opgave10(oefening2)

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 30 May 2008 03:00:10 -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/30/t1212138054mss0nl614ykkm0q.htm/, Retrieved Fri, 30 May 2008 09:00:59 +0000

User-defined keywords:

Inleiding tot kwantitatief onderzoek

Dataseries X:

» Textbox « » Textfile « » CSV «

107,5 107,5 113,3 107,8 104,5 105,1 104,2 106,6 103,8 107,7 106,4 110 113,2 113,9 112 113,9 113,1 111,7 110,7 113,5 114 112,7 112,2 115,8 118,4 118,8 123,9 118 120,2 118,7 119,8 124,8 121,3 120,2 118,3 129,6 130,2 127,19 133,1 129,12 123,28 123,36 124,13 126,96 127,14 123,7 123,67 130,19 134,01 124,96 129,96 128,32 132,38 126,25 128,91 131,42 129,44 126,86 126,71 131,63 132,78 126,61 132,84 123,14 128,13 125,49 126,48 130,86 127,32 126,56 126,64 129,26 126,47 135,38 135,5 132,22 122,62 125,16 128,5 133,86 128,87 125,07 125,25 132,16 130,24

Text written by user:

Kara Van den Acker

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 9 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.208973562504445 beta 0.109887621724869 gamma 0.279719189082164 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 113.2 109.900444444445 3.2995555555555 14 113.9 111.380791994234 2.51920800576609 15 112 110.001750974464 1.99824902553620 16 113.9 112.438896974226 1.46110302577384 17 113.1 112.280679190987 0.819320809013234 18 111.7 111.373827119935 0.326172880064505 19 110.7 110.796410275419 -0.0964102754186626 20 113.5 113.965970795695 -0.465970795694773 21 114 114.468435900229 -0.468435900228599 22 112.7 113.192962218133 -0.492962218133187 23 112.2 112.901042992979 -0.701042992979126 24 115.8 116.528708577351 -0.728708577350915 25 118.4 121.388936070923 -2.98893607092288 26 118.8 121.409624807102 -2.60962480710229 27 123.9 118.752880184995 5.14711981500547 28 118 121.710871602031 -3.71087160203068 29 120.2 120.192742968145 0.00725703185524651 30 118.7 118.851325841396 -0.151325841396485 31 119.8 117.913907633313 1.88609236668715 32 124.8 121.294799519731 3.50520048026935 33 121.3 122.596593046716 -1.29659304671632 34 120.2 121.093616172693 -0.893616172692958 35 118.3 120.613715933197 -2.31371593319659 36 129.6 123.803007405571 5.79699259442884 37 130.2 129.581431038813 0.618568961187009 38 127.19 130.577369667350 -3.38736966735038 39 133.1 129.593983627967 3.50601637203326 40 129.12 130.330964737036 -1.21096473703628 41 123.28 130.297252996741 -7.0172529967407 42 123.36 127.430811708914 -4.07081170891371 43 124.13 126.013130544339 -1.88313054433884 44 126.96 128.766048005480 -1.80604800547955 45 127.14 127.574936543771 -0.434936543771229 46 123.7 126.04045031653 -2.34045031652990 47 123.67 124.610019127134 -0.940019127134306 48 130.19 129.578577988909 0.611422011091292 49 134.01 132.706052664744 1.3039473352558 50 124.96 132.553084430357 -7.59308443035728 51 129.96 131.713746041498 -1.75374604149775 52 128.32 129.684752523245 -1.36475252324536 53 132.38 127.707522496390 4.67247750361025 54 126.25 127.577658615698 -1.32765861569837 55 128.91 126.922062130703 1.98793786929713 56 131.42 130.294660268441 1.12533973155871 57 129.44 129.880499966701 -0.440499966701083 58 126.86 127.784088617249 -0.924088617249467 59 126.71 126.852892655279 -0.142892655279169 60 131.63 132.243001110282 -0.613001110281886 61 132.78 135.151409544114 -2.37140954411387 62 126.61 132.060959281453 -5.45095928145291 63 132.84 132.809676704996 0.0303232950044219 64 123.14 131.128911419740 -7.98891141973972 65 128.13 128.840456227516 -0.71045622751592 66 125.49 125.871687732967 -0.381687732967038 67 126.48 125.782731406189 0.697268593811103 68 130.86 128.300443240701 2.55955675929891 69 127.32 127.478157694923 -0.158157694922977 70 126.56 124.978857901530 1.58114209847038 71 126.64 124.446680461753 2.19331953824712 72 129.26 129.977264682529 -0.717264682529446 73 126.47 132.228703652032 -5.75870365203167 74 135.38 127.425110152802 7.95488984719839 75 135.5 132.172068873498 3.32793112650157 76 132.22 129.465719011051 2.75428098894949 77 122.62 131.339159575819 -8.71915957581882 78 125.16 126.892003326774 -1.73200332677361 79 128.5 126.851068653386 1.64893134661386 80 133.86 130.093032501031 3.76696749896905 81 128.87 129.062774510051 -0.192774510051493 82 125.07 127.081338898747 -2.01133889874713 83 125.25 125.991636727422 -0.741636727421522 84 132.16 130.255239494892 1.90476050510765 85 130.24 131.989686221112 -1.74968622111246 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 86 131.200844084039 125.230256164462 137.171432003615 87 133.221613565442 127.092535767388 139.350691363496 88 129.576421638786 123.261217991057 135.891625286515 89 128.155904512373 121.626423390558 134.685385634188 90 127.097348687425 120.325334901273 133.869362473577 91 128.226724946338 121.184173253020 135.269276639655 92 131.615172763445 124.274613461765 138.955732065124 93 128.857480769471 121.192195615821 136.522765923121 94 126.454287599707 118.438460289278 134.470114910136 95 126.052373491941 117.661182869943 134.443564113939 96 131.060075601273 122.26974167811 139.850409524436 97 131.547696476016 122.335489629103 140.759903322928

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/30/t1212138054mss0nl614ykkm0q/1wgua1212138000.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/30/t1212138054mss0nl614ykkm0q/1wgua1212138000.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/30/t1212138054mss0nl614ykkm0q/2lt8u1212138000.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/30/t1212138054mss0nl614ykkm0q/2lt8u1212138000.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/30/t1212138054mss0nl614ykkm0q/375yo1212138000.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/30/t1212138054mss0nl614ykkm0q/375yo1212138000.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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