Exponential Smoothing – Vooruitzichten kledingprijs (additief) - Matthias Spillemaeckers

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 15:06:52 -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/t1211836379im75deul9yf0ijr.htm/, Retrieved Mon, 26 May 2008 23:13:02 +0200

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Dataseries X:

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8 5 2 5 -4 -4 -1 5 16 5 11 16 22 12 8 4 17 5 11 9 4 7 -5 9 11 11 -4 -7 9 -3 14 11 8 -14 -8 -2 15 -8 -4 -17 -13 0 9 -7 -14 -21 -10 -1 7 -14 -12 -16 -15 -15 -24 -14 -8 -14 -13 0 -6 -37 -12 -36 -32 -18 -22 -13 -17 -18 -19 -24 -14 -3 -6 -25 -19 -11 -13 -11 -22 -10 -4 5 -8 -7 5 -13 -15 3 3 7 16 16 18 10

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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 12 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.0294665928016946 beta 0.872429013811499 gamma 0.295401379572641 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 22 21.1494444444445 0.850555555555545 14 12 10.2899600410509 1.71003995894914 15 8 6.49976258478878 1.50023741521122 16 4 2.82528366483654 1.17471633516346 17 17 16.3380784469556 0.661921553044351 18 5 5.2277792693132 -0.227779269313201 19 11 11.8770746685325 -0.877074668532503 20 9 10.2346901383658 -1.23469013836584 21 4 5.59169375574241 -1.59169375574241 22 7 9.31392587562775 -2.31392587562775 23 -5 -2.21127566467869 -2.78872433532131 24 9 12.0528409420129 -3.05284094201288 25 11 18.9745456389925 -7.9745456389925 26 11 7.71544529177046 3.28455470822954 27 -4 3.56598873356366 -7.56598873356366 28 -7 -1.04754191787462 -5.95245808212538 29 9 11.3464256781728 -2.34642567817278 30 -3 -0.946727796177753 -2.05327220382225 31 14 4.57656260479749 9.42343739520251 32 11 2.51390938370622 8.48609061629378 33 8 -2.31636590675085 10.3163659067509 34 -14 1.48445564884403 -15.4844556488440 35 -8 -10.9687801059443 2.96878010594427 36 -2 3.13345990457096 -5.13345990457096 37 15 8.27352157941668 6.72647842058332 38 -8 0.744189547425426 -8.74418954742543 39 -4 -7.11112946161042 3.11112946161042 40 -17 -10.9135645365030 -6.08643546349696 41 -13 2.54073235050789 -15.5407323505079 42 0 -10.3659201589828 10.3659201589828 43 9 -1.17582877403988 10.1758287740399 44 -7 -3.45519134772467 -3.54480865227533 45 -14 -8.39467179203912 -5.60532820796088 46 -21 -13.1487609903597 -7.85123900964026 47 -10 -20.5790921673784 10.5790921673784 48 -1 -8.87235309839778 7.87235309839778 49 7 0.0886365323900051 6.91136346761 50 -14 -11.8284039746170 -2.17159602538298 51 -12 -15.8799664789478 3.87996647894783 52 -16 -22.0656938090174 6.06569380901745 53 -15 -10.4204656082173 -4.5795343917827 54 -15 -14.7516195454207 -0.248380454579340 55 -24 -5.3765090315148 -18.6234909684852 56 -14 -12.6262275502268 -1.37377244977323 57 -8 -18.2247414025256 10.2247414025256 58 -14 -22.8815782495183 8.88157824951826 59 -13 -23.8300824703794 10.8300824703794 60 0 -12.1806600641247 12.1806600641247 61 -6 -2.54617498650440 -3.45382501349560 62 -37 -16.8171047952368 -20.1828952047632 63 -12 -19.5718664427720 7.57186644277202 64 -36 -24.8346870163289 -11.1653129836711 65 -32 -17.0046403904448 -14.9953596095552 66 -18 -20.9242382152398 2.9242382152398 67 -22 -17.1654221152343 -4.83457788476569 68 -13 -19.1506020848484 6.15060208484844 69 -17 -21.0959219582125 4.0959219582125 70 -18 -26.3697733979883 8.36977339798826 71 -19 -26.8392243021567 7.83922430215669 72 -24 -15.0321090664354 -8.96789093356457 73 -14 -11.1882180369779 -2.81178196302213 74 -3 -30.9049561706655 27.9049561706655 75 -6 -23.7178638671898 17.7178638671898 76 -25 -33.2251150402384 8.22511504023835 77 -19 -24.5947886374582 5.59478863745824 78 -11 -20.913877764617 9.913877764617 79 -13 -17.1375492459445 4.13754924594448 80 -11 -13.4423028845703 2.44230288457030 81 -22 -13.9146640894396 -8.08533591056042 82 -10 -16.4640054696531 6.46400546965314 83 -4 -15.3325619608783 11.3325619608783 84 5 -6.34209522737418 11.3420952273742 85 -8 2.28628118007011 -10.2862811800701 86 -7 -6.61538003449939 -0.384619965500612 87 5 -1.68081647059639 6.68081647059639 88 -13 -13.0168920284697 0.0168920284697158 89 -15 -4.37561188717197 -10.6243881128280 90 3 0.655618496562547 2.34438150343745 91 3 2.94822521631488 0.0517747836851212 92 7 6.32740173394379 0.672598266056214 93 16 3.02950307648641 12.9704969235136 94 16 6.05800076830959 9.94199923169041 95 18 9.56328379505027 8.43671620494973 96 10 19.2722627961366 -9.27226279613664 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 21.3635816735299 4.73087987940464 37.9962834676551 98 16.1393984397394 -0.51860059966631 32.7973974791451 99 23.6564225144511 6.94419017890096 40.3686548500013 100 10.5867006649311 -6.2193030351551 27.3927043650173 101 16.5499678319675 -0.399478845132617 33.4994145090677 102 26.2588023284380 9.10682532902565 43.4107793278504 103 28.4112100970715 10.9891799103753 45.8332402837676 104 32.5516834003487 14.7848642239594 50.3185025767381 105 33.3272784890618 15.1351330157324 51.5194239623911 106 35.3394231341257 16.6371325223251 54.0417137459262 107 38.0987095065667 18.7987075963018 57.3987114168316 108 42.2436109205234 22.2570400735760 62.2301817674707

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211836379im75deul9yf0ijr/1kukc1211835998.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211836379im75deul9yf0ijr/1kukc1211835998.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211836379im75deul9yf0ijr/2jzsf1211835998.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211836379im75deul9yf0ijr/2jzsf1211835998.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211836379im75deul9yf0ijr/38jqb1211835999.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211836379im75deul9yf0ijr/38jqb1211835999.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')

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