inschrijvingsgeld studenten-exponential smoothing-Natalie Van Nylen

R Software Module: rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Tue, 27 May 2008 05:53:50 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/27/t1211889334bmvt3eogty6w8b6.htm/, Retrieved Tue, 27 May 2008 13:55:34 +0200

User-defined keywords:

Dataseries X:

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513,13 513,13 513,13 513,13 513,13 513,13 513,13 513,13 513,13 527,96 527,96 527,96 527,96 527,96 527,96 527,96 527,96 527,96 527,96 527,96 527,96 536,61 536,61 536,61 536,61 536,61 536,61 536,61 536,61 536,61 536,61 536,61 536,61 545,06 545,06 545,06 545,06 545,06 545,06 545,06 545,06 545,06 545,06 545,06 545,06 564,24 564,24 564,24 564,24 564,24 564,24 564,24 564,24 564,24 564,24 564,24 564,24 573,68 573,68 573,68 573,68 573,68 573,68 573,68 573,68 573,68 573,68 573,68 573,68 576,3 576,29 576,29 576,29 576,29 576,29 576,29 576,29 576,3 576,29 576,3 576,29 589,85 589,85 589,85 589,85 589,85 589,85 589,85 589,85 589,85 589,85 589,85 589,85 599,12 599,12 599,12

Text written by user:

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 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.826917432391495 beta 0.00124120623207274 gamma 0.000613968311953702 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 527.96 521.992083333334 5.9679166666665 14 527.96 526.580365951964 1.37963404803634 15 527.96 527.375933710503 0.584066289496946 16 527.96 527.771732091937 0.188267908063494 17 527.96 528.097931125538 -0.137931125537875 18 527.96 528.154248922756 -0.194248922756174 19 527.96 528.163797179449 -0.203797179448998 20 527.96 528.165240643889 -0.205240643889169 21 527.96 528.16527982854 -0.205279828540256 22 536.61 536.815075916622 -0.205075916622036 23 536.61 536.814830138215 -0.204830138215243 24 536.61 536.81457736571 -0.204577365709952 25 536.61 538.102457835952 -1.49245783595245 26 536.61 536.520213895132 0.0897861048678124 27 536.61 536.246850246725 0.36314975327457 28 536.61 536.457450974799 0.152549025200983 29 536.61 536.751566258199 -0.141566258199418 30 536.61 536.802355866071 -0.192355866071466 31 536.61 536.810954202613 -0.20095420261282 32 536.61 536.812237031668 -0.20223703166846 33 536.61 536.812251645196 -0.202251645196384 34 545.06 545.46204661433 -0.402046614329947 35 545.06 545.29621499441 -0.236214994409806 36 545.06 545.267269987405 -0.207269987405084 37 545.06 546.550044682062 -1.49004468206192 38 545.06 544.967224497414 0.0927755025863917 39 545.06 544.693625088429 0.366374911570574 40 545.06 544.904136891134 0.155863108865901 41 545.06 545.198231309737 -0.138231309737193 42 545.06 545.249046586726 -0.189046586725681 43 545.06 545.257657246254 -0.197657246254039 44 545.06 545.258946369516 -0.198946369516420 45 545.06 545.258965584685 -0.198965584685197 46 564.24 553.908743492912 10.3312565070883 47 564.24 562.626788218473 1.61321178152718 48 564.24 564.137370998639 0.102629001360697 49 564.24 565.686789795405 -1.44678979540538 50 564.24 564.150469971103 0.0895300288967746 51 564.24 563.884776505568 0.35522349443238 52 564.24 564.096593798579 0.143406201421499 53 564.24 564.390892507245 -0.150892507245089 54 564.24 564.441756000741 -0.201756000740943 55 564.24 564.450366446048 -0.210366446047601 56 564.24 564.451643265865 -0.211643265865177 57 564.24 564.451647454694 -0.211647454693662 58 573.68 573.102528765152 0.577471234848417 59 573.68 573.754532177217 -0.0745321772166108 60 573.68 573.868057474968 -0.188057474967650 61 573.68 575.175367495233 -1.49536749523281 62 573.68 573.597420916153 0.0825790838468947 63 573.68 573.324380424822 0.355619575177798 64 573.68 573.534875738535 0.145124261465298 65 573.68 573.828938633934 -0.148938633933767 66 573.68 573.879789186852 -0.199789186852172 67 573.68 573.888403901173 -0.208403901172915 68 573.68 573.889684253513 -0.209684253513387 69 573.68 573.88969119968 -0.209691199680606 70 576.3 582.540658853125 -6.24065885312518 71 576.29 577.545949217969 -1.25594921796858 72 576.29 576.672702394204 -0.382702394203648 73 576.29 577.808892723166 -1.51889272316566 74 576.29 576.201610771014 0.0883892289864434 75 576.29 575.923360132646 0.366639867354024 76 576.29 576.132913587683 0.157086412317085 77 576.29 576.426816860924 -0.136816860923773 78 576.3 576.477678073012 -0.177678073012316 79 576.29 576.494590989154 -0.204590989154212 80 576.3 576.489043134129 -0.189043134128838 81 576.29 576.496158731808 -0.206158731808500 82 589.85 585.139450326843 4.71054967315717 83 589.85 589.202299462886 0.647700537114133 84 589.85 589.906544286791 -0.0565442867909951 85 589.85 591.31589214378 -1.46589214377946 86 589.85 589.756234937563 0.0937650624367734 87 589.85 589.486091597673 0.363908402326615 88 589.85 589.696993643659 0.153006356341280 89 589.85 589.991117183196 -0.141117183195547 90 589.85 590.042038995871 -0.192038995871144 91 589.85 590.050679969148 -0.200679969147586 92 589.85 590.051978085697 -0.201978085696965 93 589.85 590.051992680225 -0.201992680224748 94 599.12 598.702852969377 0.417147030622914 95 599.12 599.214175455488 -0.0941754554883119 96 599.12 599.303308394385 -0.183308394384994 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 600.605986070096 597.366650388677 603.845321751516 98 600.258473963714 596.052959150077 604.463988777351 99 599.910534720117 594.92081938788 604.900250052353 100 599.819829999531 594.151847067988 605.487812931074 101 599.986579465223 593.711813238305 606.261345692142 102 600.153513769703 593.324365706026 606.98266183338 103 600.320476966478 592.977468806333 607.663485126623 104 600.487449431184 592.663113676393 608.311785185974 105 600.65441925074 592.375610829532 608.933227671949 106 609.472519949444 600.76188808015 618.183151818737 107 609.638557144742 600.515533075183 618.7615812143 108 609.80536779441 600.286855682872 619.323879905947

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211889334bmvt3eogty6w8b6/1o8nl1211889224.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211889334bmvt3eogty6w8b6/1o8nl1211889224.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211889334bmvt3eogty6w8b6/2qe4k1211889224.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211889334bmvt3eogty6w8b6/2qe4k1211889224.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211889334bmvt3eogty6w8b6/3g9vw1211889224.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211889334bmvt3eogty6w8b6/3g9vw1211889224.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) if (par2 == 'Single') K <- 1 if (par2 == 'Double') K <- 2 if (par2 == 'Triple') K <- par1 nx <- length(x) nxmK <- nx - K x <- ts(x, frequency = par1) if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0) if (par2 == 'Double') fit <- HoltWinters(x, gamma=0) if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) fit myresid <- x - fit$fitted[,'xhat'] bitmap(file='test1.png') op <- par(mfrow=c(2,1)) plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing') plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors') par(op) dev.off() bitmap(file='test2.png') p <- predict(fit, par1, prediction.interval=TRUE) np <- length(p[,1]) plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing') dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF') spectrum(myresid,main='Residals Periodogram') cpgram(myresid,main='Residal Cumulative Periodogram') qqnorm(myresid,main='Residual Normal QQ Plot') qqline(myresid) par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'alpha',header=TRUE) a<-table.element(a,fit$alpha) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'beta',header=TRUE) a<-table.element(a,fit$beta) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'gamma',header=TRUE) a<-table.element(a,fit$gamma) 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,'Interpolation Forecasts of Exponential Smoothing',4,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,'Residuals',header=TRUE) a<-table.row.end(a) for (i in 1:nxmK) { a<-table.row.start(a) a<-table.element(a,i+K,header=TRUE) a<-table.element(a,x[i+K]) a<-table.element(a,fit$fitted[i,'xhat']) a<-table.element(a,myresid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Forecast',header=TRUE) a<-table.element(a,'95% Lower Bound',header=TRUE) a<-table.element(a,'95% Upper Bound',header=TRUE) a<-table.row.end(a) for (i in 1:np) { a<-table.row.start(a) a<-table.element(a,nx+i,header=TRUE) a<-table.element(a,p[i,'fit']) a<-table.element(a,p[i,'lwr']) a<-table.element(a,p[i,'upr']) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab')

Copyright

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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