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 06:23:00 -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/t1243945617c3shpjb71jj8wyq.htm/, Retrieved Tue, 02 Jun 2009 14:27:00 +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/t1243945617c3shpjb71jj8wyq.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 1 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.892317039957039 beta 0.637835382133787 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 3855.8 3849.53009387408 6.26990612591726 14 3860.4 3864.82369864823 -4.42369864822604 15 3855.1 3858.91748719337 -3.81748719336747 16 3839.5 3841.8247905871 -2.32479058710305 17 3833 3834.19969985771 -1.19969985770558 18 3833.6 3833.43364314785 0.166356852148510 19 3826.8 3840.93065989168 -14.1306598916790 20 3818.2 3811.00326413081 7.19673586919407 21 3811.4 3807.42024537009 3.97975462991508 22 3806.8 3807.36773811876 -0.567738118757461 23 3810.3 3803.58227688331 6.71772311669474 24 3818.2 3802.71818193957 15.4818180604279 25 3858.9 3824.89226842743 34.0077315725721 26 3867.8 3887.21966999135 -19.4196699913455 27 3872.3 3882.88471468827 -10.5847146882652 28 3873.3 3870.86709559954 2.4329044004603 29 3876.7 3881.29822741484 -4.59822741484231 30 3882.6 3889.48576212567 -6.88576212567432 31 3883.5 3897.06539473905 -13.5653947390542 32 3882.2 3877.99679139012 4.20320860987795 33 3888.1 3877.75117863627 10.3488213637256 34 3893.7 3892.94757223902 0.752427760975479 35 3901.9 3901.98838317014 -0.0883831701371491 36 3914.3 3902.80222420262 11.4977757973820 37 3930.3 3928.11521863562 2.18478136437625 38 3948.3 3942.79350738877 5.5064926112309 39 3971.5 3962.31436404575 9.18563595424848 40 3990.1 3980.98904834867 9.11095165133156 41 3993 4012.23183109414 -19.2318310941419 42 3998 4014.61995026851 -16.6199502685085 43 4015.8 4014.90439035163 0.895609648369827 44 4041.2 4020.67514813521 20.5248518647863 45 4060.7 4054.92028150715 5.77971849284768 46 4076.7 4081.77150743348 -5.07150743348393 47 4103 4099.1263864333 3.87361356669680 48 4125.3 4120.26719472626 5.03280527374227 49 4139.7 4150.96422013967 -11.2642201396657 50 4146.7 4158.38153890182 -11.6815389018202 51 4158 4157.49720918301 0.502790816988636 52 4155.1 4157.58286774021 -2.48286774021199 53 4144.8 4158.25524055099 -13.4552405509930 54 4148.2 4152.60315481844 -4.40315481843663 55 4142.5 4159.38170602198 -16.8817060219781 56 4142.1 4134.57999945594 7.52000054405744 57 4145.4 4131.31658535965 14.0834146403540 58 4146.3 4144.8958293194 1.40417068059924 59 4143.5 4153.23768022431 -9.73768022430613 60 4149.2 4138.76658286933 10.4334171306718 61 4158.9 4152.03540078109 6.86459921891128 62 4166.1 4165.40295922001 0.697040779987219 63 4179.1 4173.74127722054 5.35872277946328 64 4194.4 4177.41001842248 16.9899815775198 65 4211.7 4204.89654688303 6.80345311696783 66 4226.3 4240.63916135374 -14.3391613537424 67 4235.8 4254.0367061512 -18.2367061512032 68 4243.6 4246.60749624002 -3.0074962400231 69 4258.7 4244.4552500071 14.2447499928994 70 4278.2 4266.71732052612 11.4826794738838 71 4298 4298.66598326539 -0.665983265386785 72 4315.1 4315.30603415217 -0.206034152173743 73 4334.3 4333.53628359973 0.763716400270823 74 4356 4352.12627323457 3.87372676542873 75 4374 4376.9981395221 -2.99813952209843 76 4395.5 4382.3587164746 13.1412835254023 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 77 4411.06916759503 4390.6524880597 4431.48584713037 78 4440.92794829645 4404.75174630854 4477.10415028436 79 4477.68752859277 4422.53731975864 4532.83773742690 80 4509.3492702715 4432.64454073959 4586.0539998034 81 4534.24672071274 4433.81340119611 4634.68004022937 82 4557.80957642029 4431.63886347340 4683.98028936718 83 4586.2815576748 4432.33915528869 4740.2239600609 84 4611.84193461819 4428.43903075032 4795.24483848606 85 4638.84775115004 4424.25185822533 4853.44364407474 86 4665.09501819883 4417.74770328521 4912.44233311245 87 4691.5859107927 4409.95803114562 4973.21379043979 88 4708.19832144278 4392.15577222294 5024.24087066262

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243945617c3shpjb71jj8wyq/1sc5p1243945377.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243945617c3shpjb71jj8wyq/1sc5p1243945377.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243945617c3shpjb71jj8wyq/22ilc1243945377.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243945617c3shpjb71jj8wyq/22ilc1243945377.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243945617c3shpjb71jj8wyq/35ny71243945377.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243945617c3shpjb71jj8wyq/35ny71243945377.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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