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 11:49:36 -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/t1244397007o982fbhv17fsyza.htm/, Retrieved Sun, 07 Jun 2009 19:50:07 +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/t1244397007o982fbhv17fsyza.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 2 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.953285713274383 beta 0.626443540081187 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 5 3833.3 3808.75 24.5500000000002 6 3844.8 3861.02642532958 -16.2264253295775 7 3851.3 3861.11617551798 -9.81617551798354 8 3851.8 3862.40470474576 -10.6047047457605 9 3854.1 3852.28046191128 1.81953808872413 10 3858.4 3860.18498607354 -1.78498607354140 11 3861.6 3862.16670331421 -0.56670331421401 12 3856.3 3865.58508257386 -9.28508257386284 13 3855.8 3851.4365537923 4.36344620769842 14 3860.4 3857.25428412109 3.14571587890759 15 3855.1 3862.59431297464 -7.49431297464389 16 3839.5 3853.46543302548 -13.9654330254793 17 3833 3827.16176911767 5.83823088233294 18 3833.6 3826.87821144426 6.7217885557402 19 3826.8 3829.81548209852 -3.01548209852126 20 3818.2 3822.01384482077 -3.81384482077237 21 3811.4 3809.73491205652 1.66508794347692 22 3806.8 3806.44456856149 0.355431438508731 23 3810.3 3799.98629014547 10.3137098545340 24 3818.2 3809.94208659367 8.25791340632577 25 3858.9 3821.72414200832 37.17585799168 26 3867.8 3885.72804787394 -17.9280478739352 27 3872.3 3884.89058072043 -12.5905807204313 28 3873.3 3881.82302928699 -8.52302928698646 29 3876.7 3877.84471515636 -1.14471515636251 30 3882.6 3878.74554118941 3.85445881059331 31 3883.5 3887.93194746546 -4.43194746546169 32 3882.2 3886.71367232607 -4.51367232606708 33 3888.1 3883.17815509049 4.92184490950831 34 3893.7 3889.9945668923 3.70543310769926 35 3901.9 3898.46170829823 3.43829170177150 36 3914.3 3909.25204164376 5.04795835623554 37 3930.3 3925.49211495791 4.8078850420884 38 3948.3 3942.29486328686 6.00513671314275 39 3971.5 3964.46693287085 7.03306712915264 40 3990.1 3992.43116843819 -2.33116843819334 41 3993 4010.89080592883 -17.8908059288269 42 3998 4001.8211434419 -3.82114344190131 43 4015.8 4004.51592300609 11.2840769939053 44 4041.2 4028.47570208736 12.7242979126399 45 4060.7 4061.93202184942 -1.23202184942102 46 4076.7 4080.71986042767 -4.01986042766794 47 4103 4095.13183173568 7.86816826431914 48 4125.3 4125.06363765741 0.236362342592656 49 4139.7 4147.66697093726 -7.96697093725743 50 4146.7 4157.58581576732 -10.8858157673249 51 4158 4159.58927061899 -1.58927061898885 52 4155.1 4168.08249039810 -12.9824903980953 53 4144.8 4157.74080674139 -12.9408067413915 54 4148.2 4139.85107893624 8.348921063759 55 4142.5 4149.18087474119 -6.68087474118784 56 4142.1 4137.8033720707 4.29662792929685 57 4145.4 4139.76956772944 5.63043227056005 58 4146.3 4147.50243316825 -1.20243316824599 59 4143.5 4148.24544058326 -4.7454405832641 60 4149.2 4141.60205512947 7.59794487053114 61 4158.9 4151.1254254438 7.77457455619697 62 4166.1 4166.211285515 -0.11128551499678 63 4179.1 4174.10877739726 4.99122260274453 64 4194.4 4189.4181817393 4.98181826069685 65 4211.7 4206.98794485687 4.71205514312805 66 4226.3 4227.48915003755 -1.18915003755046 67 4235.8 4242.65699375052 -6.85699375052172 68 4243.6 4247.65521403769 -4.05521403769308 69 4258.7 4252.18476019441 6.51523980558704 70 4278.2 4270.79332880678 7.40667119322461 71 4298 4295.68801040755 2.31198959245285 72 4315.1 4316.8306387632 -1.73063876319702 73 4334.3 4332.73101374313 1.56898625686881 74 4356 4352.37328321141 3.62671678859078 75 4374 4376.87653303087 -2.87653303086518 76 4395.5 4393.23562729915 2.2643727008508 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 77 4415.83572781942 4398.26369470676 4433.40776093207 78 4435.87866237079 4403.45865212122 4468.29867262035 79 4456.25525050476 4406.50335898572 4506.00714202381 80 4476.94889371746 4407.6553793896 4546.24240804533

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244397007o982fbhv17fsyza/1rqel1244396971.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244397007o982fbhv17fsyza/1rqel1244396971.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244397007o982fbhv17fsyza/2bk921244396971.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244397007o982fbhv17fsyza/2bk921244396971.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244397007o982fbhv17fsyza/3kbtq1244396971.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244397007o982fbhv17fsyza/3kbtq1244396971.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 4 ;

Parameters (R input):

par1 = 4 ; par2 = Triple ; par3 = additive ; par4 = 0 ; par5 = 4 ;

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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