Decomposition by Loess bis

*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: Mon, 20 Dec 2010 22:28:35 +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/20/t12928842120an8fr4mifugf43.htm/, Retrieved Mon, 20 Dec 2010 23:30:12 +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/20/t12928842120an8fr4mifugf43.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:

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1038.00 934.00 988.00 870.00 854.00 834.00 872.00 954.00 870.00 1238.00 1082.00 1053.00 934.00 787.00 1081.00 908.00 995.00 825.00 822.00 856.00 887.00 1094.00 990.00 936.00 1097.00 918.00 926.00 907.00 899.00 971.00 1087.00 1000.00 1071.00 1190.00 1116.00 1070.00 1314.00 1068.00 1185.00 1215.00 1145.00 1251.00 1363.00 1368.00 1535.00 1853.00 1866.00 2023.00 1373.00 1968.00 1424.00 1160.00 1243.00 1375.00 1539.00 1773.00 1906.00 2076.00 2004.00

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Seasonal Decomposition by Loess - Parameters Component Window Degree Jump Seasonal 6 0 1 Trend 25 1 3 Low-pass 13 1 2 Seasonal Decomposition by Loess - Time Series Components t Observed Fitted Seasonal Trend Remainder 1 1038 1047.25308898752 64.707688883149 964.039222129333 9.25308898751814 2 934 976.730174708071 -72.1574524069796 963.427277698908 42.7301747080714 3 988 991.114445925043 22.0702208064731 962.815333268484 3.11444592504336 4 870 855.764671488434 -77.9680603264932 962.203388838059 -14.2353285115656 5 854 822.834606651786 -76.3940462852162 961.55943963343 -31.165393348214 6 834 811.002461782162 -103.917952210964 960.915490428801 -22.9975382178376 7 872 837.47723979627 -53.7487810204431 960.271541224173 -34.5227602037297 8 954 990.989417830787 -42.3563127856579 959.366894954871 36.9894178307869 9 870 804.557712169087 -23.0199608546557 958.46224868557 -65.4422878309133 10 1238 1304.07368885219 214.368708731541 957.557602416267 66.0736888521923 11 1082 1097.42734940098 109.748193528962 956.824457070058 15.4273494009803 12 1053 1103.57689552158 46.331792754568 956.091311723848 50.5768955215839 13 934 847.441537603957 65.2002960184042 955.358166377639 -86.558462396043 14 787 688.34614226978 -66.6034159115078 952.257273641727 -98.6538577302196 15 1081 1200.90670283678 11.9369162574081 949.156380905816 119.906702836776 16 908 954.737523225179 -84.7930113950834 946.055488169904 46.737523225179 17 995 1133.21573852982 -87.7471284622162 944.531389932395 138.215738529821 18 825 812.826156407136 -105.833448102022 943.007291694886 -12.1738435928644 19 822 753.642518197847 -51.1257116552236 941.483193457377 -68.3574818021532 20 856 810.351017681616 -42.4045069995284 944.053489317913 -45.6489823183842 21 887 840.273593545218 -12.8973787236666 946.623785178448 -46.7264064547818 22 1094 1020.43692208564 218.368996875377 949.194081038984 -73.5630779143611 23 990 905.601902564848 119.605242711981 954.79285472317 -84.3980974351517 24 936 855.98665091519 55.6217206774537 960.391628407357 -80.0133490848107 25 1097 1167.51945019339 60.4901477150676 965.990402091543 70.519450193389 26 918 917.104785086843 -55.1391513463279 974.034366259485 -0.895214913157133 27 926 879.017457952376 -9.0957883798033 982.078330427427 -46.9825420476237 28 907 925.857219736293 -101.979514331662 990.122294595369 18.8572197362928 29 899 903.776547079 -110.162723634454 1004.38617655545 4.77654707900047 30 971 1034.86569901149 -111.515757527024 1018.65005851554 63.8656990114871 31 1087 1187.96196952376 -46.87590999938 1032.91394047562 100.961969523758 32 1000 992.120490816448 -46.3664151341763 1054.24592431773 -7.87950918355205 33 1071 1052.86301280933 13.5590790308391 1075.57790815984 -18.1369871906743 34 1190 1063.06099336022 220.029114637842 1096.90989200194 -126.939006639784 35 1116 970.29433804276 137.642031897751 1124.06363005949 -145.705661957241 36 1070 869.842946445146 118.939685437818 1151.21736811704 -200.157053554854 37 1314 1424.46798784454 25.1609059808768 1178.37110617458 110.467987844539 38 1068 903.475353228097 17.8649391779011 1214.65970759400 -164.524646771903 39 1185 1166.58715489789 -47.5354639113122 1250.94830901342 -18.4128451021074 40 1215 1306.66895616705 -163.905866599885 1287.23691043284 91.6689561670476 41 1145 1131.09793082367 -168.503391540194 1327.40546071652 -13.9020691763285 42 1251 1274.20704256757 -139.781053567780 1367.57401100021 23.2070425675724 43 1363 1375.85959608781 -57.6021573717008 1407.74256128389 12.859596087809 44 1368 1326.35760762263 -27.3175065697746 1436.95989894714 -41.642392377365 45 1535 1552.51528267021 51.3074807193994 1466.17723661039 17.5152826702129 46 1853 1964.6120336583 245.993392068066 1495.39457427364 111.612033658299 47 1866 2045.97489449676 169.193783967088 1516.83132153615 179.974894496760 48 2023 2363.99272101815 143.739210183185 1538.26806879867 340.992721018148 49 1373 1172.64896558872 13.6462183500993 1559.70481606118 -200.351034411282 50 1968 2320.65664273674 33.0559814268651 1582.28737583640 352.656642736738 51 1424 1308.63255777776 -65.5024933893735 1604.86993561161 -115.367442222237 52 1160 877.826843709907 -185.279339096731 1627.45249538682 -282.173156290093 53 1243 1030.05691891226 -192.091227416451 1648.03430850419 -212.943081087744 54 1375 1232.53328161228 -151.149403233844 1668.61612162157 -142.466718387722 55 1539 1451.53200402531 -62.7299387642474 1689.19793473894 -87.4679959746884 56 1773 1861.83695608635 -24.9277042659407 1709.09074817959 88.8369560863507 57 1906 2021.24558359371 61.7708547860487 1728.98356162024 115.245583593707 58 2076 2148.26899026611 254.854634672988 1748.8763750609 72.2689902661141 59 2004 2056.71685236325 182.097495239380 1769.18565239737 52.7168523632542

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928842120an8fr4mifugf43/1zfym1292884111.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t12928842120an8fr4mifugf43/1zfym1292884111.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t12928842120an8fr4mifugf43/2soyp1292884111.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t12928842120an8fr4mifugf43/2soyp1292884111.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t12928842120an8fr4mifugf43/3soyp1292884111.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t12928842120an8fr4mifugf43/3soyp1292884111.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t12928842120an8fr4mifugf43/4lyfs1292884111.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t12928842120an8fr4mifugf43/4lyfs1292884111.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t12928842120an8fr4mifugf43/7dhta1292884111.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t12928842120an8fr4mifugf43/7dhta1292884111.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = 6 ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = 6 ; 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') bitmap(file='test5.png') myresid <- m$time.series[!is.na(m$time.series[,'remainder']),'remainder'] hist(as.numeric(myresid), main='Residual Histogram', xlab='Residual Value') dev.off()

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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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