Goudprijs opgave 10 verbeterd - Elke Van Buggenhout

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 01 Jun 2008 03:49:05 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Jun/01/t1212313822091tm7nt4r4hs1b.htm/, Retrieved Sun, 01 Jun 2008 09:50:22 +0000

User-defined keywords:

Dataseries X:

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10.893 10.756 10.940 10.997 10.827 10.166 10.186 10.457 10.368 10.244 10.511 10.812 10.738 10.171 9.721 9.897 9.828 9.924 10.371 10.846 10.413 10.709 10.662 10.570 10.297 10.635 10.872 10.296 10.383 10.431 10.574 10.653 10.805 10.872 10.625 10.407 10.463 10.556 10.646 10.702 11.353 11.346 11.451 11.964 12.574 13.031 13.812 14.544 14.931 14.886 16.005 17.064 15.168 16.050 15.839 15.137 14.954 15.648 15.305 15.579 16.348 15.928 16.171 15.937 15.713 15.594 15.683 16.438 17.032 17.696 17.745 19.394

Text written by user:

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 0.994007474033322 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 10.756 10.893 -0.137000000000000 3 10.94 10.7568209760574 0.183179023942564 4 10.997 10.9389022949425 0.0580977050575271 5 10.827 10.9966518479938 -0.169651847993839 6 10.166 10.8280166431044 -0.662016643104398 7 10.186 10.1699671519242 0.0160328480758238 8 10.457 10.1859039227416 0.271096077258415 9 10.368 10.4553754497176 -0.0873754497175643 10 10.244 10.3685235996513 -0.124523599651283 11 10.511 10.2447462109044 0.266253789095625 12 10.812 10.5094044672551 0.302595532744881 13 10.738 10.8101866884126 -0.072186688412625 14 10.171 10.7384325806048 -0.567432580604761 15 9.721 10.1744003544736 -0.453400354473612 16 9.897 9.72371701339748 0.173282986602516 17 9.828 9.8959615972032 -0.067961597203201 18 9.924 9.82840726163598 0.0955927383640223 19 10.371 9.92342715803313 0.447572841966872 20 10.846 10.3683179081225 0.477682091877465 21 10.413 10.8431374776606 -0.430137477660606 22 10.709 10.4155776100041 0.293422389995877 23 10.662 10.7072416587087 -0.0452416587087434 24 10.57 10.6622711118146 -0.092271111814588 25 10.297 10.5705529370335 -0.273552937033523 26 10.635 10.2986392730784 0.336360726921566 27 10.872 10.6329843496098 0.239015650390249 28 10.296 10.8705676925086 -0.574567692508595 29 10.383 10.2994431118170 0.0835568881830273 30 10.431 10.3824992831779 0.0485007168221312 31 10.574 10.4307093581950 0.143290641804960 32 10.653 10.5731413271082 0.079858672891799 33 10.805 10.6525214448290 0.152478555170967 34 10.872 10.8040862682988 0.067913731701223 35 10.625 10.8715930251993 -0.246593025199287 36 10.407 10.6264777151067 -0.219477715106708 37 10.463 10.4083152259069 0.0546847740931149 38 10.556 10.4626723000713 0.093327699928734 39 10.646 10.5554407313348 0.0905592686652348 40 10.702 10.645457321231 0.0565426787689987 41 11.353 10.7016611665293 0.651338833470749 42 11.346 11.3490968351273 -0.00309683512732128 43 11.451 11.3460185578649 0.104981442135086 44 11.964 11.4503708959820 0.513629104018014 45 12.574 11.9609220642569 0.613077935743069 46 13.031 12.5703261145505 0.460673885449538 47 13.812 13.0282393997793 0.783760600220726 48 14.544 13.8073032942515 0.736696705748482 49 14.931 14.5395853258612 0.391414674138762 50 14.886 14.9286544374015 -0.0426544374014846 51 16.005 14.8862556078237 1.11874439217628 52 17.064 15.9982958951798 1.06570410482019 53 15.168 17.0576137404791 -1.88961374047907 54 16.05 15.1793235594068 0.87067644059319 55 15.839 16.0447824488212 -0.205782448821170 56 15.137 15.8402331566680 -0.703233156668047 57 14.954 15.1412141429520 -0.187214142951962 58 15.648 14.9551218856130 0.69287811438703 59 15.305 15.6438479099078 -0.338847909907793 60 15.579 15.3070305548989 0.271969445101124 61 16.348 15.5773702160381 0.77062978396191 62 15.928 16.3433819810089 -0.41538198100891 63 16.171 15.9304891873073 0.240510812692712 64 15.937 16.1695587327097 -0.232558732709672 65 15.713 15.9383936142445 -0.22539361424454 66 15.594 15.7143506770861 -0.120350677086083 67 15.683 15.5947212045575 0.088278795442454 68 16.438 15.682470987026 0.755529012973994 69 17.032 16.4334724727712 0.598527527228825 70 17.696 17.0284133082513 0.667586691748692 71 17.745 17.6919994694147 0.0530005305853116 72 19.394 17.7446823929442 1.64931760705578 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 19.3841164214124 18.4064413692449 20.3617914735800 74 19.3841164214124 18.0056116350122 20.7626212078127 75 19.3841164214124 17.6974918678659 21.0707409749589 76 19.3841164214124 17.4375478191989 21.3306850236260 77 19.3841164214124 17.2084426725196 21.5597901703052 78 19.3841164214124 17.0012645166313 21.7669683261935 79 19.3841164214124 16.8107120344930 21.9575208083319 80 19.3841164214124 16.6333279749640 22.1349048678608 81 19.3841164214124 16.4667093508082 22.3015234920166 82 19.3841164214124 16.3091056971857 22.4591271456391 83 19.3841164214124 16.1591950436721 22.6090377991528 84 19.3841164214124 16.0159500313562 22.7522828114686

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212313822091tm7nt4r4hs1b/1kcha1212313740.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212313822091tm7nt4r4hs1b/1kcha1212313740.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212313822091tm7nt4r4hs1b/2mjka1212313740.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212313822091tm7nt4r4hs1b/2mjka1212313740.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212313822091tm7nt4r4hs1b/3pf111212313740.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212313822091tm7nt4r4hs1b/3pf111212313740.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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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