Paper statistiek - decomposition by Loess 3

*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 13:25:49 +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/t1292851475o9arp9030ftft5j.htm/, Retrieved Mon, 20 Dec 2010 14:24:40 +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/t1292851475o9arp9030ftft5j.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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16306977 16307888 16307482 16308869 16311019 16312596 16315238 16319511 16327575 16330818 16331930 16334210 16334715 16335459 16334090 16333559 16334600 16336676 16337253 16342333 16348917 16352678 16352972 16357992 16359133 16362938 16365065 16367596 16371278 16374541 16377339 16383275 16393843 16399139 16401009 16405399 16409106 16414307 16418055 16423337 16428686 16434935 16440452 16449092 16464859 16473709 16479291 16485787 16489042 16495231 16501683 16506782 16513615 16520661 16528400 16538542 16554596 16562317 16568499 16574989

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 'Gwilym Jenkins' @ 72.249.127.135 Seasonal Decomposition by Loess - Parameters Component Window Degree Jump Seasonal 601 0 61 Trend 19 1 2 Low-pass 13 1 2 Seasonal Decomposition by Loess - Time Series Components t Observed Fitted Seasonal Trend Remainder 1 16306977 16307832.0173111 -2299.11856067163 16308421.1012496 855.017311051488 2 16307888 16308574.9467278 -3013.15079272071 16310214.2040649 686.946727849543 3 16307482 16307943.4767738 -4986.78365396811 16312007.3068801 461.476773848757 4 16308869 16309605.6732511 -5721.83743844782 16313854.1641874 736.67325108312 5 16311019 16311736.4698659 -5399.49136055637 16315701.0214946 717.469865949824 6 16312596 16312152.5512176 -4568.22344373013 16317607.6722261 -443.448782371357 7 16315238 16314886.233442 -3924.55639959976 16319514.3229576 -351.76655799523 8 16319511 16318157.3276472 -596.478651230666 16321461.1510041 -1353.67235284112 9 16327575 16324417.2220498 7324.79889964671 16323407.9790506 -3157.77795019746 10 16330818 16327471.4668826 8684.2579782709 16325480.2751391 -3346.53311737627 11 16331930 16329029.9125319 7277.51624040198 16327552.5712277 -2900.08746805973 12 16334210 16331539.2064962 7223.06938144133 16329657.7241223 -2670.79350379109 13 16334715 16339966.2415436 -2299.11856067163 16331762.8770170 5251.24154363014 14 16335459 16340205.1794807 -3013.15079272071 16333725.9713120 4746.1794806812 15 16334090 16337477.7180469 -4986.78365396811 16335689.0656070 3387.71804693528 16 16333559 16335405.3323986 -5721.83743844782 16337434.5050398 1846.33239862323 17 16334600 16335419.5468879 -5399.49136055637 16339179.9444726 819.546887941658 18 16336676 16337014.2323888 -4568.22344373013 16340905.9910549 338.232388813049 19 16337253 16335798.5187624 -3924.55639959976 16342632.0376372 -1454.48123761825 20 16342333 16340478.3332964 -596.478651230666 16344784.1453549 -1854.66670363955 21 16348917 16343572.9480278 7324.79889964671 16346936.2530725 -5344.05197217129 22 16352678 16346896.8889728 8684.2579782709 16349774.8530489 -5781.11102716252 23 16352972 16346053.0307343 7277.51624040198 16352613.4530253 -6918.96926565655 24 16357992 16352776.9210321 7223.06938144133 16355984.0095865 -5215.07896792516 25 16359133 16361210.5524130 -2299.11856067163 16359354.5661477 2077.55241296254 26 16362938 16365825.1707247 -3013.15079272071 16363063.9800680 2887.17072473653 27 16365065 16368343.3896657 -4986.78365396811 16366773.3939883 3278.38966571353 28 16367596 16370320.3228011 -5721.83743844782 16370593.5146373 2724.32280113362 29 16371278 16373541.8560742 -5399.49136055637 16374413.6352864 2263.85607418232 30 16374541 16375396.045324 -4568.22344373013 16378254.1781197 855.045324010774 31 16377339 16376507.8354465 -3924.55639959976 16382094.7209531 -831.164553463459 32 16383275 16380955.6922115 -596.478651230666 16386190.7864397 -2319.30778845958 33 16393843 16390074.3491740 7324.79889964671 16390286.8519263 -3768.65082596242 34 16399139 16394670.576628 8684.2579782709 16394923.1653937 -4468.42337200046 35 16401009 16395181.0048985 7277.51624040198 16399559.4788611 -5827.99510154314 36 16405399 16398824.5908236 7223.06938144133 16404750.3397949 -6574.40917638317 37 16409106 16410569.9178319 -2299.11856067163 16409941.2007287 1463.9178319294 38 16414307 16415967.0384242 -3013.15079272071 16415660.1123685 1660.03842419200 39 16418055 16419717.7596457 -4986.78365396811 16421379.0240083 1662.75964565761 40 16423337 16424859.6610732 -5721.83743844782 16427536.1763652 1522.66107320786 41 16428686 16429078.1626384 -5399.49136055637 16433693.3287222 392.162638388574 42 16434935 16434292.7920860 -4568.22344373013 16440145.4313577 -642.207913963124 43 16440452 16438231.0224064 -3924.55639959976 16446597.5339932 -2220.97759361751 44 16449092 16445460.5386879 -596.478651230666 16453319.9399633 -3631.46131208353 45 16464859 16462350.8551669 7324.79889964671 16460042.3459334 -2508.14483305998 46 16473709 16471621.1924721 8684.2579782709 16467112.5495496 -2087.80752789229 47 16479291 16477121.7305938 7277.51624040198 16474182.7531658 -2169.26940622926 48 16485787 16482842.5799240 7223.06938144133 16481508.3506946 -2944.42007604241 49 16489042 16491549.1703373 -2299.11856067163 16488833.9482234 2507.17033729888 50 16495231 16497197.6011167 -3013.15079272071 16496277.549676 1966.60111671872 51 16501683 16504631.6325253 -4986.78365396811 16503721.1511286 2948.63252533786 52 16506782 16508317.0217016 -5721.83743844782 16510968.8157369 1535.02170155011 53 16513615 16514413.0110154 -5399.49136055637 16518216.4803452 798.011015394703 54 16520661 16520455.8099358 -4568.22344373013 16525434.4135079 -205.190064189956 55 16528400 16528072.2097289 -3924.55639959976 16532652.3466707 -327.790271077305 56 16538542 16537851.4042278 -596.478651230666 16539829.0744235 -690.595772240311 57 16554596 16554861.3989241 7324.79889964671 16547005.8021763 265.398924088106 58 16562317 16561803.3968594 8684.2579782709 16554146.3451623 -513.60314056091 59 16568499 16568433.5956113 7277.51624040198 16561286.8881483 -65.4043887145817 60 16574989 16574348.8712034 7223.06938144133 16568406.0594151 -640.128796555102

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292851475o9arp9030ftft5j/1o3mu1292851546.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292851475o9arp9030ftft5j/1o3mu1292851546.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292851475o9arp9030ftft5j/2o3mu1292851546.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292851475o9arp9030ftft5j/2o3mu1292851546.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292851475o9arp9030ftft5j/3yu3x1292851546.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292851475o9arp9030ftft5j/3yu3x1292851546.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292851475o9arp9030ftft5j/49m301292851546.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292851475o9arp9030ftft5j/49m301292851546.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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