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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 16:31:23 +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/t1293640131g2l63ttymt27mqq.htm/, Retrieved Wed, 29 Dec 2010 17:28:52 +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/t1293640131g2l63ttymt27mqq.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 «
2030 1855 1834 2092 2164 2368 2072 2521 1823 1947 2226 1754 1786 2072 1846 2137 2466 2154 2289 2628 2074 2798 2194 2442 2565 2063 2069 2539 1898 2139 2408 2725 2201 2311 2548 2276 2351 2280 2057 2479 2379 2295 2456 2546 2844 2260 2981 2678 3440 2842 2450 2669 2570 2540 2318 2930 2947 2799 2695 2498 2260 2160 2058 2533 2150 2172 2155 3016 2333 2355 2825 2214 2360 2299 1746 2069 2267 1878 2266 2282 2085 2277 2251 1828 1954 1851 1570 1852 2187 1855 2218 2253 2028 2169 1997 2034 1791 1627 1631 2319 1707 1747 2397 2059 2251 2558 2406 2049 2074 1734 1983 2121 1905 2126 2363 2173 2710 2137 2742 2419 2194 2660 2189 2310 2349 2540 2434 2916 2446 2375 3032 2218 1920 2039 1889 2014 2105 2153 2309 2955 2225 2160 2386 1653 1099 5010 2672 2729 2955 2409 3086 3384 2458 2913 2448 2215 2179 2461 2098 2621 2703 2388 3880 3310 3093 3237 3002 2670 2311 2062 2059 etc...
 
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'RServer@AstonUniversity' @ vre.aston.ac.uk


Seasonal Decomposition by Loess - Parameters
ComponentWindowDegreeJump
Seasonal24110242
Trend1912
Low-pass1312


Seasonal Decomposition by Loess - Time Series Components
tObservedFittedSeasonalTrendRemainder
120302073.17374531016-187.4402628931352174.2665175829743.1737453101632
218551566.57982236058-13.46089228490192156.88106992432-288.420177639423
318341890.55303815545-362.0486604211332139.4956222656856.5530381554549
420922062.42835560095-0.643255883278422122.21490028233-29.5716443990477
521642308.25350968789-85.18768798686432104.93417829897144.25350968789
623682825.24399799669-179.655888570822090.41189057413457.243997996688
720721989.0844044994279.02599265129282075.88960284929-82.9155955005824
825212577.57626000955399.1386821207912065.2850578696656.5762600095459
918231535.4178950358855.90159207407972054.68051289004-287.582104964117
1019471780.9888560062763.43306767434712049.57807631938-166.011143993728
1122262105.40973693981302.1146233114642044.47563974872-120.590263060189
1217541522.14529741021-71.17729169589622057.03199428569-231.854702589794
1317861689.85191407048-187.4402628931352069.58834882266-96.1480859295207
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1518461929.76313244313-362.0486604211332124.2855279780183.7631324431281
1621372115.23652671537-0.643255883278422159.40672916791-21.76347328463
1724662822.65975762905-85.18768798686432194.52793035781356.659757629052
1821542257.70508563-179.655888570822229.95080294082103.705085629997
1922892233.6003318248779.02599265129282265.37367552383-55.399668175125
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2321941759.04492352598302.1146233114642326.84045316256-434.95507647402
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3423112244.1278434255163.43306767434712314.43908890014-66.8721565744913
3525482467.22419840042302.1146233114642326.66117828811-80.7758015995782
3622762281.14277304003-71.17729169589622342.034518655875.14277304002826
3723512532.03240386951-187.4402628931352357.40785902362181.032403869513
3822802201.79755973937-13.46089228490192371.66333254553-78.2024402606271
3920572090.1298543537-362.0486604211332385.9188060674433.1298543536968
4024792553.91703160751-0.643255883278422404.7262242757774.9170316075092
4123792419.65404550276-85.18768798686432423.533642484140.6540455027621
4222952308.29876339088-179.655888570822461.3571251799413.298763390881
4324562333.7933994729379.02599265129282499.18060787577-122.206600527067
4425462145.86186037055399.1386821207912546.99945750866-400.138139629453
4528443037.2801007843755.90159207407972594.81830714155193.280100784371
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4729812988.58229753855302.1146233114642671.303079149987.58229753855221
4826782734.85093996542-71.17729169589622692.3263517304856.8509399654195
4934404354.09063858217-187.4402628931352713.34962431097914.090638582165
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5523181899.3561188685879.02599265129282657.61788848013-418.643881131419
5629302848.05019237643399.1386821207912612.81112550278-81.949807623575
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5926952577.60066546352302.1146233114642510.28471122502-117.399334536481
6024982581.76442641246-71.17729169589622485.4128652834383.7644264124638
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6221601897.65249110619-13.46089228490192435.80840117871-262.347508893809
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6521502015.46785283527-85.18768798686432369.71983515159-134.532147164729
6621722159.22593761093-179.655888570822364.42995095989-12.7740623890722
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6830163278.23681791498399.1386821207912354.62449996423262.236817914975
6923332259.9894747656455.90159207407972350.10893316028-73.0105252343569
7023552307.6801520330263.43306767434712338.88678029263-47.3198479669804
7128253020.22074926355302.1146233114642327.66462742499195.220749263546
7222142187.94533996727-71.17729169589622311.23195172863-26.0546600327325
7323602612.64098686087-187.4402628931352294.79927603227252.640986860868
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7620691927.52232356464-0.643255883278422211.12093231864-141.477676435357
7722672440.22665665849-85.18768798686432178.96103132838173.226656658489
7818781789.17212452138-179.655888570822146.48376404944-88.8278754786184
7922662338.9675105782179.02599265129282114.006496770572.9675105782062
8022822078.31650365209399.1386821207912086.54481422711-203.683496347905
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8322512173.05557377263302.1146233114642026.8298029159-77.9444262273691
8418281707.00422051287-71.17729169589622020.17307118302-120.995779487127
8519542081.92392344299-187.4402628931352013.51633945014127.923923442994
8618511704.28516486404-13.46089228490192011.17572742086-146.714835135959
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8818521700.73473005038-0.643255883278422003.9085258329-151.265269949622
8921872460.20575171265-85.18768798686431998.98193627422273.205751712645
9018551895.04183140414-179.655888570821994.6140571666840.0418314041376
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9222532121.47204872633399.1386821207911985.38926915287-131.527951273666
9320282019.5660476793255.90159207407971980.5323602466-8.43395232068428
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10217471636.34709071423-179.655888570822037.30879785659-110.652909285766
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10420591642.98216696043399.1386821207912075.87915091878-416.017833039573
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10625582949.6859803316163.43306767434712102.88095199405391.685980331605
10724062396.24058347944302.1146233114642113.64479320909-9.75941652055644
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20129122851.1696326007155.90159207407972916.92877532521-60.8303673992923
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20522261813.47272685569-187.4402628931352825.96753603744-412.527273144305
20629423096.98210875761-13.46089228490192800.47878352729154.982108757612
20724202427.05862940399-362.0486604211332774.990031017147.05862940399265
20825162269.39910332464-0.643255883278422763.24415255864-246.600896675364
20924212175.68941388672-85.18768798686432751.49827410014-245.31058611328
21026312687.13169170265-179.655888570822754.5241968681756.1316917026502
21128872937.4238877125179.02599265129282757.5501196361950.4238877125131
21233283493.41687201369399.1386821207912763.44444586551165.416872013695
21325872348.7596358310955.90159207407972769.33877209483-238.240364168914
21426952561.6308523045263.43306767434712764.93608002113-133.36914769548
21536694275.3519887411302.1146233114642760.53338794743606.351988741105
21627732875.00172124534-71.17729169589622742.17557045055102.001721245344
21725272517.62250993946-187.4402628931352723.81775295367-9.37749006053855
21827502819.58823396263-13.46089228490192693.8726583222769.5882339626314
21920141726.12109673027-362.0486604211332663.92756369087-287.878903269734
22027632900.50134582905-0.643255883278422626.14191005422137.501345829054
22127262948.83143156928-85.18768798686432588.35625641758222.831431569282
22218261274.87505862095-179.655888570822556.78082994987-551.12494137905
22327132821.7686038665579.02599265129282525.20540348216108.768603866551
22430403163.08408755016399.1386821207912517.77723032905123.084087550158
22524052243.7493507499755.90159207407972510.34905717595-161.250649250026
22625262474.3439499951263.43306767434712514.22298233053-51.656050004879
22725262231.78846920342302.1146233114642518.09690748512-294.211530796583
22825292608.02353109468-71.17729169589622521.1537606012279.023531094675
22924742611.22964917581-187.4402628931352524.21061371732137.229649175811
23025762630.46601980629-13.46089228490192534.9948724786154.466019806287
23122192254.26952918123-362.0486604211332545.7791312399135.2695291812274
23229003209.40932587808-0.643255883278422591.2339300052309.409325878078
23322741996.49895921637-85.18768798686432636.68872877049-277.501040783631
23421841839.07544318066-179.655888570822708.58044539016-344.924556819343
23526292398.5018453388879.02599265129282780.47216200983-230.498154661123
23627392226.6508363587399.1386821207912852.21048152051-512.349163641297
23729332886.1496068947455.90159207407972923.94880103118-46.8503931052628
23831443225.2479046138563.43306767434712999.319027711881.2479046138546
23933543331.19612229612302.1146233114643074.68925439241-22.8038777038778
24033573628.43149463895-71.17729169589623156.74579705695271.431494638949
24133293606.63792317165-187.4402628931353238.80233972148277.637923171653
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293640131g2l63ttymt27mqq/1nkqt1293640277.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293640131g2l63ttymt27mqq/1nkqt1293640277.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293640131g2l63ttymt27mqq/2nkqt1293640277.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293640131g2l63ttymt27mqq/2nkqt1293640277.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293640131g2l63ttymt27mqq/3yu7e1293640277.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293640131g2l63ttymt27mqq/3yu7e1293640277.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293640131g2l63ttymt27mqq/4yu7e1293640277.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293640131g2l63ttymt27mqq/4yu7e1293640277.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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa


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