TRIPLE MULTIPLICATIEF MODEL - YANNICK DE ROEY

*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 03:28:15 -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/t1244107742d6bwi13p4diyz13.htm/, Retrieved Thu, 04 Jun 2009 11:29:06 +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/t1244107742d6bwi13p4diyz13.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 «

509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516 528 533 536

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 0.925280347580736 beta 0.165816466300062 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 544 528.442883744037 15.5571162559626 14 537 537.378698514021 -0.378698514021266 15 543 544.731804700173 -1.73180470017314 16 594 596.476649925471 -2.47664992547072 17 611 613.719625312852 -2.71962531285180 18 613 615.31410933032 -2.31410933032021 19 611 602.244773909927 8.75522609007328 20 594 593.032988621761 0.967011378239022 21 595 604.853693582238 -9.8536935822376 22 591 604.515635463498 -13.5156354634979 23 589 590.423307994928 -1.42330799492834 24 584 581.642964466603 2.35703553339715 25 573 572.059307540346 0.940692459653974 26 567 562.581886711723 4.41811328827657 27 569 572.063750596237 -3.06375059623747 28 621 622.06367893834 -1.06367893834022 29 629 638.634970946013 -9.63497094601337 30 628 630.167367714709 -2.16736771470903 31 612 614.128093997443 -2.12809399744322 32 595 589.176556550921 5.82344344907892 33 597 600.343446850948 -3.34344685094777 34 593 602.391054742139 -9.3910547421391 35 590 590.287693049705 -0.287693049705467 36 580 580.31821521348 -0.318215213480357 37 574 565.399988188764 8.6000118112363 38 573 561.622457299325 11.3775427006746 39 573 576.430545340811 -3.43054534081125 40 620 625.934080279697 -5.93408027969667 41 626 635.870713426092 -9.87071342609158 42 620 626.23959092589 -6.23959092588962 43 588 604.532171809272 -16.5321718092722 44 566 563.555770918319 2.44422908168121 45 557 566.036993300667 -9.0369933006674 46 561 556.497685414845 4.50231458515543 47 549 554.58604374114 -5.58604374113975 48 532 536.124309648753 -4.12430964875284 49 526 514.745770788043 11.2542292119573 50 511 510.457828716342 0.542171283657808 51 499 508.173718923415 -9.17371892341492 52 555 538.359838660178 16.6401613398219 53 565 563.407366899615 1.59263310038455 54 542 562.416032968823 -20.4160329688227 55 527 524.40172927411 2.5982707258903 56 510 503.371808890359 6.6281911096413 57 514 507.915041342689 6.084958657311 58 517 514.682287120647 2.31771287935328 59 508 511.532567059128 -3.53256705912838 60 493 497.31029623578 -4.3102962357799 61 490 479.248929082315 10.7510709176845 62 469 475.970869776737 -6.97086977673683 63 478 466.28705338427 11.71294661573 64 528 519.498521997746 8.50147800225363 65 534 537.940389677992 -3.94038967799202 66 518 531.978838335852 -13.9788383358521 67 506 504.82331285159 1.17668714841028 68 502 485.879997472133 16.1200025278666 69 516 502.97698980361 13.0230101963904 70 528 520.855911789069 7.14408821093105 71 533 527.350973982746 5.64902601725419 72 536 528.172138124312 7.82786187568786 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 530.356264275624 514.416922606288 546.29560594496 74 521.636905178924 498.505713150667 544.768097207181 75 527.889913899619 497.549901767127 558.22992603211 76 581.293210889454 540.982524363375 621.603897415533 77 597.45282110578 548.89343870434 646.012203507222 78 600.194587239946 544.143972408241 656.24520207165 79 593.58051043906 530.791429856036 656.369591022085 80 579.465535528515 510.779989602941 648.151081454088 81 586.91584592234 509.778690078375 664.053001766305 82 596.002932010828 509.887647349099 682.118216672558 83 597.472547730085 503.212183858289 691.732911601881 84 593.475860075264 493.03054314667 693.921177003858

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244107742d6bwi13p4diyz13/12wws1244107693.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244107742d6bwi13p4diyz13/12wws1244107693.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244107742d6bwi13p4diyz13/258vz1244107693.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244107742d6bwi13p4diyz13/258vz1244107693.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244107742d6bwi13p4diyz13/3uovt1244107693.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244107742d6bwi13p4diyz13/3uovt1244107693.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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