Opgave 10-Daphné Van den Buys

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 18 May 2011 17:52:00 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/18/t1305740965ufxzk05ni4h71p5.htm/, Retrieved Wed, 18 May 2011 19:49:28 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

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

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 'Herman Ole Andreas Wold' @ www.yougetit.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.908493182493487 beta 0.125208658779051 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 519 495.152617126488 23.8473828735125 14 517 517.093475249971 -0.093475249970652 15 510 512.075431881386 -2.07543188138561 16 509 511.36144411155 -2.36144411154982 17 501 503.739744728424 -2.7397447284236 18 507 509.599514771422 -2.59951477142238 19 569 568.142108052314 0.857891947686085 20 580 579.564628466076 0.435371533924354 21 578 579.7485661572 -1.74856615719955 22 565 575.222868009268 -10.2228680092677 23 547 555.126370653665 -8.12637065366516 24 555 550.066078555828 4.93392144417248 25 562 563.853913698699 -1.85391369869876 26 561 556.633552583712 4.36644741628822 27 555 552.159275307456 2.84072469254409 28 544 553.671275484217 -9.67127548421706 29 537 536.032135560618 0.967864439381515 30 543 543.342096864995 -0.342096864995142 31 594 606.108805718683 -12.1088057186828 32 611 602.340918240364 8.65908175963557 33 613 606.844563375133 6.15543662486709 34 611 606.456753862507 4.5432461374935 35 594 598.731864300194 -4.73186430019359 36 595 598.322465538278 -3.32246553827792 37 591 603.750211721385 -12.7502117213853 38 589 584.94184326524 4.05815673476013 39 584 577.638588660561 6.36141133943897 40 573 579.485372333632 -6.48537233363197 41 567 564.12536917417 2.87463082583042 42 569 572.439615455722 -3.43961545572233 43 621 632.876389185919 -11.876389185919 44 629 630.297068467522 -1.29706846752219 45 628 622.977335692903 5.02266430709665 46 612 618.743104942904 -6.74310494290387 47 595 596.259424804809 -1.25942480480876 48 597 595.9178199803 1.08218001969976 49 593 601.742170238892 -8.74217023889207 50 590 585.824577509745 4.1754224902545 51 580 576.632240223109 3.36775977689069 52 574 572.145468448562 1.8545315514383 53 573 563.686419856645 9.3135801433549 54 573 576.507065028749 -3.50706502874903 55 620 635.67105170788 -15.6710517078805 56 626 629.288303079767 -3.28830307976693 57 620 619.222827817911 0.77717218208943 58 588 608.209040035549 -20.2090400355493 59 566 571.170539247736 -5.17053924773575 60 557 563.598761917183 -6.59876191718297 61 561 556.553592066412 4.44640793358781 62 549 550.91896141542 -1.91896141541974 63 532 533.191940704597 -1.19194070459707 64 526 520.809127254844 5.1908727451555 65 511 513.069113956602 -2.06911395660245 66 499 509.072928369888 -10.0729283698878 67 555 547.006316908343 7.99368309165686 68 565 558.395887036329 6.60411296367135 69 542 555.560954425597 -13.5609544255969 70 527 526.910833315446 0.089166684553902 71 510 509.281998402158 0.718001597842317 72 514 505.645085464273 8.3549145357266 73 517 513.329523320383 3.67047667961651 74 508 507.299261478986 0.700738521014387 75 493 493.578755031763 -0.578755031763194 76 490 483.547118108978 6.45288189102206 77 469 477.816520286092 -8.81652028609182 78 478 466.966634952398 11.033365047602 79 528 526.076198547861 1.92380145213906 80 534 533.484758782627 0.515241217373386 81 518 525.003655631961 -7.00365563196101 82 506 506.05922847729 -0.0592284772903895 83 502 490.858817286509 11.1411827134908 84 516 500.539641228043 15.4603587719569 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 518.261494818009 503.834489756166 532.688499879853 86 512.155297010596 491.656341035812 532.65425298538 87 500.9753663982 475.166427439476 526.784305356925 88 495.424374409046 464.332533030446 526.516215787647 89 484.920491026349 448.952230550487 520.888751502211 90 487.587968155072 445.864114796691 529.311821513452 91 539.482715176359 487.517508683408 591.447921669309 92 547.625260089619 488.845066984406 606.405453194832 93 540.136685567944 476.044819437564 604.228551698324 94 530.886999145872 461.720459962608 600.053538329137 95 519.206889045054 445.351424820548 593.06235326956 96 520.929590304987 434.237970543672 607.621210066301

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/18/t1305740965ufxzk05ni4h71p5/1r4bk1305741119.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305740965ufxzk05ni4h71p5/1r4bk1305741119.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305740965ufxzk05ni4h71p5/2qczd1305741119.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305740965ufxzk05ni4h71p5/2qczd1305741119.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305740965ufxzk05ni4h71p5/3esx31305741119.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305740965ufxzk05ni4h71p5/3esx31305741119.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=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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