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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: Tue, 28 Dec 2010 08:59:30 +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/28/t1293526709iogluq3f79cd4hp.htm/, Retrieved Tue, 28 Dec 2010 09:58:29 +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/28/t1293526709iogluq3f79cd4hp.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'Sir Ronald Aylmer Fisher' @ 193.190.124.24


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


Seasonal Decomposition by Loess - Time Series Components
tObservedFittedSeasonalTrendRemainder
120302073.17374531016-187.4402628931352174.2665175829743.1737453101637
218551566.57982236058-13.46089228490192156.88106992432-288.420177639423
318341890.55303815545-362.0486604211332139.4956222656856.5530381554549
420922062.42835560095-0.6432558832783712122.21490028233-29.5716443990473
521642308.25350968789-85.18768798686432104.93417829897144.253509687891
623682825.24399799669-179.6558885708202090.41189057413457.243997996688
720721989.0844044994279.02599265129282075.88960284929-82.915595500582
825212577.57626000955399.138682120792065.2850578696656.5762600095463
918231535.4178950358855.9015920740792054.68051289004-287.582104964116
1019471780.9888560062763.43306767434692049.57807631938-166.011143993728
1122262105.40973693981302.1146233114652044.47563974872-120.590263060189
1217541522.14529741021-71.17729169589582057.03199428569-231.854702589794
1317861689.85191407048-187.4402628931352069.58834882266-96.1480859295209
1420722060.52395388457-13.46089228490192096.93693840033-11.4760461154283
1518461929.76313244313-362.0486604211332124.2855279780083.7631324431286
1621372115.23652671537-0.6432558832783712159.40672916791-21.76347328463
1724662822.65975762905-85.18768798686432194.52793035781356.659757629052
1821542257.70508563-179.6558885708202229.95080294082103.705085629998
1922892233.6003318248879.02599265129282265.37367552383-55.3996681751246
2026282567.76403576115399.138682120792289.09728211806-60.2359642388506
2120741779.2775192136355.9015920740792312.82088871229-294.722480786368
2227983212.7362613882363.43306767434692319.83067093742414.736261388231
2321941759.04492352598302.1146233114652326.84045316255-434.955076474019
2424422628.22353055099-71.17729169589582326.95376114491186.223530550987
2525652990.37319376587-187.4402628931352327.06706912726425.373193765872
2620631812.24338083686-13.46089228490192327.21751144805-250.756619163145
2720692172.68070665230-362.0486604211332327.36795376883103.680706652302
2825392757.98403351732-0.6432558832783712320.65922236596218.984033517318
2918981567.23719702378-85.18768798686432313.95049096309-330.762802976225
3021392150.39164071574-179.6558885708202307.2642478550811.3916407157408
3124082436.3960026016479.02599265129282300.5780047470728.3960026016384
3227252749.46381574959399.138682120792301.3975021296224.4638157495883
3322012043.8814084137555.9015920740792302.21699951217-157.118591586253
3423112244.1278434255163.43306767434692314.43908890014-66.8721565744904
3525482467.22419840042302.1146233114652326.66117828811-80.7758015995778
3622762281.14277304003-71.17729169589582342.034518655875.14277304002871
3723512532.03240386951-187.4402628931352357.40785902362181.032403869513
3822802201.79755973937-13.46089228490192371.66333254553-78.2024402606266
3920572090.12985435370-362.0486604211332385.9188060674433.1298543536973
4024792553.91703160751-0.6432558832783712404.7262242757774.9170316075097
4123792419.65404550276-85.18768798686432423.533642484140.6540455027625
4222952308.29876339088-179.6558885708202461.3571251799413.2987633908820
4324562333.7933994729379.02599265129282499.18060787577-122.206600527067
4425462145.86186037055399.138682120792546.99945750866-400.138139629452
4528443037.2801007843755.9015920740792594.81830714155193.280100784372
4622601823.5062391798963.43306767434692633.06069314577-436.493760820113
4729812988.58229753855302.1146233114652671.303079149987.58229753855267
4826782734.85093996542-71.17729169589582692.3263517304856.8509399654199
4934404354.09063858217-187.4402628931352713.34962431097914.090638582165
5028422971.2312317568-13.46089228490192726.2296605281129.231231756802
5124502522.9389636759-362.0486604211332739.1096967452372.938963675902
5226692605.69017142674-0.6432558832783712732.95308445654-63.3098285732626
5325702498.39121581901-85.18768798686432726.79647216785-71.6087841809867
5425402567.44870824683-179.6558885708202692.2071803239927.4487082468318
5523181899.3561188685879.02599265129282657.61788848012-418.643881131417
5629302848.05019237643399.138682120792612.81112550278-81.9498076235736
5729473270.0940454004855.9015920740792568.00436252544323.094045400479
5827992995.4223954504263.43306767434692539.14453687523196.422395450425
5926952577.60066546352302.1146233114652510.28471122502-117.399334536480
6024982581.76442641246-71.17729169589582485.4128652834383.7644264124642
6122602246.89924355129-187.4402628931352460.54101934185-13.1007564487127
6221601897.65249110619-13.46089228490192435.80840117871-262.347508893808
6320582066.97287740556-362.0486604211332411.075783015578.97287740556067
6425332676.24544679970-0.6432558832783712390.39780908358143.245446799696
6521502015.46785283527-85.18768798686432369.71983515159-134.532147164728
6621722159.22593761093-179.6558885708202364.42995095989-12.7740623890718
6721551871.8339405805279.02599265129282359.14006676819-283.166059419483
6830163278.23681791498399.138682120792354.62449996423262.236817914977
6923332259.9894747656455.9015920740792350.10893316028-73.0105252343551
7023552307.6801520330263.43306767434692338.88678029263-47.3198479669795
7128253020.22074926355302.1146233114652327.66462742499195.220749263546
7222142187.94533996727-71.17729169589582311.23195172863-26.0546600327320
7323602612.64098686087-187.4402628931352294.79927603227252.640986860869
7422992342.42083761432-13.46089228490192269.0400546705843.4208376143215
7517461610.76782711224-362.0486604211332243.28083330890-135.232172887762
7620691927.52232356464-0.6432558832783712211.12093231863-141.477676435356
7722672440.22665665849-85.18768798686432178.96103132837173.22665665849
7818781789.17212452138-179.6558885708202146.48376404944-88.8278754786174
7922662338.9675105782179.02599265129282114.006496770572.9675105782071
8022822078.31650365210399.138682120792086.54481422711-203.683496347904
8120852055.0152762421955.9015920740792059.08313168373-29.9847237578051
8222772447.6104650258463.43306767434692042.95646729981170.610465025838
8322512173.05557377263302.1146233114652026.82980291590-77.9444262273685
8418281707.00422051287-71.17729169589582020.17307118302-120.995779487127
8519542081.92392344299-187.4402628931352013.51633945014127.923923442994
8618511704.28516486404-13.46089228490192011.17572742086-146.714835135959
8715701493.21354502955-362.0486604211332008.83511539158-76.7864549704475
8818521700.73473005038-0.6432558832783712003.9085258329-151.265269949621
8921872460.20575171265-85.18768798686431998.98193627422273.205751712646
9018551895.04183140414-179.6558885708201994.6140571666840.0418314041381
9122182366.7278292895679.02599265129281990.24617805914148.727829289563
9222532121.47204872634399.138682120791985.38926915287-131.527951273665
9320282019.5660476793255.9015920740791980.53236024660-8.43395232068292
9421692298.5421866931963.43306767434691976.02474563246129.542186693189
9519971720.36824567021302.1146233114651971.51713101832-276.631754329789
9620342171.40435107825-71.17729169589581967.77294061765137.404351078246
9717911805.41151267616-187.4402628931351964.0287502169814.4115126761592
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10023192643.03338551471-0.6432558832783711995.60987036857324.033385514708
10117071484.21128333225-85.18768798686432014.97640465461-222.788716667746
10217471636.34709071423-179.6558885708202037.30879785659-110.652909285766
10323972655.3328162901579.02599265129282059.64119105856258.332816290147
10420591642.98216696043399.138682120792075.87915091878-416.017833039572
10522512353.9812971469255.9015920740792092.11711077900102.981297146917
10625582949.6859803316163.43306767434692102.88095199405391.685980331605
10724062396.24058347944302.1146233114652113.64479320909-9.75941652055599
10820492044.55277457225-71.17729169589582124.62451712364-4.44722542774844
10920742199.83602185494-187.4402628931352135.60424103820125.836021854938
11017341338.67923383873-13.46089228490192142.78165844617-395.320766161273
11119832178.08958456698-362.0486604211332149.95907585415195.08958456698
11221212083.51114064292-0.6432558832783712159.13211524036-37.4888593570786
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11421262239.44188966728-179.6558885708202192.21399890354113.441889667284
11523632430.8511641682079.02599265129282216.1228431805167.8511641681966
11621731695.41584376937399.138682120792251.44547410984-477.584156230625
11727103077.3303028867655.9015920740792286.76810503916367.330302886761
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11927422828.71798812806302.1146233114652353.1673885604886.7179881280572
12024192525.98353972187-71.17729169589582383.19375197402106.983539721871
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12226602899.14809831972-13.46089228490192434.31279396518239.148098319722
12321892284.64318787834-362.0486604211332455.4054725427995.6431878783446
12423102156.59958957577-0.6432558832783712464.04366630751-153.400410424228
12523492310.50582791464-85.18768798686432472.68186007222-38.4941720853599
12625402796.31013225017-179.6558885708202463.34575632065256.310132250167
12724342334.9643547796379.02599265129282454.00965256908-99.0356452203732
12829163005.18641744218399.138682120792427.6749004370289.1864174421848
12924462434.7582596209555.9015920740792401.34014830497-11.2417403790487
13023752316.4649513443863.43306767434692370.10198098127-58.5350486556172
13130323423.02156303096302.1146233114652338.86381365757391.021563030965
13222182192.72571522792-71.17729169589582314.45157646798-25.2742847720815
13319201737.40092361475-187.4402628931352290.03933927838-182.599076385250
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17726872839.1270993410855.9015920740792478.97130858484152.127099341084
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18728702622.0762472548279.02599265129283038.89776009389-247.923752745181
18837564062.0520665243399.138682120793050.80925135491306.052066524303
18934433767.3776653155.9015920740793062.72074261592324.377665309997
19029482782.3368501570463.43306767434693050.23008216861-165.663149842961
19135603780.14595496723302.1146233114653037.7394217213220.145954967233
19232573567.14919582756-71.17729169589583018.02809586834310.149195827559
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19627832613.76021524075-0.6432558832783712952.88304064253-169.239784759251
19728452833.74662124563-85.18768798686432941.44106674123-11.2533787543662
19829873219.24063827067-179.6558885708202934.41525030015232.24063827067
19926962385.5845734896479.02599265129282927.38943385907-310.415426510361
20038744426.70221328707399.138682120792922.15910459214552.70221328707
20129122851.1696326007155.9015920740792916.92877532521-60.8303673992905
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20426602538.6841724976-71.17729169589582852.4931191983-121.315827502402
20522261813.47272685570-187.4402628931352825.96753603744-412.527273144303
20629423096.98210875761-13.46089228490192800.47878352729154.982108757614
20724202427.05862940399-362.0486604211332774.990031017147.05862940399447
20825162269.39910332464-0.6432558832783712763.24415255864-246.600896675362
20924212175.68941388672-85.18768798686432751.49827410014-245.310586113279
21026312687.13169170265-179.6558885708202754.5241968681756.1316917026502
21128872937.4238877125179.02599265129282757.5501196361950.4238877125126
21233283493.41687201370399.138682120792763.44444586551165.416872013695
21325872348.7596358310955.9015920740792769.33877209483-238.240364168913
21426952561.6308523045263.43306767434692764.93608002113-133.369147695479
21536694275.35198874111302.1146233114652760.53338794743606.351988741106
21627732875.00172124535-71.17729169589582742.17557045055102.001721245345
21725272517.62250993946-187.4402628931352723.81775295367-9.37749006053627
21827502819.58823396263-13.46089228490192693.8726583222769.5882339626341
21920141726.12109673027-362.0486604211332663.92756369086-287.878903269731
22027632900.50134582906-0.6432558832783712626.14191005422137.501345829057
22127262948.83143156928-85.18768798686432588.35625641758222.831431569285
22218261274.87505862095-179.6558885708202556.78082994987-551.124941379048
22327132821.7686038665579.02599265129282525.20540348215108.768603866552
22430403163.08408755016399.138682120792517.77723032905123.084087550159
22524052243.7493507499855.9015920740792510.34905717595-161.250649250024
22625262474.3439499951263.43306767434692514.22298233053-51.6560500048786
22725262231.78846920342302.1146233114652518.09690748512-294.211530796583
22825292608.02353109467-71.17729169589582521.1537606012279.0235310946746
22924742611.22964917581-187.4402628931352524.21061371732137.229649175811
23025762630.46601980629-13.46089228490192534.9948724786154.466019806287
23122192254.26952918123-362.0486604211332545.7791312399135.2695291812274
23229003209.40932587808-0.6432558832783712591.2339300052309.409325878078
23322741996.49895921637-85.18768798686432636.68872877049-277.501040783631
23421841839.07544318066-179.6558885708202708.58044539016-344.924556819345
23526292398.5018453388779.02599265129282780.47216200983-230.498154661126
23627392226.65083635869399.138682120792852.21048152052-512.349163641307
23729332886.1496068947255.9015920740792923.9488010312-46.8503931052796
23831443225.2479046138563.43306767434692999.3190277118181.247904613846
23933543331.19612229612302.1146233114653074.68925439241-22.8038777038778
24033573628.43149463895-71.17729169589583156.74579705694271.431494638954
24133293606.63792317166-187.4402628931353238.80233972147277.637923171664
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/28/t1293526709iogluq3f79cd4hp/137v81293526764.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/28/t1293526709iogluq3f79cd4hp/137v81293526764.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/28/t1293526709iogluq3f79cd4hp/237v81293526764.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/28/t1293526709iogluq3f79cd4hp/237v81293526764.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/28/t1293526709iogluq3f79cd4hp/3vgcb1293526764.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/28/t1293526709iogluq3f79cd4hp/3vgcb1293526764.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/28/t1293526709iogluq3f79cd4hp/4vgcb1293526764.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/28/t1293526709iogluq3f79cd4hp/4vgcb1293526764.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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