opdracht 10

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 20 Dec 2010 10:32:55 +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/t12928412632r5c0bolbv9bk3z.htm/, Retrieved Mon, 20 Dec 2010 11:34:27 +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/t12928412632r5c0bolbv9bk3z.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:

KDGP2W102 - Evi Van Dingenen

Dataseries X:

» Textbox « » Textfile « » CSV «

84,9 81,9 95,9 81 89,2 102,5 89,8 88,8 83,2 90,2 100,4 187,1 87,6 85,4 86,1 86,7 89,1 103,7 86,9 85,2 80,8 91,2 102,8 182,5 80,9 83,1 88,3 86,6 93 105,3 93,8 86,4 87 96,7 100,5 196,7 86,8 88,2 93,8 85 90,4 115,9 94,9 87,7 91,7 95,9 106,8 204,5 90,2 90,5 93,2 97,8 99,4 120 108,2 98,5 104,3 102,9 111,1 188,1 93,8 94,5 112,4 102,5 115,8 136,5 122,1 110,6 116,4 112,6 121,5 199,3 102,1 100,6 119 106,8 121,3 145,5 129,7 117,7 121,3 124,3 135,2 210,1 106,8 110,5 111,5 122,1 126,3 143,2 137,3 121,5 121,9 123,9 131,6 220,9

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 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.0545658791491502 beta 0.25774916210425 gamma 0.484979752162203 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 87.6 87.4374732905983 0.162526709401661 14 85.4 85.4574707694395 -0.0574707694395045 15 86.1 86.3438222724077 -0.243822272407698 16 86.7 86.9249094831851 -0.224909483185087 17 89.1 89.1038654903233 -0.00386549032332084 18 103.7 103.728161925143 -0.0281619251432375 19 86.9 89.263236525602 -2.36323652560203 20 85.2 87.7751584373825 -2.57515843738254 21 80.8 82.160132151459 -1.36013215145903 22 91.2 89.1006088566335 2.09939114336653 23 102.8 99.0552173122356 3.74478268776444 24 182.5 185.839775787221 -3.33977578722073 25 80.9 86.181975289146 -5.28197528914602 26 83.1 83.668516015986 -0.568516015986035 27 88.3 84.2988489052085 4.00115109479145 28 86.6 85.0372535044138 1.56274649558621 29 93 87.357263836485 5.64273616351507 30 105.3 102.300104302552 2.99989569744844 31 93.8 86.993897618399 6.80610238160105 32 86.4 86.1021034188466 0.297896581153410 33 87 81.434485449809 5.56551455019095 34 96.7 90.6700468404298 6.0299531595702 35 100.5 101.979782024187 -1.47978202418733 36 196.7 185.543604488798 11.1563955112018 37 86.8 86.3028818725309 0.497118127469122 38 88.2 86.8638531606971 1.3361468393029 39 93.8 90.3180616041513 3.48193839584873 40 85 90.5274626381015 -5.52746263810151 41 90.4 94.8489890207248 -4.44898902072482 42 115.9 108.405104118965 7.49489588103494 43 94.9 95.5283225539246 -0.628322553924605 44 87.7 91.5811265114215 -3.8811265114215 45 91.7 89.376373876203 2.323626123797 46 95.9 98.8780047194497 -2.97800471944967 47 106.8 106.356198492784 0.443801507216449 48 204.5 195.949254076707 8.55074592329348 49 90.2 91.7726280734287 -1.57262807342873 50 90.5 92.6699904442213 -2.16999044422133 51 93.2 96.9320728302648 -3.73207283026477 52 97.8 92.5307255072453 5.26927449275469 53 99.4 98.0015805305656 1.3984194694344 54 120 117.501168892219 2.49883110778102 55 108.2 100.704814643964 7.49518535603633 56 98.5 95.9013434063614 2.59865659363864 57 104.3 97.178202817712 7.12179718228789 58 102.9 104.86130443706 -1.96130443705988 59 111.1 114.328767906606 -3.22876790660592 60 188.1 207.751779632248 -19.6517796322481 61 93.8 97.3110620246897 -3.51106202468972 62 94.5 97.7180259149318 -3.21802591493179 63 112.4 101.081215347127 11.3187846528730 64 102.5 101.714611058633 0.785388941367344 65 115.8 105.189099981901 10.6109000180992 66 136.5 125.848651000864 10.6513489991358 67 122.1 112.055434753528 10.0445652464716 68 110.6 105.449167474752 5.15083252524811 69 116.4 109.278350938839 7.12164906116134 70 112.6 113.135819450739 -0.535819450739439 71 121.5 122.459087510953 -0.959087510953069 72 199.3 208.866822068269 -9.56682206826866 73 102.1 106.910116854964 -4.81011685496409 74 100.6 107.895222227845 -7.2952222278455 75 119 118.158622725819 0.841377274181042 76 106.8 113.700537986824 -6.90053798682369 77 121.3 121.462661551200 -0.162661551199690 78 145.5 141.603233506010 3.89676649398976 79 129.7 127.118571954011 2.58142804598928 80 117.7 117.711596156171 -0.0115961561713505 81 121.3 121.940513740341 -0.640513740340609 82 124.3 121.531963481098 2.76803651890198 83 135.2 130.55650585504 4.64349414495996 84 210.1 213.11703099708 -3.01703099708001 85 106.8 113.584734859316 -6.78473485931625 86 110.5 113.180846833161 -2.68084683316064 87 111.5 127.349912094680 -15.8499120946802 88 122.1 118.119618813076 3.98038118692401 89 126.3 129.406290293180 -3.10629029318035 90 143.2 151.047548918185 -7.84754891818466 91 137.3 134.95376252927 2.34623747073013 92 121.5 123.976519736902 -2.47651973690213 93 121.9 127.379410643105 -5.47941064310531 94 123.9 127.798485263545 -3.89848526354541 95 131.6 136.754218408707 -5.15421840870664 96 220.9 214.564875538885 6.33512446111544 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 113.244094803911 102.467369407242 124.020820200579 98 114.616305249382 103.814229925541 125.418380573224 99 122.455308528548 111.616534345608 133.294082711489 100 122.967200226293 112.078383074296 133.85601737829 101 130.516148052962 119.562029371918 141.470266734005 102 149.925471584574 138.888982000064 160.961961169083 103 138.816794562731 127.679180679348 149.954408446115 104 125.350098416348 114.091071668384 136.609125164312 105 127.395963051111 115.993868135220 138.798057967002 106 128.800685877624 117.232685024923 140.368686730326 107 137.409977678774 125.652245996318 149.167709361230 108 220.859030615277 208.886957049244 232.831104181309

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t12928412632r5c0bolbv9bk3z/106271292841171.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t12928412632r5c0bolbv9bk3z/106271292841171.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t12928412632r5c0bolbv9bk3z/2sxka1292841171.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t12928412632r5c0bolbv9bk3z/2sxka1292841171.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t12928412632r5c0bolbv9bk3z/3sxka1292841171.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t12928412632r5c0bolbv9bk3z/3sxka1292841171.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=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) 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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