opgave10oef2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 05 Jun 2009 02:16:34 -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/05/t1244189877vry99gsnzl0opwi.htm/, Retrieved Fri, 05 Jun 2009 10:17:57 +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/05/t1244189877vry99gsnzl0opwi.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 «

0,8832 0,8707 0,8766 0,8860 0,9170 0,9561 0,9935 0,9781 0,9806 0,9812 1,0013 1,0194 1,0622 1,0785 1,0797 1,0862 1,1556 1,1674 1,1365 1,1155 1,1267 1,1714 1,1710 1,2298 1,2638 1,2640 1,2261 1,1989 1,2000 1,2146 1,2266 1,2191 1,2224 1,2507 1,2997 1,3406 1,3123 1,3013 1,3185 1,2943 1,2697 1,2155 1,2041 1,2295 1,2234 1,2022 1,0000 1,1861 1,2126 1,1940 1,2028 1,2273 1,2767 1,2661 1,2681 1,2810 1,2722 1,2617 1,2888 1,3205 1,2993 1,3080 1,3246 1,3513 1,3518 1,3421 1,3726 1,3626 1,3910 1,4233 1,4683 1,4559 1,4728 1,4759 1,5520 1,5754 1,5554 1,5562 1,5759 1,4955 1,4342 1,3266 1,2744 1,3511 1,3244 1,2797 1,3050 1,3203

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 0.983881209935916 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 0.8766 0.8707 0.00590000000000002 4 0.886 0.876504899138622 0.00949510086137806 5 0.917 0.885846950462578 0.0311530495374219 6 0.9561 0.91649785053465 0.0396021494653497 7 0.9935 0.955461661266682 0.0380383387333185 8 0.9781 0.992886868003571 -0.0147868680035712 9 0.9806 0.978338346421055 0.00226165357894514 10 0.9812 0.980563544880763 0.000636455119236601 11 1.0013 0.981189741113548 0.0201102588864523 12 1.0194 1.00097584695887 0.0184241530411251 13 1.0622 1.01910302494502 0.0430969750549783 14 1.0785 1.06150532890669 0.0169946710933082 15 1.0797 1.07822606646444 0.00147393353556136 16 1.0862 1.07967624197477 0.00652375802522798 17 1.1556 1.08609484491396 0.0695051550860375 18 1.1674 1.15447966099680 0.0129203390032036 19 1.1365 1.16719173976805 -0.0306917397680504 20 1.1155 1.13699471371002 -0.0214947137100228 21 1.1267 1.11584646877778 0.0108535312222207 22 1.1714 1.12652505420878 0.044874945791225 23 1.171 1.17067667016965 0.000323329830345997 24 1.2298 1.17099478831434 0.0588052116856568 25 1.2638 1.22885213113816 0.0349478688618352 26 1.264 1.26323668263863 0.00076331736137103 27 1.2261 1.2639876962477 -0.0378876962476999 28 1.1989 1.22671070382183 -0.0278107038218283 29 1.2 1.19934827489644 0.000651725103561374 30 1.2146 1.19998949497988 0.0146105050201237 31 1.2266 1.21436449633685 0.0122355036631496 32 1.2191 1.22640277848513 -0.00730277848512517 33 1.2224 1.21921771195329 0.00318228804671361 34 1.2507 1.22234870536705 0.0283512946329485 35 1.2997 1.25024301143377 0.0494569885662337 36 1.3406 1.2989028131841 0.0416971868159008 37 1.3123 1.33992789179945 -0.0276278917994517 38 1.3013 1.31274532818783 -0.0114453281878286 39 1.3185 1.30148448484227 0.0170155151577260 40 1.2943 1.31822573048334 -0.0239257304833405 41 1.2697 1.29468565382679 -0.0249856538267907 42 1.2155 1.27010273850865 -0.054602738508648 43 1.2041 1.21638013007894 -0.0122801300789450 44 1.2295 1.20429794083870 0.0252020591612980 45 1.2234 1.22909377329920 -0.0056937732991964 46 1.2022 1.22349177673648 -0.0212917767364824 47 1 1.20254319767931 -0.202543197679307 48 1.1861 1.0032647512823 0.182835248717699 49 1.2126 1.18315291700960 0.0294470829903952 50 1.194 1.21212534865128 -0.018125348651278 51 1.2028 1.19429215868975 0.00850784131025195 52 1.2273 1.20266286389202 0.0246371361079785 53 1.2767 1.22690287917530 0.0497971208247046 54 1.2661 1.27589733066363 -0.00979733066363075 55 1.2681 1.26625792111616 0.00184207888384447 56 1.281 1.26807030791719 0.0129296920828101 57 1.2722 1.28079158900772 -0.00859158900772394 58 1.2617 1.27233848601953 -0.0106384860195323 59 1.2888 1.26187147952275 0.0269285204772514 60 1.3205 1.28836594483169 0.0321340551683094 61 1.2993 1.31998203791083 -0.0206820379108343 62 1.308 1.29963336942718 0.00836663057281806 63 1.3246 1.30786514003825 0.0167348599617470 64 1.3513 1.32433025430552 0.0269697456944753 65 1.3518 1.35086528033107 0.000934719668930883 66 1.3421 1.35178493344989 -0.00968493344988763 67 1.3726 1.34225610940906 0.0303438905909366 68 1.3626 1.37211089319784 -0.00951089319783716 69 1.391 1.36275330409078 0.028246695909222 70 1.4233 1.39054469743864 0.0327553025613647 71 1.4683 1.42277202415453 0.0455279758454721 72 1.4559 1.46756614411530 -0.0116661441153041 73 1.4728 1.45608804412785 0.0167119558721482 74 1.4759 1.47253062349174 0.00336937650826319 75 1.552 1.47584568972742 0.0761543102725837 76 1.5754 1.55077248466024 0.0246275153397588 77 1.5554 1.57500303425044 -0.0196030342504385 78 1.5562 1.55571597719370 0.000484022806298334 79 1.5759 1.556192198138 0.0197078018620009 80 1.4955 1.57558233407916 -0.0800823340791619 81 1.4342 1.49679083033086 -0.062590830330864 82 1.3266 1.43520888845404 -0.108608888454040 83 1.2744 1.32835064387208 -0.0539506438720843 84 1.3511 1.27526961910240 0.0758303808976037 85 1.3244 1.34987770600983 -0.0254777060098319 86 1.2797 1.32481066979449 -0.045110669794487 87 1.305 1.28042712941607 0.0245728705839323 88 1.3203 1.30460391505779 0.0156960849422143 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 89 1.32004699810199 1.23453042725961 1.40556356894436 90 1.32004699810199 1.20007903695736 1.44001495924662 91 1.32004699810199 1.17351529670683 1.46657869949715 92 1.32004699810199 1.15107727499658 1.4890167212074 93 1.32004699810199 1.13128790523788 1.50880609096609 94 1.32004699810199 1.11338489961405 1.52670909658993 95 1.32004699810199 1.09691374024023 1.54318025596374 96 1.32004699810199 1.08157754811612 1.55851644808785 97 1.32004699810199 1.06716974252308 1.57292425368090 98 1.32004699810199 1.05353971076883 1.58655428543515 99 1.32004699810199 1.04057363261926 1.59952036358471 100 1.32004699810199 1.02818300610092 1.61191099010306

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244189877vry99gsnzl0opwi/1pyo51244189788.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244189877vry99gsnzl0opwi/1pyo51244189788.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244189877vry99gsnzl0opwi/2e8c01244189788.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244189877vry99gsnzl0opwi/2e8c01244189788.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244189877vry99gsnzl0opwi/3000m1244189788.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244189877vry99gsnzl0opwi/3000m1244189788.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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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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