Robin Bosmans- Datareeks werkloosheid

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 03 Jun 2009 11:20:49 -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/03/t12440497091f94b41vyl1ft4m.htm/, Retrieved Wed, 03 Jun 2009 19:21:53 +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/03/t12440497091f94b41vyl1ft4m.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 «

467 460 448 443 436 431 484 510 513 503 471 471 476 475 470 461 455 456 517 525 523 519 509 512 519 517 510 509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516 528

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 1 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.562952218589531 beta 0.0858271961966097 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 476 465.269197541118 10.7308024588818 14 475 470.610318136485 4.38968186351536 15 470 469.514909097349 0.485090902650995 16 461 462.154835841513 -1.15483584151264 17 455 455.688271059507 -0.688271059506519 18 456 455.488090672002 0.5119093279975 19 517 506.518665783334 10.4813342166659 20 525 541.980873253753 -16.9808732537530 21 523 536.173392747286 -13.1733927472857 22 519 518.319204046485 0.68079595351503 23 509 485.738649471905 23.2613505280948 24 512 499.641354500286 12.3586454997137 25 519 517.839262962876 1.16073703712357 26 517 515.634967962987 1.36503203701307 27 510 511.431449157141 -1.43144915714072 28 509 502.205951318738 6.7940486812617 29 501 500.86750916928 0.132490830719860 30 507 502.755450374614 4.24454962538562 31 569 567.45371906746 1.54628093254007 32 580 588.368267814747 -8.36826781474736 33 578 590.940298202399 -12.9402982023992 34 565 580.166219772499 -15.1662197724987 35 547 546.523936373711 0.476063626289374 36 555 541.930343368793 13.0696566312072 37 562 555.550047780436 6.44995221956435 38 561 555.890698958946 5.10930104105432 39 555 551.931457044903 3.06854295509697 40 544 548.462736569939 -4.46273656993912 41 537 536.838876593712 0.161123406288198 42 543 540.342785030406 2.65721496959407 43 594 606.580432142004 -12.5804321420038 44 611 614.784867324054 -3.78486732405418 45 613 617.154246372086 -4.15424637208571 46 611 609.393034492785 1.60696550721514 47 594 590.791840666605 3.2081593333952 48 595 593.558935712455 1.44106428754469 49 591 597.723180425056 -6.72318042505606 50 589 588.992908003014 0.00709199698576413 51 584 579.82764356426 4.17235643573997 52 573 572.28285376094 0.717146239059502 53 567 564.502348264783 2.49765173521746 54 569 570.03951166734 -1.03951166734009 55 621 629.440004697 -8.44000469699927 56 629 644.140849730675 -15.1408497306750 57 628 638.956021174525 -10.9560211745252 58 612 628.337375525677 -16.3373755256772 59 595 597.894877543472 -2.89487754347158 60 597 594.012422639647 2.98757736035293 61 593 593.114305172382 -0.114305172381705 62 590 589.021228229762 0.978771770238268 63 580 580.278248995199 -0.278248995199078 64 574 566.720412757222 7.27958724277778 65 573 561.705546457029 11.2944535429713 66 573 569.330494152471 3.66950584752942 67 620 627.152635579839 -7.1526355798386 68 626 638.449907212287 -12.4499072122871 69 620 635.533751599433 -15.5337515994333 70 588 618.647754874405 -30.6477548744048 71 566 584.401715489263 -18.4017154892629 72 557 571.71987540367 -14.7198754036706 73 561 556.28432046314 4.71567953685974 74 549 552.413903995036 -3.41390399503587 75 532 537.988317669999 -5.98831766999888 76 526 521.76713898095 4.23286101904966 77 511 513.800564988936 -2.80056498893566 78 499 506.211878883097 -7.21187888309674 79 555 541.817899920436 13.1821000795644 80 565 556.52356786827 8.47643213173 81 542 560.404248347054 -18.4042483470541 82 527 533.218076268099 -6.21807626809903 83 510 516.741928476132 -6.74192847613176 84 514 510.327113491383 3.67288650861724 85 517 512.580749386121 4.41925061387872 86 508 504.780909828342 3.21909017165774 87 493 493.305087308172 -0.305087308171608 88 490 484.926002382029 5.07399761797126 89 469 474.965392741366 -5.96539274136592 90 478 463.720572223338 14.2794277766620 91 528 518.212682876411 9.78731712358876 92 534 529.0924136205 4.90758637950012 93 518 520.117735768265 -2.11773576826465 94 506 508.958853313268 -2.95885331326770 95 502 495.76006630481 6.23993369518951 96 516 503.051774891344 12.9482251086557 97 528 513.254061326063 14.7459386739371 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 98 513.567323657776 495.706964982874 531.427682332679 99 501.286574407515 480.48396057643 522.0891882386 100 498.046386059857 474.217344626514 521.875427493201 101 482.49717156837 456.003689453227 508.990653683512 102 486.130049200579 456.32092534526 515.939173055897 103 533.534687009506 498.173975110009 568.895398909003 104 538.516658372643 499.470365020603 577.562951724683 105 525.023239660407 483.370200731166 566.676278589647 106 516.074263852053 471.554149860144 560.594377843962 107 510.061725604094 462.463442070661 557.660009137526 108 518.174265982155 466.245980490147 570.102551474164 109 522.511828362385 455.514249522678 589.509407202092

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t12440497091f94b41vyl1ft4m/1arv71244049647.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t12440497091f94b41vyl1ft4m/1arv71244049647.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t12440497091f94b41vyl1ft4m/2xc3m1244049647.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t12440497091f94b41vyl1ft4m/2xc3m1244049647.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t12440497091f94b41vyl1ft4m/3gmox1244049647.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t12440497091f94b41vyl1ft4m/3gmox1244049647.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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