622325722998.08846677345
89211142217211.066118164-16334.146044135221407.0799259716069.06611816364
90211457218120.427521818-14155.6645696925218949.2370478756663.42752181791
91240048245210.95213971518393.6536905069216491.3941697785162.95213971534
92240636240582.05132301827148.947749881213541.000927101-53.948676982458
93230580239314.39740005611254.9949155186210590.6076844258734.39740005642
94208795207748.875517742771.38997611625207069.734506144-1046.12448225979
95197922197047.688968047-4752.55029590942203548.861327862-874.311031952704
96194596189334.298929286-87.0840112223662199944.785081937-5261.70107071422
97194581193099.458180682-278.167016693425196340.708836011-1481.54181931759
98185686182461.980256938-4093.16961067612193003.189353738-3224.01974306154
99178106174690.085836211-8143.75570767551189665.669871464-3415.91416378881
100172608170170.110371966-11724.450699345186770.340327379-2437.8896280335
101167302167063.135260842-16334.146044135183875.010783293-238.864739157812
102168053168651.55974815-14155.6645696925181610.104821543598.55974814971
103202300206861.147449718393.6536905069179345.1988597934561.14744970039
104202388200033.73713096427148.947749881177593.315119155-2354.26286903585
105182516177935.57370596511254.9949155186175841.431378517-4580.42629403542
106173476169695.5199577822771.38997611625174485.090066102-3780.48004221777
107166444164511.801542223-4752.55029590942173128.748753686-1932.19845777674
108171297170609.237822002-87.0840112223662172071.84618922-687.762177997531
109169701168665.22339194-278.167016693425171014.943624754-1035.77660806017
110164182162276.012608613-4093.16961067612170181.157002063-1905.98739138682
111161914162624.385328303-8143.75570767551169347.370379372710.385328303179
112159612161996.551965578-11724.450699345168951.8987337672384.55196557756
113151001149779.718955972-16334.146044135168556.427088163-1221.28104402765
114158114161374.133545677-14155.6645696925169009.5310240153260.13354567735
115186530185203.71134962618393.6536905069169462.634959868-1326.28865037448
116187069175873.50406538127148.947749881171115.548184738-11195.4959346191
117174330164636.54367487311254.9949155186172768.461409609-9693.45632512716
118169362160501.1901115862771.38997611625175451.419912297-8860.8098884137
119166827160272.171880923-4752.55029590942178134.378414986-6554.82811907688
120178037174617.566858656-87.0840112223662181543.517152567-3419.43314134417
121186413188151.511126547-278.167016693425184952.6558901471738.51112654665
122189226194035.884477418-4093.16961067612188509.2851332584809.88447741792
123191563199203.841331306-8143.75570767551192065.914376377640.84133130588
124188906194287.695773808-11724.450699345195248.7549255375381.695773808
125186005189912.550569431-16334.146044135198431.5954747043907.55056943052
126195309203757.563973539-14155.6645696925201016.1005961548448.56397353881
127223532225069.7405918918393.6536905069203600.6057176031537.74059189027
128226899221208.1222460927148.947749881205440.930004029-5690.87775391011
129214126209715.75079402611254.9949155186207281.254290455-4410.24920597387
130206903202577.2473880522771.38997611625208457.362635832-4325.75261194794
131204442204003.079314701-4752.55029590942209633.470981208-438.920685298683
132220375230456.056663188-87.0840112223662210381.02734803410081.0566631883
133214320217789.583301833-278.167016693425211128.583714863469.58330183334
134212588218320.430056142-4093.16961067612210948.7395545345732.43005614242
135205816209006.860313468-8143.75570767551210768.8953942073190.86031346818
136202196206210.366817123-11724.450699345209906.0838822224014.36681712308
137195722198734.873673898-16334.146044135209043.2723702373012.8736738984
138198563203186.429182857-14155.6645696925208095.2353868364623.42918285669
139229139232737.14790605818393.6536905069207147.1984034353598.14790605815
140229527225850.23820253527148.947749881206054.814047584-3676.76179746535
141211868207518.57539274811254.9949155186204962.429691734-4349.42460725221
142203555200624.1834140142771.38997611625203714.426609869-2930.81658598565
143195770193826.126767904-4752.55029590942202466.423528005-1943.87323209576
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/29/t12936616919bikiulwnyrnxaq/14byi1293661730.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t12936616919bikiulwnyrnxaq/14byi1293661730.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t12936616919bikiulwnyrnxaq/24byi1293661730.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t12936616919bikiulwnyrnxaq/24byi1293661730.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t12936616919bikiulwnyrnxaq/3wkyl1293661730.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t12936616919bikiulwnyrnxaq/3wkyl1293661730.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t12936616919bikiulwnyrnxaq/4wkyl1293661730.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t12936616919bikiulwnyrnxaq/4wkyl1293661730.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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