Paper: Decomposition by 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: Wed, 29 Dec 2010 16:00:25 +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/t1293638335xzqvwh30r7c9w9k.htm/, Retrieved Wed, 29 Dec 2010 16:58:59 +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/t1293638335xzqvwh30r7c9w9k.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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31245 30951 30872 30752 30967 30781 30681 31356 31434 31594 31949 32396 32441 32447 32288 32418 32346 32091 31855 31683 31615 31840 31536 31383 31638 31626 31720 31472 31372 31419 31341 31171 31036 30532 30666 30571 30173 30032 29874 30018 29911 29963 30050 29901 29544 29451 29293 29334 29389 29563

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 2 seconds R Server 'Herman Ole Andreas Wold' @ www.yougetit.org Seasonal Decomposition by Loess - Parameters Component Window Degree Jump Seasonal 501 0 51 Trend 19 1 2 Low-pass 13 1 2 Seasonal Decomposition by Loess - Time Series Components t Observed Fitted Seasonal Trend Remainder 1 31245 31756.5620480696 158.923126403573 30574.5148255268 511.562048069587 2 30951 31092.6251090379 119.08061157183 30690.2942793902 141.625109037937 3 30872 30895.7139465703 42.2123201760979 30806.0737332536 23.7139465702785 4 30752 30540.9704524502 35.8524880923426 30927.1770594575 -211.029547549813 5 30967 30848.7269877832 36.9926265554592 31048.2803856613 -118.273012216774 6 30781 30415.7807896402 -24.2427384327288 31170.4619487925 -365.219210359759 7 30681 30151.0846399455 -81.7281518691755 31292.6435119237 -529.915360054485 8 31356 31302.5185849713 -4.36537592935271 31413.846790958 -53.4814150286875 9 31434 31426.4523285206 -93.5023985130588 31535.0500699924 -7.54767147936218 10 31594 31635.4391264096 -117.952224029251 31670.5130976197 41.4391264095902 11 31949 32174.6759287805 -82.6520540274419 31805.9761252469 225.67592878054 12 32396 32867.6024023954 11.3815704833911 31913.0160271213 471.60240239535 13 32441 32703.0209446008 158.923126403573 32020.0559289956 262.020944600808 14 32447 32707.5038814463 119.08061157183 32067.4155069819 260.503881446282 15 32288 32419.0125948557 42.2123201760979 32114.7750849682 131.012594855747 16 32418 32699.6407128484 35.8524880923426 32100.5067990592 281.640712848428 17 32346 32568.7688602942 36.9926265554592 32086.2385131503 222.768860294233 18 32091 32178.4865139249 -24.2427384327288 32027.7562245078 87.4865139248977 19 31855 31822.4542160038 -81.7281518691755 31969.2739358654 -32.5457839961819 20 31683 31473.5255204979 -4.36537592935271 31896.8398554314 -209.474479502096 21 31615 31499.0966235155 -93.5023985130588 31824.4057749975 -115.903376484483 22 31840 32042.3017593443 -117.952224029251 31755.6504646849 202.301759344329 23 31536 31467.7568996551 -82.6520540274419 31686.8951543723 -68.2431003448582 24 31383 31123.5277461497 11.3815704833911 31631.0906833669 -259.472253850272 25 31638 31541.790661235 158.923126403573 31575.2862123615 -96.2093387650348 26 31626 31608.7178207848 119.08061157183 31524.2015676433 -17.2821792151735 27 31720 31924.6707568987 42.2123201760979 31473.1169229252 204.670756898671 28 31472 31500.8492894722 35.8524880923426 31407.2982224354 28.8492894722149 29 31372 31365.5278514989 36.9926265554592 31341.4795219457 -6.47214850111413 30 31419 31613.2838648216 -24.2427384327288 31248.9588736111 194.28386482158 31 31341 31607.2899265925 -81.7281518691755 31156.4382252766 266.289926592533 32 31171 31316.357990812 -4.36537592935271 31030.0073851174 145.357990811957 33 31036 31261.9258535549 -93.5023985130588 30903.5765449582 225.925853554905 34 30532 30419.3237506033 -117.952224029251 30762.6284734259 -112.676249396653 35 30666 30792.9716521338 -82.6520540274419 30621.6804018936 126.971652133794 36 30571 30637.2900071955 11.3815704833911 30493.3284223211 66.2900071954718 37 30173 29822.1004308478 158.923126403573 30364.9764427486 -350.8995691522 38 30032 29690.8850375507 119.08061157183 30254.0343508775 -341.114962449297 39 29874 29562.6954208176 42.2123201760979 30143.0922590063 -311.304579182404 40 30018 29952.4452033571 35.8524880923426 30047.7023085506 -65.5547966429185 41 29911 29832.6950153497 36.9926265554592 29952.3123580948 -78.3049846503054 42 29963 30075.9631712741 -24.2427384327288 29874.2795671586 112.963171274099 43 30050 30385.4813756468 -81.7281518691755 29796.2467762224 335.481375646759 44 29901 30081.3873921434 -4.36537592935271 29724.977983786 180.387392143359 45 29544 29527.7932071635 -93.5023985130588 29653.7091913496 -16.2067928365141 46 29451 29437.0817290345 -117.952224029251 29582.8704949948 -13.9182709655215 47 29293 29156.6202553875 -82.6520540274419 29512.03179864 -136.379744612532 48 29334 29217.3808594111 11.3815704833911 29439.2375701055 -116.619140588857 49 29389 29252.6335320255 158.923126403573 29366.443341571 -136.366467974531 50 29563 29714.7183407588 119.08061157183 29292.2010476693 151.718340758838

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293638335xzqvwh30r7c9w9k/1p7ft1293638423.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293638335xzqvwh30r7c9w9k/1p7ft1293638423.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293638335xzqvwh30r7c9w9k/2p7ft1293638423.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293638335xzqvwh30r7c9w9k/2p7ft1293638423.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293638335xzqvwh30r7c9w9k/3igwe1293638423.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293638335xzqvwh30r7c9w9k/3igwe1293638423.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293638335xzqvwh30r7c9w9k/4speh1293638423.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293638335xzqvwh30r7c9w9k/4speh1293638423.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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