Exponentail smoothing - mult+triple - pilsbier - niels baert

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 01 Jun 2008 07:40:54 -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/Jun/01/t12123277331za3i6d3wcomwlu.htm/, Retrieved Sun, 01 Jun 2008 13:42:13 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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4,43 4,43 4,44 4,44 4,44 4,45 4,47 4,48 4,48 4,5 4,52 4,52 4,53 4,53 4,63 4,66 4,67 4,68 4,69 4,69 4,7 4,71 4,72 4,72 4,72 4,73 4,74 4,76 4,81 4,82 4,83 4,83 4,84 4,89 4,92 4,95 4,95 5,01 5,05 5,08 5,11 5,14 5,17 5,18 5,2 5,22 5,24 5,28 5,29 5,33 5,4 5,43 5,46 5,46 5,46 5,47 5,49 5,5 5,54 5,55 5,55 5,56 5,6 5,61 5,63 5,64 5,66 5,67 5,69 5,77 5,77 5,78 5,8 5,82 5,85 5,87 5,88 5,9 5,91 5,94 5,97 5,98 6 6,01 6,02

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 5 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.686614575696178 beta 0.0358454934700404 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 4.53 4.43497253424839 0.0950274657516115 14 4.53 4.49969420656947 0.0303057934305313 15 4.63 4.62043652430831 0.00956347569169314 16 4.66 4.65733725550416 0.00266274449583559 17 4.67 4.67041323329498 -0.000413233294983328 18 4.68 4.68178288945708 -0.00178288945708438 19 4.69 4.69258405979525 -0.00258405979524579 20 4.69 4.69276267518553 -0.00276267518552942 21 4.7 4.70608656021938 -0.00608656021937559 22 4.71 4.72115041863392 -0.0111504186339193 23 4.72 4.73121151664716 -0.0112115166471591 24 4.72 4.72926397189902 -0.00926397189901795 25 4.72 4.74322464567819 -0.0232246456781917 26 4.73 4.70414731942536 0.0258526805746389 27 4.74 4.81776722251646 -0.0777672225164565 28 4.76 4.78992051151631 -0.0299205115163144 29 4.81 4.77576818901657 0.0342318109834272 30 4.82 4.80745383907355 0.0125461609264512 31 4.83 4.82516389657769 0.00483610342231255 32 4.83 4.82760246919499 0.00239753080501082 33 4.84 4.84114082662566 -0.00114082662566428 34 4.89 4.85595198394663 0.0340480160533714 35 4.92 4.89608776863383 0.0239122313661735 36 4.95 4.91834370470068 0.0316562952993156 37 4.95 4.95688087403988 -0.00688087403987847 38 5.01 4.94451247598575 0.0654875240142481 39 5.05 5.05744208713877 -0.00744208713877459 40 5.08 5.09855530081831 -0.0185553008183108 41 5.11 5.11741625263689 -0.00741625263689105 42 5.14 5.11613306159569 0.0238669384043142 43 5.17 5.14219806131586 0.0278019386841359 44 5.18 5.16258046388381 0.0174195361161900 45 5.2 5.18946415994598 0.0105358400540219 46 5.22 5.22885782567948 -0.00885782567948201 47 5.24 5.23985876271087 0.000141237289129847 48 5.28 5.25073755444733 0.0292624455526678 49 5.29 5.27777215560207 0.0122278443979278 50 5.33 5.304365128821 0.0256348711790002 51 5.4 5.37124064663802 0.028759353361977 52 5.43 5.43876597642108 -0.00876597642108301 53 5.46 5.47268372609452 -0.0126837260945214 54 5.46 5.48079886887492 -0.0207988688749188 55 5.46 5.47935076906593 -0.0193507690659267 56 5.47 5.4641615070581 0.00583849294190397 57 5.49 5.48154856751204 0.00845143248795921 58 5.5 5.51471987397711 -0.0147198739771062 59 5.54 5.52533266134113 0.0146673386588736 60 5.55 5.55644755958811 -0.00644755958811327 61 5.55 5.55293705142872 -0.00293705142872369 62 5.56 5.57329014389258 -0.0132901438925819 63 5.6 5.61460454049775 -0.0146045404977500 64 5.61 5.63900210036783 -0.0290021003678271 65 5.63 5.65575402171078 -0.0257540217107826 66 5.64 5.6491591406135 -0.00915914061350254 67 5.66 5.65323440948609 0.00676559051390768 68 5.67 5.66134137391522 0.00865862608477563 69 5.69 5.6793189664412 0.0106810335587983 70 5.77 5.7048506699643 0.0651493300357009 71 5.77 5.7800140278497 -0.0100140278497012 72 5.78 5.78677245691401 -0.00677245691401218 73 5.8 5.78283388605958 0.0171661139404202 74 5.82 5.81364219221143 0.0063578077885742 75 5.85 5.86985498492767 -0.0198549849276661 76 5.87 5.88687706850462 -0.0168770685046233 77 5.88 5.91443214609609 -0.0344321460960897 78 5.9 5.90736974328775 -0.00736974328775375 79 5.91 5.91796678378416 -0.00796678378416171 80 5.94 5.91598839847011 0.0240116015298897 81 5.97 5.94531779416014 0.0246822058398593 82 5.98 5.99894912596645 -0.0189491259664516 83 6 5.99104085165187 0.0089591483481275 84 6.01 6.0108270811518 -0.000827081151795639 85 6.02 6.0173444149626 0.00265558503740237 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 86 6.0336189737387 5.98556034061836 6.08167760685904 87 6.0769192576933 6.01787041815344 6.13596809723316 88 6.10826210684619 6.03936690523253 6.17715730845985 89 6.14215582659063 6.06405461868499 6.22025703449627 90 6.16806290881736 6.08126095064475 6.25486486698997 91 6.18413775367375 6.08904946722908 6.27922604011843 92 6.19834637286976 6.09522235252433 6.30147039321519 93 6.21147424919997 6.1004981903968 6.32245030800313 94 6.23436081234307 6.11550292746226 6.35321869722388 95 6.24819683261748 6.1216949653809 6.37469869985406 96 6.25839865906047 6.12438819753698 6.39240912058397 97 6.26613330853258 3.93193264423224 8.60033397283292

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123277331za3i6d3wcomwlu/1kay51212327646.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123277331za3i6d3wcomwlu/1kay51212327646.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123277331za3i6d3wcomwlu/2n0vj1212327646.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123277331za3i6d3wcomwlu/2n0vj1212327646.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123277331za3i6d3wcomwlu/31yvu1212327646.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t12123277331za3i6d3wcomwlu/31yvu1212327646.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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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Software written by Ed van Stee & Patrick Wessa

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