Ad hoc techniek 4

*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 04 Dec 2009 06:47:47 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/04/t1259934514zpfx2icerpx4p1i.htm/, Retrieved Fri, 04 Dec 2009 14:48:41 +0100

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/Dec/04/t1259934514zpfx2icerpx4p1i.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:

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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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.625571876719181 beta 0.230126132337169 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 591 576.861126495788 14.1388735042120 14 589 585.66433983762 3.33566016237990 15 584 585.633063798857 -1.63306379885705 16 573 576.86129846209 -3.86129846209042 17 567 571.662787216386 -4.66278721638628 18 569 573.281487256973 -4.28148725697292 19 621 616.717834448139 4.28216555186111 20 629 637.389877541802 -8.38987754180164 21 628 633.290343135737 -5.29034313573686 22 612 626.228391114569 -14.2283911145686 23 595 596.525335255736 -1.52533525573642 24 597 592.882378159852 4.11762184014765 25 593 593.837509098968 -0.837509098967757 26 590 584.553672719186 5.44632728081444 27 580 579.720929871371 0.279070128629201 28 574 567.47841568647 6.5215843135303 29 573 566.08824463082 6.91175536918047 30 573 574.362779103646 -1.36277910364572 31 620 622.858149258897 -2.85814925889724 32 626 632.901486894677 -6.90148689467708 33 620 629.697590903982 -9.6975909039819 34 588 614.712579243899 -26.7125792438989 35 566 578.771407689236 -12.7714076892356 36 557 565.017730232156 -8.01773023215583 37 561 549.827493569067 11.1725064309335 38 549 545.646832274876 3.35316772512385 39 532 532.991762920098 -0.991762920098495 40 526 517.71156703323 8.28843296676973 41 511 513.026355053673 -2.02635505367311 42 499 506.360137355998 -7.36013735599812 43 555 536.886620712232 18.1133792877678 44 565 552.625479363455 12.3745206365454 45 542 558.347675013975 -16.3476750139749 46 527 531.264055785635 -4.26405578563458 47 510 515.651658433519 -5.65165843351917 48 514 509.062430335897 4.93756966410268 49 517 511.811431930821 5.18856806917893 50 508 503.790565563698 4.20943443630244 51 493 493.143091175335 -0.143091175335371 52 490 484.601414592181 5.39858540781876 53 469 476.819050431286 -7.81905043128614 54 478 465.777848606887 12.2221513931132 55 528 519.606906449247 8.39309355075318 56 534 529.589972900792 4.41002709920838 57 518 521.761770699811 -3.76177069981122 58 506 510.801474889992 -4.80147488999194 59 502 497.893789183372 4.10621081662811 60 516 505.949181592234 10.0508184077656 61 528 517.445424068669 10.5545759313314 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 62 518.456173264864 501.605004414465 535.307342115262 63 508.722727332257 487.641922209766 529.803532454748 64 507.631329189336 481.689513316805 533.573145061867 65 495.486262515947 464.733072279686 526.239452752208 66 502.699924569357 465.85939319267 539.540455946044 67 554.09212190328 507.443233683123 600.741010123438 68 560.590602239493 506.584813922506 614.596390556479 69 548.632852816002 488.714377296160 608.551328335844 70 541.991645472872 475.589142810295 608.394148135448 71 538.550329696134 465.180657218607 611.920002173662 72 549.792527803856 467.207806209790 632.377249397922 73 556.963390121156 466.563912805494 647.362867436817

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259934514zpfx2icerpx4p1i/1g0dl1259934463.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259934514zpfx2icerpx4p1i/1g0dl1259934463.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259934514zpfx2icerpx4p1i/2dtiz1259934463.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259934514zpfx2icerpx4p1i/2dtiz1259934463.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259934514zpfx2icerpx4p1i/32ztf1259934463.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259934514zpfx2icerpx4p1i/32ztf1259934463.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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