Opgave 10 Oefening 2 Anke Winckelmans

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 07 Jun 2009 11:38:07 -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/07/t1244396369m9qoogd6dwqhxc3.htm/, Retrieved Sun, 07 Jun 2009 19:39:33 +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/07/t1244396369m9qoogd6dwqhxc3.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 «

3779.7 3795.5 3813.1 3826.9 3833.3 3844.8 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

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.953285713274124 beta 0.626443540095629 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 5 3833.3 3808.75 24.5500000000002 6 3844.8 3861.02642532990 -16.2264253299045 7 3851.3 3861.11617551792 -9.81617551792124 8 3851.8 3862.40470474558 -10.6047047455818 9 3854.1 3852.28046191106 1.81953808893832 10 3858.4 3860.18498607344 -1.78498607344136 11 3861.6 3862.1667033142 -0.566703314202186 12 3856.3 3865.58508257384 -9.28508257383919 13 3855.8 3851.43655379217 4.36344620782575 14 3860.4 3857.25428412105 3.14571587895216 15 3855.1 3862.59431297472 -7.49431297472165 16 3839.5 3853.46543302540 -13.9654330254048 17 3833 3827.16176911746 5.83823088254212 18 3833.6 3826.87821144419 6.72178855581296 19 3826.8 3829.81548209863 -3.01548209863267 20 3818.2 3822.01384482079 -3.8138448207892 21 3811.4 3809.7349120565 1.66508794350375 22 3806.8 3806.44456856143 0.355431438574215 23 3810.3 3799.98629014548 10.3137098545189 24 3818.2 3809.94208659384 8.2579134061607 25 3858.9 3821.72414200853 37.1758579914713 26 3867.8 3885.72804787444 -17.9280478744431 27 3872.3 3884.89058072046 -12.5905807204554 28 3873.3 3881.82302928681 -8.52302928681229 29 3876.7 3877.8447151562 -1.14471515620153 30 3882.6 3878.74554118921 3.85445881078613 31 3883.5 3887.93194746552 -4.43194746552081 32 3882.2 3886.71367232604 -4.51367232604298 33 3888.1 3883.17815509044 4.92184490955697 34 3893.7 3889.99456689224 3.70543310776475 35 3901.9 3898.46170829832 3.43829170167783 36 3914.3 3909.25204164387 5.04795835612686 37 3930.3 3925.49211495805 4.8078850419497 38 3948.3 3942.29486328687 6.00513671313138 39 3971.5 3964.46693287099 7.03306712901076 40 3990.1 3992.43116843838 -2.3311684383757 41 3993 4010.8908059289 -17.8908059288974 42 3998 4001.82114344158 -3.82114344158117 43 4015.8 4004.51592300594 11.2840769940576 44 4041.2 4028.47570208748 12.7242979125190 45 4060.7 4061.93202184969 -1.23202184968522 46 4076.7 4080.71986042768 -4.01986042768431 47 4103 4095.13183173565 7.86816826435324 48 4125.3 4125.06363765751 0.236362342488974 49 4139.7 4147.66697093734 -7.96697093734292 50 4146.7 4157.58581576719 -10.8858157671903 51 4158 4159.5892706188 -1.58927061879604 52 4155.1 4168.08249039799 -12.9824903979925 53 4144.8 4157.74080674122 -12.9408067412214 54 4148.2 4139.85107893594 8.34892106405823 55 4142.5 4149.18087474119 -6.68087474118511 56 4142.1 4137.80337207062 4.29662792938234 57 4145.4 4139.76956772951 5.63043227049184 58 4146.3 4147.50243316831 -1.2024331683142 59 4143.5 4148.24544058326 -4.74544058326228 60 4149.2 4141.60205512942 7.5979448705848 61 4158.9 4151.12542544392 7.77457455608328 62 4166.1 4166.21128551512 -0.111285515118652 63 4179.1 4174.1087773973 4.99122260270451 64 4194.4 4189.4181817394 4.98181826060045 65 4211.7 4206.98794485700 4.71205514299527 66 4226.3 4227.48915003764 -1.18915003763595 67 4235.8 4242.65699375054 -6.85699375053628 68 4243.6 4247.65521403761 -4.05521403761304 69 4258.7 4252.18476019435 6.51523980565435 70 4278.2 4270.79332880680 7.40667119319551 71 4298 4295.68801040766 2.31198959233916 72 4315.1 4316.83063876329 -1.73063876329161 73 4334.3 4332.73101374317 1.56898625683061 74 4356 4352.37328321141 3.62671678859351 75 4374 4376.87653303091 -2.87653303090610 76 4395.5 4393.23562729915 2.26437270085262 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 77 4415.83572781947 4398.26369470682 4433.40776093212 78 4435.87866237086 4403.4586521211 4468.29867262062 79 4456.25525050484 4406.50335898531 4506.00714202438 80 4476.94889371757 4407.65537938886 4546.24240804628

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244396369m9qoogd6dwqhxc3/1wvoh1244396284.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244396369m9qoogd6dwqhxc3/1wvoh1244396284.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244396369m9qoogd6dwqhxc3/2pbfs1244396284.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244396369m9qoogd6dwqhxc3/2pbfs1244396284.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244396369m9qoogd6dwqhxc3/3qngd1244396284.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244396369m9qoogd6dwqhxc3/3qngd1244396284.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 4 ; 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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Software written by Ed van Stee & Patrick Wessa

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