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: Tue, 02 Jun 2009 13:12:36 -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/02/t124397063275a4fh7l00hi0pe.htm/, Retrieved Tue, 02 Jun 2009 21:23:55 +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/02/t124397063275a4fh7l00hi0pe.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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.953329031569823 beta 0.626323202133583 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 5 3833.3 3808.76358713235 24.5364128676538 6 3844.8 3861.02704115044 -16.2270411504383 7 3851.3 3861.14357370245 -9.84357370245107 8 3851.8 3862.39634606019 -10.5963460601874 9 3854.1 3852.25156282480 1.84843717520471 10 3858.4 3860.20611213384 -1.80611213384418 11 3861.6 3862.19267532288 -0.592675322885043 12 3856.3 3865.57620559282 -9.2762055928174 13 3855.8 3851.40446615749 4.39553384251258 14 3860.4 3857.27369827321 3.12630172678837 15 3855.1 3862.62068956048 -7.52068956048197 16 3839.5 3853.45652546211 -13.9565254621148 17 3833 3827.14354727410 5.85645272589545 18 3833.6 3826.88015270464 6.71984729535689 19 3826.8 3829.84500527164 -3.04500527163873 20 3818.2 3822.00413013856 -3.80413013855605 21 3811.4 3809.72087272178 1.67912727821704 22 3806.8 3806.43206544889 0.367934551109556 23 3810.3 3800.02291122855 10.2770887714491 24 3818.2 3809.93393929074 8.26606070926118 25 3858.9 3821.70505451913 37.1949454808714 26 3867.8 3885.74113334937 -17.9411333493663 27 3872.3 3884.91421961965 -12.6142196196479 28 3873.3 3881.81730666609 -8.517306666085 29 3876.7 3877.81418623354 -1.11418623353939 30 3882.6 3878.7566553418 3.84334465820257 31 3883.5 3887.95911392597 -4.45911392597145 32 3882.2 3886.70995606965 -4.50995606964534 33 3888.1 3883.14797598595 4.95202401404731 34 3893.7 3889.99802811631 3.70197188368684 35 3901.9 3898.48858416484 3.41141583516492 36 3914.3 3909.25209658604 5.04790341396347 37 3930.3 3925.47306210611 4.82693789389123 38 3948.3 3942.27850721913 6.02149278086654 39 3971.5 3964.49016356772 7.0098364322821 40 3990.1 3992.44306525081 -2.34306525080865 41 3993 4010.8955595138 -17.8955595138009 42 3998 4001.77961145368 -3.77961145368454 43 4015.8 4004.53817920240 11.2618207976047 44 4041.2 4028.49356944477 12.7064305552340 45 4060.7 4061.94174084626 -1.24174084625793 46 4076.7 4080.67032043543 -3.97032043543049 47 4103 4095.1577237556 7.84227624440018 48 4125.3 4125.07610794788 0.223892052119481 49 4139.7 4147.67231163608 -7.97231163608012 50 4146.7 4157.53459980018 -10.8345998001769 51 4158 4159.63123052326 -1.63123052326318 52 4155.1 4168.0864119263 -12.9864119262975 53 4144.8 4157.74536911135 -12.9453691113495 54 4148.2 4139.80848546146 8.39151453854356 55 4142.5 4149.21609995201 -6.71609995201106 56 4142.1 4137.81474204853 4.28525795147380 57 4145.4 4139.77300285837 5.62699714162864 58 4146.3 4147.45750214121 -1.15750214120726 59 4143.5 4148.27467061052 -4.77467061052266 60 4149.2 4141.61474750671 7.58525249329159 61 4158.9 4151.12755275496 7.7724472450418 62 4166.1 4166.16942031988 -0.0694203198809191 63 4179.1 4174.13644842269 4.96355157731523 64 4194.4 4189.43157789836 4.9684221016405 65 4211.7 4206.9813008537 4.71869914629769 66 4226.3 4227.4485221859 -1.14852218590022 67 4235.8 4242.69597429281 -6.89597429281184 68 4243.6 4247.66840880222 -4.06840880221898 69 4258.7 4252.17028840476 6.52971159523986 70 4278.2 4270.75210954946 7.44789045054404 71 4298 4295.73348800946 2.26651199053958 72 4315.1 4316.84840386786 -1.74840386786036 73 4334.3 4332.71134031561 1.58865968439295 74 4356 4352.32230417229 3.67769582770507 75 4374 4376.92782063219 -2.92782063219056 76 4395.5 4393.25799034535 2.24200965465388 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 77 4415.81746783839 4398.24174628024 4433.39318939654 78 4435.79094375291 4403.36670091325 4468.21518659257 79 4456.17321299487 4406.4150817472 4505.93134424254 80 4476.88119531876 4409.8344569487 4543.92793368881

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t124397063275a4fh7l00hi0pe/1loq01243969954.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t124397063275a4fh7l00hi0pe/1loq01243969954.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t124397063275a4fh7l00hi0pe/2t0wy1243969954.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t124397063275a4fh7l00hi0pe/2t0wy1243969954.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t124397063275a4fh7l00hi0pe/3u3uo1243969954.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t124397063275a4fh7l00hi0pe/3u3uo1243969954.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 4 ; 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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