Tijdsreeks B - stap 27

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 07 Aug 2010 13:19:56 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Aug/07/t12811871752a05h9uov3wav2u.htm/, Retrieved Sat, 07 Aug 2010 15:19:36 +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/2010/Aug/07/t12811871752a05h9uov3wav2u.htm/}, year = {2010}, } @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 = {2010}, 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:

Gosselin Claudia

Dataseries X:

» Textbox « » Textfile « » CSV «

166 165 164 162 160 159 160 162 163 163 164 166 163 166 170 171 176 172 169 180 172 170 161 167 158 163 165 169 168 165 156 157 146 150 146 159 146 151 156 152 152 143 127 126 122 122 114 127 125 123 124 123 127 117 104 110 106 107 100 115 117 123 130 129 125 112 90 96 99 108 101 113 113 120 131 135 137 120 102 114 121 134 122 131

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 3 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.629181587767191 beta 0.0412105272936492 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 163 158.073450854701 4.92654914529911 14 166 163.966823121335 2.03317687866519 15 170 169.092456881372 0.907543118627871 16 171 170.99172753766 0.00827246233981782 17 176 176.825408150483 -0.825408150482559 18 172 173.363150342122 -1.36315034212242 19 169 168.443876718768 0.556123281231663 20 180 171.829927722174 8.17007227782608 21 172 178.843376272332 -6.84337627233197 22 170 174.899864839295 -4.89986483929459 23 161 172.635460218965 -11.6354602189646 24 167 166.664781593835 0.335218406164785 25 158 165.353047197435 -7.35304719743505 26 163 161.905237004086 1.09476299591421 27 165 165.456529433316 -0.456529433316348 28 169 165.562212860582 3.43778713941796 29 168 172.731588624257 -4.73158862425717 30 165 165.997998077423 -0.99799807742258 31 156 161.415410331597 -5.4154103315966 32 157 163.108076283288 -6.10807628328797 33 146 154.440898210801 -8.44089821080087 34 150 149.04170793013 0.958292069869628 35 146 146.946123303462 -0.946123303461746 36 159 151.397747805768 7.60225219423216 37 146 151.253594164881 -5.2535941648807 38 151 151.760008587292 -0.760008587291765 39 156 153.021656755724 2.97834324427649 40 152 156.274237268001 -4.27423726800109 41 152 154.903684124029 -2.9036841240287 42 143 150.093746917097 -7.09374691709718 43 127 139.268797712543 -12.2687977125427 44 126 135.445913664715 -9.4459136647145 45 122 122.780358420159 -0.780358420159331 46 122 124.851842927184 -2.85184292718409 47 114 118.719417983047 -4.71941798304671 48 127 122.935631332252 4.06436866774831 49 125 114.675369891487 10.3246301085129 50 123 125.930594672566 -2.93059467256623 51 124 126.437493018267 -2.43749301826719 52 123 122.677405263953 0.32259473604698 53 127 123.910777922344 3.08922207765633 54 117 120.676561420825 -3.67656142082477 55 104 109.530089069581 -5.53008906958102 56 110 110.616031918222 -0.616031918221893 57 106 106.570550405005 -0.570550405004965 58 107 107.862465025745 -0.862465025745081 59 100 102.197338571444 -2.19733857144375 60 115 111.23113218609 3.76886781390998 61 117 105.072249760517 11.9277502394833 62 123 112.428296457414 10.5717035425861 63 130 121.970992866328 8.02900713367222 64 129 126.448660003908 2.55133999609151 65 125 130.796957775159 -5.7969577751586 66 112 119.919157790429 -7.91915779042853 67 90 105.762308221345 -15.7623082213452 68 96 102.313548291892 -6.31354829189227 69 99 94.6334276458214 4.3665723541786 70 108 98.9847237569335 9.0152762430665 71 101 99.3568956337943 1.6431043662057 72 113 113.436383977466 -0.436383977465894 73 113 107.965040370215 5.03495962978531 74 120 110.610642521962 9.38935747803775 75 131 118.565112450634 12.4348875493656 76 135 123.99646078678 11.0035392132201 77 137 130.998982621513 6.00101737848746 78 120 127.495167577491 -7.49516757749142 79 102 111.445560897239 -9.44556089723908 80 114 116.3876032177 -2.38760321769955 81 121 116.152442748572 4.84755725142803 82 134 123.557104548995 10.4428954510045 83 122 123.157701531511 -1.15770153151095 84 131 135.695170433302 -4.69517043330245 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 130.454034707349 118.314640487486 142.593428927211 86 132.296755827628 117.784366395379 146.809145259877 87 135.979829744022 119.277750696334 152.681908791709 88 133.241058661304 114.463065326114 152.019051996494 89 131.364472486531 110.585435843744 152.143509129317 90 118.823837581678 96.0944824641646 141.553192699191 91 106.704695730556 82.0596791209231 131.349712340188 92 120.389729911359 93.8524675823117 146.926992240407 93 124.584442277445 96.170183920447 152.998700634443 94 131.132979019595 100.850866294637 161.415091744552 95 119.709624946226 87.5641235428816 151.85512634957 96 131.541999106187 97.5339271914234 165.55007102095

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/07/t12811871752a05h9uov3wav2u/1n1d61281187191.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/07/t12811871752a05h9uov3wav2u/1n1d61281187191.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/07/t12811871752a05h9uov3wav2u/2n1d61281187191.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/07/t12811871752a05h9uov3wav2u/2n1d61281187191.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/07/t12811871752a05h9uov3wav2u/3n1d61281187191.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/07/t12811871752a05h9uov3wav2u/3n1d61281187191.ps (open in new window)

Parameters (Session):

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) 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')

Copyright

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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