Mathieu Demoor - Opgave 10.2

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 26 May 2008 08:58:41 -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/26/t12118139862lmupso6qc5svd5.htm/, Retrieved Mon, 26 May 2008 16:59:49 +0200

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Dataseries X:

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113 110 107 103 98 98 137 148 147 139 130 128 127 123 118 114 108 111 151 159 158 148 138 137 136 133 126 120 114 116 153 162 161 149 139 135 130 127 122 117 112 113 149 157 157 147 137 132 125 123 117 114 111 112 144 150 149 134 123 116 117 111 105 102 95 93 124 130 124 115 106 105

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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.937593174294072 beta 0.0731471036939834 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 127 122.554583333333 4.44541666666665 14 123 122.669444977203 0.330555022796545 15 118 118.073910629612 -0.0739106296119871 16 114 114.177416424979 -0.177416424978730 17 108 108.296708279908 -0.29670827990779 18 111 111.283803991852 -0.283803991852068 19 151 151.221868100264 -0.221868100264260 20 159 159.161120003202 -0.161120003201972 21 158 158.187945605629 -0.187945605628727 22 148 148.343396645151 -0.343396645150591 23 138 138.412880278382 -0.412880278382204 24 137 137.430566949828 -0.430566949828261 25 136 136.179565822465 -0.179565822465264 26 133 131.534033485340 1.46596651465961 27 126 127.888434317083 -1.88843431708335 28 120 122.070374080312 -2.07037408031229 29 114 114.063752344231 -0.0637523442314603 30 116 116.942403115319 -0.94240311531891 31 153 155.893998058285 -2.89399805828549 32 162 160.775573284191 1.22442671580916 33 161 160.638730845892 0.361269154108214 34 149 150.876013973298 -1.87601397329829 35 139 138.975672785071 0.0243272149286042 36 135 137.90364608892 -2.90364608892006 37 130 133.681425394496 -3.68142539449602 38 127 124.946958923101 2.05304107689935 39 122 120.774415276996 1.22558472300449 40 117 117.210206036495 -0.210206036494895 41 112 110.545988800618 1.45401119938174 42 113 114.370038852264 -1.37003885226360 43 149 152.346752738744 -3.34675273874350 44 157 156.577655297263 0.422344702736893 45 157 155.096719959152 1.90328004084841 46 147 146.207715412651 0.792284587348945 47 137 136.678300038001 0.32169996199903 48 132 135.473309999590 -3.47330999958976 49 125 130.400316274253 -5.40031627425279 50 123 120.02609263586 2.97390736414009 51 117 116.342456409312 0.657543590687624 52 114 111.794243410588 2.20575658941212 53 111 107.302957723667 3.69704227633292 54 112 113.011533432335 -1.01153343233503 55 144 151.183321242829 -7.18332124282941 56 150 151.771482489708 -1.77148248970838 57 149 147.894774396873 1.10522560312731 58 134 137.702177581065 -3.70217758106509 59 123 123.135169070005 -0.135169070004679 60 116 120.439405733113 -4.43940573311335 61 117 113.448510415185 3.55148958481513 62 111 111.712143845337 -0.712143845337124 63 105 103.897232942921 1.10276705707878 64 102 99.3629105906158 2.63708940938416 65 95 94.8985208865902 0.101479113409752 66 93 96.2248969991282 -3.22489699912825 67 124 131.067314299266 -7.06731429926583 68 130 131.240960305020 -1.24096030502017 69 124 127.216558566435 -3.21655856643456 70 115 111.550840219442 3.44915978055781 71 106 103.280905692745 2.71909430725508 72 105 102.557841410924 2.44215858907555 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 102.554868177112 97.7048423823639 107.404893971860 74 97.0161282631429 90.1359449640257 103.896311562260 75 89.8245806846519 81.192770680428 98.4563906888758 76 84.1188327228838 73.859315439108 94.3783500066596 77 76.6095982076949 64.7856033413927 88.433593073997 78 77.2121915673532 63.856409951011 90.5679731836954 79 114.638579772467 99.7661516459297 129.511007899004 80 122.086910381982 105.702015462796 138.471805301168 81 119.472656255579 101.572232475334 137.373080035825 82 107.829268849058 88.405274205693 127.253263492423 83 96.6338347944691 75.6747019350271 117.592967653911 84 93.5115722409988 71.0031849601905 116.019959521807

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t12118139862lmupso6qc5svd5/1topz1211813915.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t12118139862lmupso6qc5svd5/1topz1211813915.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t12118139862lmupso6qc5svd5/253e41211813915.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t12118139862lmupso6qc5svd5/253e41211813915.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t12118139862lmupso6qc5svd5/3e2661211813915.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t12118139862lmupso6qc5svd5/3e2661211813915.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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