*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 06 Jun 2009 09:28:21 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/06/t1244302126n8rgayd8nf6oy7u.htm/, Retrieved Sat, 06 Jun 2009 17:28:50 +0200

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Jun/06/t1244302126n8rgayd8nf6oy7u.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

3851,3 3851,8 3854,1 3858,4 3861,6 3856,3 3855,8 3860,4 3855,1 3839,5 3833 3833,6 3826,8 3818,2 3811,4 3806,8 3810,3 3818,2 3858,9 3867,8 3872,3 3873,3 3876,7 3882,6 3883,5 3882,2 3888,1 3893,7 3901,9 3914,3 3930,3 3948,3 3971,5 3990,1 3993 3998 4015,8 4041,2 4060,7 4076,7 4103 4125,3 4139,7 4146,7 4158 4155,1 4144,8 4148,2 4142,5 4142,1 4145,4 4146,3 4143,5 4149,2 4158,9 4166,1 4179,1 4194,4 4211,7 4226,3 4235,8 4243,6 4258,7 4278,2 4298 4315,1 4334,3 4356 4374 4395,5 4417,8 4432,8 4446,3

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.94877810070843 beta 0.264457573588829 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 3826.8 3847.46652333828 -20.6665233382782 14 3818.2 3812.58612823781 5.61387176218886 15 3811.4 3805.27815675902 6.12184324098416 16 3806.8 3801.10364874457 5.69635125542572 17 3810.3 3804.95756172977 5.34243827022692 18 3818.2 3813.58246489585 4.61753510415292 19 3858.9 3847.88707427319 11.0129257268072 20 3867.8 3868.79801811904 -0.99801811903717 21 3872.3 3868.91152689762 3.38847310238089 22 3873.3 3864.41756566221 8.88243433778916 23 3876.7 3876.84934061016 -0.149340610159925 24 3882.6 3887.29222191269 -4.69222191268636 25 3883.5 3881.3794905313 2.12050946870113 26 3882.2 3881.12950734367 1.07049265633032 27 3888.1 3880.02270112858 8.07729887142432 28 3893.7 3888.63425096381 5.06574903619139 29 3901.9 3902.80779413922 -0.90779413922246 30 3914.3 3914.93366863109 -0.633668631090586 31 3930.3 3953.44356592619 -23.1435659261888 32 3948.3 3940.99809918287 7.30190081713363 33 3971.5 3950.79851694274 20.7014830572607 34 3990.1 3968.67428694186 21.4257130581386 35 3993 4001.55741553316 -8.55741553315966 36 3998 4010.90624409420 -12.9062440941962 37 4015.8 4002.28843232084 13.5115676791561 38 4041.2 4020.29095933323 20.9090406667701 39 4060.7 4050.77480597862 9.92519402138396 40 4076.7 4073.83187865341 2.86812134659067 41 4103 4098.21928017374 4.7807198262617 42 4125.3 4130.01735958948 -4.71735958948011 43 4139.7 4178.18844262100 -38.4884426210047 44 4146.7 4162.46619561426 -15.7661956142592 45 4158 4154.49655834073 3.5034416592689 46 4155.1 4154.72188833281 0.378111667188932 47 4144.8 4159.828803484 -15.0288034839996 48 4148.2 4155.24402569768 -7.04402569768263 49 4142.5 4147.10663009876 -4.60663009876225 50 4142.1 4137.27634866624 4.82365133376061 51 4145.4 4136.94710886691 8.45289113308718 52 4146.3 4142.96740352183 3.3325964781734 53 4143.5 4152.89200115352 -9.39200115352196 54 4149.2 4152.21907764142 -3.01907764141743 55 4158.9 4182.14579974345 -23.2457997434476 56 4166.1 4167.60261032765 -1.50261032764593 57 4179.1 4163.23873231294 15.8612676870607 58 4194.4 4167.17968326724 27.2203167327561 59 4211.7 4195.86169141356 15.8383085864371 60 4226.3 4227.74430753045 -1.44430753044799 61 4235.8 4233.04407960619 2.75592039380808 62 4243.6 4240.43664769167 3.16335230832556 63 4258.7 4247.99775743772 10.7022425622763 64 4278.2 4265.70116933602 12.4988306639816 65 4298 4295.98162233503 2.01837766496828 66 4315.1 4321.82695392218 -6.72695392218247 67 4334.3 4362.69599795859 -28.3959979585907 68 4356 4357.9570673634 -1.95706736340071 69 4374 4367.07687241394 6.92312758606477 70 4395.5 4373.28554728340 22.2144527166038 71 4417.8 4405.80726240786 11.9927375921388 72 4432.8 4441.84042947121 -9.04042947120615 73 4446.3 4446.49322031745 -0.193220317454688 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 4456.56236578211 4432.2305628018 4480.89416876242 75 4466.12237425687 4428.16446547746 4504.08028303627 76 4475.70135942832 4423.96205941843 4527.44065943822 77 4492.73870637014 4426.5283009389 4558.94911180139 78 4515.09613555611 4433.57959006340 4596.61268104882 79 4562.92111935879 4464.77897652941 4661.06326218817 80 4594.67828075623 4479.34006847531 4710.01649303716 81 4614.19085856373 4481.15137181569 4747.23034531176 82 4620.23815838518 4469.17886875643 4771.29744801392 83 4631.50858652224 4461.61070562862 4801.40646741586 84 4652.90899197386 4463.11975097493 4842.6982329728 85 4666.31048846046 4457.69204391334 4874.92893300759

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244302126n8rgayd8nf6oy7u/1x5901244302099.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244302126n8rgayd8nf6oy7u/1x5901244302099.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244302126n8rgayd8nf6oy7u/20au01244302099.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244302126n8rgayd8nf6oy7u/20au01244302099.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244302126n8rgayd8nf6oy7u/3c2x51244302099.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244302126n8rgayd8nf6oy7u/3c2x51244302099.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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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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