Gemiddelde consumptieprijs - broodje - Elisa Somers

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 10:48:13 -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/t1211820525j164k043yvz8tbt.htm/, Retrieved Mon, 26 May 2008 18:48:45 +0200

User-defined keywords:

Dataseries X:

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4.07 4.07 4.08 4.09 4.08 4.09 4.12 4.14 4.14 4.14 4.14 4.14 4.23 4.29 4.32 4.33 4.35 4.35 4.35 4.35 4.36 4.36 4.38 4.4 4.4 4.4 4.43 4.44 4.46 4.47 4.49 4.49 4.57 4.62 4.64 4.66 4.67 4.68 4.72 4.74 4.75 4.76 4.77 4.76 4.77 4.77 4.78 4.81 4.81 4.85 4.92 4.96 4.95 4.96 4.97 5 5 5.01 5.01 5.02 5.04 5.04 5.19 5.22 5.22 5.22 5.24 5.28 5.34 5.36 5.38 5.39 5.41 5.44 5.51 5.55 5.56 5.57 5.58 5.58 5.59 5.61 5.63 5.64 5.64

Text written by user:

Additief Double

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.0708297900210963 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 4.08 4.07 0.00999999999999979 4 4.09 4.08070829790021 0.00929170209978913 5 4.08 4.09136642720888 -0.0113664272088769 6 4.09 4.08056134555638 0.00943865444361691 7 4.12 4.09122988346871 0.0287701165312946 8 4.14 4.1232676647815 0.0167323352184994 9 4.14 4.14445281257159 -0.00445281257158836 10 4.14 4.14413742079214 -0.00413742079213986 11 4.14 4.1438443681462 -0.00384436814620326 12 4.14 4.14357207235764 -0.00357207235764445 13 4.23 4.14331906322261 0.0866809367773884 14 4.29 4.23945865577339 0.0505413442266134 15 4.32 4.30303848857234 0.0169615114276587 16 4.33 4.3342398688652 -0.004239868865203 17 4.35 4.34393955984376 0.00606044015623564 18 4.35 4.36436881954747 -0.0143688195474656 19 4.35 4.36335107907607 -0.0133510790760676 20 4.35 4.36240542494855 -0.0124054249485548 21 4.36 4.36152675130433 -0.00152675130432556 22 4.36 4.37141861183003 -0.0114186118300257 23 4.38 4.37060983395177 0.00939016604822651 24 4.4 4.39127493744123 0.00872506255876804 25 4.4 4.41189293179019 -0.0118929317901904 26 4.4 4.41105055792876 -0.0110505579287556 27 4.43 4.41026784923105 0.0197321507689532 28 4.44 4.44166547332668 -0.00166547332667477 29 4.46 4.45154750820066 0.00845249179933827 30 4.47 4.47214619641996 -0.00214619641996450 31 4.49 4.48199418177819 0.00800581822180657 32 4.49 4.50256123220179 -0.0125612322017918 33 4.57 4.50167152276253 0.0683284772374675 34 4.62 4.58651121445772 0.0334887855422767 35 4.64 4.63888321810574 0.00111678189425479 36 4.66 4.65896231953281 0.00103768046718677 37 4.67 4.67903581822241 -0.00903581822241417 38 4.68 4.68839581311505 -0.00839581311505189 39 4.72 4.69780113943506 0.0221988605649441 40 4.74 4.73937348006758 0.00062651993242202 41 4.75 4.75941785634284 -0.00941785634283576 42 4.76 4.76875079155562 -0.00875079155562375 43 4.77 4.77813097482722 -0.00813097482722114 44 4.76 4.78755505958754 -0.0275550595875416 45 4.77 4.77560334050294 -0.00560334050293765 46 4.77 4.7852064570717 -0.0152064570716979 47 4.78 4.78412938691034 -0.00412938691034359 48 4.81 4.79383690330257 0.0161630966974302 49 4.81 4.82498173204774 -0.0149817320477386 50 4.85 4.82392057911264 0.0260794208873554 51 4.92 4.86576777901797 0.0542322209820325 52 4.96 4.9396090358425 0.0203909641574969 53 4.95 4.98105332355211 -0.031053323552106 54 4.96 4.96885382316545 -0.00885382316545336 55 4.97 4.97822670872976 -0.00822670872976072 56 5 4.98764401267787 0.0123559873221337 57 5 5.0185191846654 -0.0185191846653971 58 5.01 5.01720747470419 -0.00720747470418548 59 5.01 5.0266969707843 -0.016696970784305 60 5.02 5.02551432784966 -0.00551432784966455 61 5.04 5.03512374916596 0.00487625083403564 62 5.04 5.05546913298863 -0.0154691329886303 63 5.19 5.05437345754724 0.135626542452763 64 5.22 5.21397985707045 0.00602014292954589 65 5.22 5.24440626253005 -0.0244062625300501 66 5.22 5.24267757207985 -0.0226775720798473 67 5.24 5.24107132441124 -0.00107132441124236 68 5.28 5.26099544272815 0.0190045572718498 69 5.34 5.30234153152916 0.0376584684708403 70 5.36 5.36500887294346 -0.0050088729434643 71 5.38 5.38465409552464 -0.00465409552463747 72 5.39 5.40432444691589 -0.0143244469158894 73 5.41 5.41330984934867 -0.00330984934866763 74 5.44 5.4330754134143 0.00692458658569972 75 5.51 5.46356588042815 0.0464341195718507 76 5.55 5.53685479936724 0.0131452006327626 77 5.56 5.57778587116784 -0.0177858711678409 78 5.57 5.58652610164768 -0.0165261016476803 79 5.58 5.59535556133811 -0.015355561338108 80 5.58 5.60426793015287 -0.0242679301528739 81 5.59 5.6025490377559 -0.0125490377558997 82 5.61 5.61166019204668 -0.00166019204668189 83 5.63 5.63154260099262 -0.0015426009926216 84 5.64 5.65143333888823 -0.0114333388882271 85 5.64 5.66062351789553 -0.0206235178955341 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 86 5.6591627584535 5.6091231800252 5.70920233688179 87 5.67832551690699 5.60500982507633 5.75164120873766 88 5.69748827536049 5.60454303448527 5.79043351623571 89 5.71665103381399 5.60565569683589 5.82764637079209 90 5.73581379226748 5.60758058369589 5.86404700083908 91 5.75497655072098 5.60994098724163 5.90001211420034 92 5.77413930917448 5.61252320374598 5.93575541460298 93 5.79330206762798 5.61519470566828 5.97140942958767 94 5.81246482608147 5.61786821961506 6.00706143254788 95 5.83162758453497 5.62048377063258 6.04277139843735 96 5.85079034298847 5.62299883939226 6.07858184658467 97 5.86995310144196 5.62538257959655 6.11452362328737

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211820525j164k043yvz8tbt/1mjhw1211820488.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211820525j164k043yvz8tbt/1mjhw1211820488.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211820525j164k043yvz8tbt/2u3s31211820488.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211820525j164k043yvz8tbt/2u3s31211820488.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211820525j164k043yvz8tbt/3evm51211820488.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211820525j164k043yvz8tbt/3evm51211820488.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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