Paper

*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 18:45:08 +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/t1293561809myg0vs24cvp3pb8.htm/, Retrieved Tue, 28 Dec 2010 19:43:30 +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/t1293561809myg0vs24cvp3pb8.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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9782 9938 10111 10259 10419 10622 11173 11542 11538 11837 12060 12423 12791 12891 13098 13418 13614 13653 13980 14087 14332 14232 14226 14186 14310 14152 14127 14163 13964 13811 14440 14724 14790 14961 15117 15452 16080 16284 16524 16782 16663 16678 17448 17745 17789 17864 18079 18483 19037 19344 19590 19862 20207 20593 21253 21507 21528 21818 22205 22621 23006 23178 23358 23519 23725 23789 24472 24773 24477 24669 24827

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 'RServer@AstonUniversity' @ vre.aston.ac.uk R Framework error message Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Seasonal Decomposition by Loess - Parameters Component Window Degree Jump Seasonal 711 0 72 Trend 19 1 2 Low-pass 13 1 2 Seasonal Decomposition by Loess - Time Series Components t Observed Fitted Seasonal Trend Remainder 1 9782 9863.40550811548 35.9659433984505 9664.62854848607 81.4055081154838 2 9938 10024.5465560593 -51.5338547507709 9902.98729869147 86.5465560592984 3 10111 10179.6875712004 -99.0336200973157 10141.3460488969 68.6875712004367 4 10259 10216.6568732057 -81.3912954687744 10382.7344222631 -42.3431267942942 5 10419 10378.6263281802 -164.749123809497 10624.1227956293 -40.3736718197615 6 10622 10618.1146805578 -242.051830079097 10867.9371495213 -3.88531944216993 7 11173 11042.6029299119 191.645566674855 11111.7515034133 -130.397070088131 8 11542 11451.2925852828 276.043362582321 11356.6640521349 -90.7074147172498 9 11538 11369.9820829042 104.441316239227 11601.5766008566 -168.017917095807 10 11837 11775.4224646241 42.0844417876842 11856.4930935882 -61.5775353759218 11 12060 11994.5294448229 14.0609688572449 12111.4095863199 -65.4705551771367 12 12423 12505.2112538105 -25.4819399295251 12366.270686119 82.2112538105193 13 12791 12924.9022706834 35.9659433984505 12621.1317859181 133.902270683431 14 12891 12980.2301408163 -51.5338547507709 12853.3037139345 89.2301408162639 15 13098 13209.5579781464 -99.0336200973157 13085.4756419509 111.557978146418 16 13418 13635.2999186144 -81.3912954687744 13282.0913768543 217.299918614428 17 13614 13914.0420120517 -164.749123809497 13478.7071117578 300.042012051703 18 13653 13918.6177237655 -242.051830079097 13629.4341063136 265.617723765481 19 13980 13988.1933324557 191.645566674855 13780.1611008694 8.19333245570851 20 14087 14015.3771214539 276.043362582321 13882.5795159637 -71.6228785460662 21 14332 14574.5607527027 104.441316239227 13984.9979310581 242.560752702719 22 14232 14377.2402174526 42.0844417876842 14044.6753407597 145.240217452631 23 14226 14333.5862806814 14.0609688572449 14104.3527504613 107.586280681444 24 14186 14260.4291249839 -25.4819399295251 14137.0528149456 74.4291249838752 25 14310 14414.2811771716 35.9659433984505 14169.75287943 104.281177171562 26 14152 14152.5446037679 -51.5338547507709 14202.9892509829 0.544603767859371 27 14127 14116.8079975615 -99.0336200973157 14236.2256225358 -10.1920024385181 28 14163 14116.3219385685 -81.3912954687744 14291.0693569003 -46.6780614314866 29 13964 13746.8360325448 -164.749123809497 14345.9130912647 -217.163967455192 30 13811 13412.6740502982 -242.051830079097 14451.3777797809 -398.32594970183 31 14440 14131.511965028 191.645566674855 14556.8424682972 -308.488034972022 32 14724 14443.8218243729 276.043362582321 14728.1348130448 -280.17817562709 33 14790 14576.1315259684 104.441316239227 14899.4271577924 -213.868474031598 34 14961 14755.8774128193 42.0844417876842 15124.038145393 -205.122587180676 35 15117 14871.2898981491 14.0609688572449 15348.6491329936 -245.710101850855 36 15452 15330.9646540346 -25.4819399295251 15598.517285895 -121.035345965442 37 16080 16275.6486178052 35.9659433984505 15848.3854387963 195.648617805226 38 16284 16518.3796683194 -51.5338547507709 16101.1541864314 234.37966831935 39 16524 16793.1106860308 -99.0336200973157 16353.9229340665 269.110686030795 40 16782 17048.4559714511 -81.3912954687744 16596.9353240176 266.455971451123 41 16663 16650.8014098407 -164.749123809497 16839.9477139688 -12.1985901592889 42 16678 16521.1734520662 -242.051830079097 17076.8783780129 -156.826547933848 43 17448 17390.545391268 191.645566674855 17313.8090420571 -57.4546087319613 44 17745 17653.5556588117 276.043362582321 17560.400978606 -91.4443411882748 45 17789 17666.565768606 104.441316239227 17806.9929151548 -122.434231394025 46 17864 17602.2692205993 42.0844417876842 18083.646337613 -261.730779400659 47 18079 17783.6392710716 14.0609688572449 18360.2997600711 -295.360728928394 48 18483 18320.2968986775 -25.4819399295251 18671.185041252 -162.703101322484 49 19037 19055.9637341687 35.9659433984505 18982.0703224329 18.9637341686794 50 19344 19431.011592396 -51.5338547507709 19308.5222623548 87.0115923959675 51 19590 19644.0594178206 -99.0336200973157 19634.9742022767 54.0594178205793 52 19862 19839.4432184734 -81.3912954687744 19965.9480769953 -22.5567815265713 53 20207 20281.8271720955 -164.749123809497 20296.9219517139 74.8271720955454 54 20593 20801.2126999515 -242.051830079097 20626.8391301276 208.212699951499 55 21253 21357.5981247839 191.645566674855 20956.7563085413 104.598124783894 56 21507 21461.1055592112 276.043362582321 21276.8510782065 -45.8944407888484 57 21528 21354.612835889 104.441316239227 21596.9458478718 -173.387164111031 58 21818 21693.1243448866 42.0844417876842 21900.7912133257 -124.87565511341 59 22205 22191.3024523631 14.0609688572449 22204.6365787796 -13.6975476368898 60 22621 22778.1565188395 -25.4819399295251 22489.32542109 157.156518839507 61 23006 23202.0197932012 35.9659433984505 22774.0142634004 196.019793201154 62 23178 23383.5114459547 -51.5338547507709 23024.0224087961 205.511445954682 63 23358 23541.0030659055 -99.0336200973157 23274.0305541918 183.003065905537 64 23519 23624.2033347774 -81.3912954687744 23495.1879606914 105.203334777394 65 23725 23898.4037566185 -164.749123809497 23716.345367191 173.403756618514 66 23789 23886.1400055072 -242.051830079097 23933.9118245719 97.1400055072409 67 24472 24600.8761513724 191.645566674855 24151.4782819527 128.876151372409 68 24773 24906.0550815544 276.043362582321 24363.9015558633 133.055081554405 69 24477 24273.233853987 104.441316239227 24576.3248297738 -203.766146013037 70 24669 24513.36996422 42.0844417876842 24782.5455939923 -155.630035779992 71 24827 24651.1726729319 14.0609688572449 24988.7663582108 -175.827327068051

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561809myg0vs24cvp3pb8/19mb81293561903.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561809myg0vs24cvp3pb8/19mb81293561903.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561809myg0vs24cvp3pb8/2kvbb1293561903.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561809myg0vs24cvp3pb8/2kvbb1293561903.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561809myg0vs24cvp3pb8/30ph31293561903.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561809myg0vs24cvp3pb8/30ph31293561903.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561809myg0vs24cvp3pb8/40ph31293561903.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293561809myg0vs24cvp3pb8/40ph31293561903.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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