Exponential Smoothing - werkloosheid - Tim Vervaet

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 04 Jun 2009 09:24:33 -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/04/t1244130057dt77942jjigupol.htm/, Retrieved Thu, 04 Jun 2009 17:40:57 +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/04/t1244130057dt77942jjigupol.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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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 2 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.962561580125543 beta 0.116796775763424 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 561 544.081463675214 16.9185363247861 14 555 556.558129119468 -1.55812911946839 15 544 545.449695031399 -1.4496950313993 16 537 537.782654787202 -0.782654787201523 17 543 543.919692602988 -0.919692602988107 18 594 595.571427479194 -1.57142747919352 19 611 618.669161100307 -7.66916110030672 20 613 608.951918828219 4.04808117178140 21 611 600.343345630332 10.656654369668 22 594 594.668995751822 -0.66899575182174 23 595 603.97613229179 -8.97613229178955 24 591 603.736338194922 -12.7363381949217 25 589 591.286979743087 -2.28697974308682 26 584 581.896853567659 2.10314643234096 27 573 572.039735262059 0.960264737940975 28 567 564.711393167011 2.28860683298876 29 569 572.13885326425 -3.13885326425054 30 621 619.719896630727 1.28010336927298 31 629 643.744482744384 -14.7444827443841 32 628 625.27041410104 2.72958589895984 33 612 613.106823292582 -1.10682329258202 34 595 591.829589807564 3.17041019243618 35 597 601.09722913439 -4.09722913438941 36 593 602.537254045668 -9.53725404566762 37 590 591.042423120945 -1.04242312094493 38 580 580.638541430146 -0.638541430146006 39 574 565.415282987133 8.5847170128668 40 573 563.648539800356 9.35146019964384 41 573 576.638133569976 -3.63813356997639 42 620 622.814794422308 -2.81479442230830 43 626 640.748255682119 -14.7482556821191 44 620 621.374734321672 -1.37473432167224 45 588 603.105406445297 -15.1054064452967 46 566 564.928582532826 1.07141746717400 47 557 568.082520856144 -11.0825208561444 48 561 557.988589018299 3.01141098170058 49 549 555.694908836947 -6.69490883694652 50 532 536.034061557883 -4.03406155788343 51 526 513.674751162263 12.3252488377366 52 511 511.744772780309 -0.744772780308608 53 499 509.602317846058 -10.6023178460578 54 555 543.39591205311 11.6040879468902 55 565 570.672260350964 -5.67226035096371 56 542 557.466582187049 -15.4665821870493 57 527 520.465620416788 6.53437958321229 58 510 501.503583216902 8.49641678309837 59 514 509.963790505804 4.03620949419621 60 517 515.264205805959 1.73579419404120 61 508 511.549850206385 -3.54985020638537 62 493 495.540087370842 -2.54008737084217 63 490 475.923398468675 14.0766015313247 64 469 476.078890784724 -7.07889078472442 65 478 467.647305696880 10.3526943031205 66 528 524.975509797849 3.02449020215101 67 534 544.914861835572 -10.9148618355715 68 518 527.274972356671 -9.27497235667124 69 506 498.732383054772 7.26761694522787 70 502 482.306906565759 19.6930934342413 71 516 504.393716708211 11.6062832917889 72 528 520.761824138634 7.23817586136613 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 526.631717651185 510.611639755492 542.651795546878 74 518.961550934514 495.440965593726 542.482136275303 75 507.582364900449 477.332248940955 537.832480859944 76 496.984093874623 460.259644967862 533.708542781384 77 500.40268661038 457.268566242008 543.536806978753 78 550.71123483899 501.141500098332 600.280969579649 79 570.097242235192 514.017018949475 626.177465520909 80 567.131848422131 504.437842537551 629.825854306711 81 553.285924029266 483.857637993591 622.71421006494 82 534.662658138819 458.368985156615 610.956331121023 83 539.609466907692 456.312775562834 622.90615825255 84 545.456022240819 455.014786253802 635.897258227836

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244130057dt77942jjigupol/16yxj1244129068.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244130057dt77942jjigupol/16yxj1244129068.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244130057dt77942jjigupol/2n2ta1244129068.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244130057dt77942jjigupol/2n2ta1244129068.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244130057dt77942jjigupol/3mdc01244129068.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244130057dt77942jjigupol/3mdc01244129068.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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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