opgave10oef2-MerelBoels-MAR204A

*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 13:05:26 -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/t1243969573b314re07dxo1nu2.htm/, Retrieved Tue, 02 Jun 2009 21:06:17 +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/t1243969573b314re07dxo1nu2.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 «

672.1 674.4 676.6 678.7 680.8 682.9 684 684.1 684.1 684.2 685.9 689.2 692.4 695.7 697.2 696.8 696.4 695.9 696.2 697.2 705.2 706.2 707.4 708.7 710 711.3 711.5 710.7 710 709.2 707.9 706.1 704.4 702.7 701.5 700.8 700 699.3 698.8 698.4 696.8 695.1 694.3 693.4 692.4 691 689.7 688.3 686 683.6 682.6 681.9 681 679.9 678.5 677.5 678 679 679.8 681.3 684.2 687 688.4 689.5 691.1 693.3 695.9 698 699.6 701.6 703.5 705.5 708.1 709.6 710.3

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.90268835297018 beta 0.176277296760850 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 692.4 684.005145123652 8.39485487634829 14 695.7 696.594880733925 -0.894880733925334 15 697.2 698.486464448622 -1.28646444862147 16 696.8 697.544674972548 -0.744674972548069 17 696.4 696.955381403424 -0.555381403424462 18 695.9 696.451132961243 -0.551132961242729 19 696.2 702.754426404273 -6.55442640427282 20 697.2 696.253012988138 0.946987011861552 21 705.2 696.560081459623 8.63991854037715 22 706.2 705.405656445939 0.794343554061243 23 707.4 709.157720691802 -1.75772069180198 24 708.7 712.198845026445 -3.49884502644522 25 710 713.99324936466 -3.99324936466064 26 711.3 713.02706703545 -1.72706703544986 27 711.5 712.493418892771 -0.993418892770933 28 710.7 710.239579364326 0.460420635674041 29 710 709.324137741663 0.67586225833702 30 709.2 708.699841314163 0.500158685837505 31 707.9 714.412560412607 -6.51256041260751 32 706.1 707.641520449921 -1.54152044992099 33 704.4 705.013467569147 -0.613467569147474 34 702.7 701.865790811907 0.834209188093041 35 701.5 702.531651568538 -1.03165156853834 36 700.8 703.275296545231 -2.47529654523146 37 700 703.297219569422 -3.29721956942183 38 699.3 700.648722065727 -1.34872206572754 39 698.8 698.076857128041 0.723142871959453 40 698.4 695.380860079703 3.01913992029665 41 696.8 695.078022781015 1.72197721898533 42 695.1 693.837713310525 1.26228668947465 43 694.3 698.009258771678 -3.70925877167838 44 693.4 693.235055135697 0.164944864302583 45 692.4 691.501613878311 0.898386121688645 46 691 689.385493647455 1.61450635254516 47 689.7 690.189028164016 -0.489028164015735 48 688.3 690.948805642573 -2.64880564257339 49 686 690.351764831617 -4.35176483161717 50 683.6 686.406798071727 -2.80679807172692 51 682.6 681.981412809902 0.618587190098424 52 681.9 678.708019538264 3.19198046173631 53 681 677.77273079973 3.2272692002698 54 679.9 677.422359559103 2.47764044089661 55 678.5 681.856404706074 -3.35640470607404 56 677.5 677.551304835978 -0.0513048359782715 57 678 675.451583691593 2.54841630840667 58 679 674.938154678045 4.06184532195516 59 679.8 678.141321272975 1.65867872702495 60 681.3 681.338164067972 -0.0381640679718203 61 684.2 684.055026479838 0.144973520162011 62 687 686.186362589232 0.813637410768251 63 688.4 687.816370682944 0.583629317056079 64 689.5 687.18791274486 2.31208725513989 65 691.1 687.728357004058 3.37164299594247 66 693.3 689.708947950441 3.59105204955858 67 695.9 697.115371278848 -1.21537127884847 68 698 697.904808626593 0.0951913734072605 69 699.6 699.026130401835 0.573869598164947 70 701.6 699.349291524335 2.25070847566496 71 703.5 702.908244756669 0.591755243331249 72 705.5 707.103683877399 -1.60368387739868 73 708.1 710.35574720215 -2.25574720215036 74 709.6 711.910659925909 -2.31065992590914 75 710.3 711.67951757201 -1.37951757200995 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 76 710.051098077342 704.612480579747 715.489715574936 77 708.820264466602 700.900829447093 716.739699486111 78 707.460950791398 697.154156568736 717.767745014059 79 710.364874086449 697.59574101564 723.134007157258 80 711.748664191939 696.475068322154 727.022260061723 81 712.16666262262 694.330986273687 730.002338971553 82 711.360379630604 690.913822607338 731.806936653871 83 711.616771213069 688.44968128461 734.783861141527 84 713.883003828457 687.841054684109 739.924952972805 85 717.606573058886 688.535385202097 746.677760915676 86 720.63167034423 688.454354912587 752.808985775873 87 722.368428596778 687.041333199465 757.695523994091

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243969573b314re07dxo1nu2/1pmg61243969523.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243969573b314re07dxo1nu2/1pmg61243969523.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243969573b314re07dxo1nu2/2qsdp1243969523.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243969573b314re07dxo1nu2/2qsdp1243969523.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243969573b314re07dxo1nu2/3rjdh1243969523.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243969573b314re07dxo1nu2/3rjdh1243969523.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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