Ben Eysackers, opgave 10, oef 2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 06 Jun 2009 08:27:52 -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/06/t12442985311htsfc9ee4p66hw.htm/, Retrieved Sat, 06 Jun 2009 16:28:54 +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/06/t12442985311htsfc9ee4p66hw.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 «

46 33 34 25 33 18 26 21 23 24 26 32 47 45 47 43 48 48 43 44 46 36 32 18 31 37 32 29 29 40 26 29 19 30 12 24 40 43 49 49 48 33 46 46 43 44 38 38 39 47 41 36 38 11 24 30 18 21 22 15 15 16 26 39 28 25 25 13 20 13 10 19 31 36 26 33 42 44 45 42 60 42 63 71

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 0.770094354773406 beta 0.00308092481798597 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 47 36.0576378610913 10.9423621389087 14 45 42.4781443000762 2.52185569992385 15 47 45.9194098481166 1.0805901518834 16 43 42.8119929470837 0.188007052916312 17 48 48.7905776544218 -0.790577654421796 18 48 50.2640287424153 -2.26402874241529 19 43 40.1426050322917 2.85739496770831 20 44 34.6404208225834 9.35957917741658 21 46 45.4087918973583 0.59120810264168 22 36 47.0515459369091 -11.0515459369091 23 32 41.1804620027384 -9.18046200273838 24 18 41.0580182564942 -23.0580182564942 25 31 34.1925531755259 -3.19255317552587 26 37 30.7023550042105 6.29764499578953 27 32 37.0085270935604 -5.00852709356036 28 29 30.7125533282961 -1.71255332829606 29 29 33.8115427512704 -4.81154275127042 30 40 31.9274319447801 8.07256805521995 31 26 31.7731366027537 -5.77313660275368 32 29 22.6636189347051 6.33638106529493 33 19 30.1976331330650 -11.1976331330650 34 30 22.6355260425087 7.36447395749127 35 12 30.4856433037945 -18.4856433037945 36 24 20.1554835909907 3.84451640900933 37 40 33.8684200887625 6.13157991123752 38 43 36.9395605726258 6.0604394273742 39 49 42.9887379156576 6.01126208434241 40 49 43.4702635130574 5.52973648694257 41 48 53.9199901029233 -5.91999010292332 42 33 51.3365903810986 -18.3365903810986 43 46 30.9820842262297 15.0179157737703 44 46 34.7274490397107 11.2725509602893 45 43 46.9839975693075 -3.98399756930755 46 44 45.0172850121569 -1.01728501215685 47 38 47.0249415113234 -9.02494151132343 48 38 47.9268770335403 -9.9268770335403 49 39 57.7376485077695 -18.7376485077695 50 47 41.2123687529744 5.78763124702562 51 41 46.9819512891653 -5.98195128916534 52 36 38.775022580714 -2.77502258071402 53 38 41.6640069362547 -3.66400693625471 54 11 40.6440713520483 -29.6440713520483 55 24 15.3794756993723 8.62052430062773 56 30 18.3695845762136 11.6304154237864 57 18 29.8904874376668 -11.8904874376668 58 21 21.7151636263480 -0.715163626348044 59 22 22.9711162989545 -0.97111629895446 60 15 27.0381213660788 -12.0381213660788 61 15 26.283383542732 -11.2833835427320 62 16 17.5381210367758 -1.53812103677583 63 26 17.6806573942699 8.31934260573013 64 39 22.5320632272767 16.4679367727233 65 28 40.0448912488407 -12.0448912488407 66 25 32.4286864783348 -7.42868647833483 67 25 22.467995698673 2.53200430132701 68 13 20.2441149134746 -7.24411491347459 69 20 16.4284004800255 3.57159951997445 70 13 20.1198125513801 -7.11981255138008 71 10 16.1398077524889 -6.1398077524889 72 19 14.3721503099422 4.62784969005781 73 31 26.4602189490352 4.53978105096484 74 36 28.8398970541384 7.16010294586158 75 26 35.5854394083182 -9.5854394083182 76 33 26.1308400737941 6.8691599262059 77 42 35.8220573334454 6.17794266655459 78 44 42.2964939317744 1.70350606822559 79 45 35.9793799962435 9.02062000375651 80 42 34.9267796796334 7.07322032036662 81 60 43.6584529703194 16.3415470296806 82 42 57.2809909808047 -15.2809909808047 83 63 48.2458270728917 14.7541729271083 84 71 70.6055311869901 0.394468813009908 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 100.262973391805 85.7994225502783 114.726524233332 86 93.362418864202 73.7236598143192 113.001177914085 87 94.3988816510647 70.0465346184716 118.751228683658 88 84.699962491882 58.7341826226396 110.665742361125 89 94.3691925568812 62.3566150954734 126.381770018289 90 96.6254975461178 61.1752602937451 132.075734798490 91 78.448800902719 46.5546361139309 110.342965691507 92 63.134081997768 33.9423124180872 92.3258515774488 93 67.7590229261784 33.5893163466899 101.928729505667 94 68.8006044423329 31.5851829369906 106.016025947675 95 72.4491317733298 31.0975794990895 113.80068404757 96 85.5541468744254 36.1588133095561 134.949480439295

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t12442985311htsfc9ee4p66hw/1bn2g1244298470.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t12442985311htsfc9ee4p66hw/1bn2g1244298470.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t12442985311htsfc9ee4p66hw/2hmih1244298470.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t12442985311htsfc9ee4p66hw/2hmih1244298470.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t12442985311htsfc9ee4p66hw/3eh4u1244298470.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t12442985311htsfc9ee4p66hw/3eh4u1244298470.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')

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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