W8-exponentieel smoothing (triple)

*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: Mon, 29 Nov 2010 11:59:42 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/29/t1291031908a89acssmtqceg6m.htm/, Retrieved Mon, 29 Nov 2010 12:58:40 +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/2010/Nov/29/t1291031908a89acssmtqceg6m.htm/}, year = {2010}, } @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 = {2010}, 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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593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516 528 533 536 537 524 536 587 597 581 564 558 575 580 575 563 552 537 545 601

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 0.827978722117885 beta 0.145260654323399 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 561 589.803151709402 -28.8031517094020 14 549 550.714443159717 -1.71444315971678 15 532 529.390074804629 2.60992519537126 16 526 522.960094264952 3.03990573504825 17 511 507.335079560942 3.66492043905816 18 499 494.918353722749 4.08164627725125 19 555 559.587578756035 -4.5875787560351 20 565 557.193775965782 7.80622403421842 21 542 554.66732072158 -12.6673207215804 22 527 507.95733946303 19.0426605369699 23 510 500.376194085807 9.62380591419253 24 514 500.23725224688 13.7627477531198 25 517 513.3507944761 3.64920552390004 26 508 511.602361406719 -3.6023614067185 27 493 495.042235148799 -2.04223514879880 28 490 489.858317469109 0.141682530890648 29 469 476.616561063489 -7.61656106348914 30 478 458.249249324366 19.7507506756338 31 528 539.603989229005 -11.6039892290052 32 534 537.891983809622 -3.89198380962216 33 518 525.110038801985 -7.1100388019853 34 506 492.076812446307 13.9231875536930 35 502 481.641528188325 20.3584718116750 36 516 495.398654175243 20.6013458247569 37 528 517.553169314065 10.4468306859353 38 533 526.121674047233 6.878325952767 39 536 525.704322337047 10.2956776629529 40 537 539.792142227226 -2.79214222722590 41 524 531.114327230819 -7.1143272308193 42 536 526.258688251446 9.74131174855438 43 587 601.116354618332 -14.1163546183316 44 597 605.532835435446 -8.53283543544649 45 581 594.678664491881 -13.6786644918808 46 564 565.35876615169 -1.35876615168979 47 558 547.073200753187 10.9267992468126 48 575 555.624354562131 19.3756454378687 49 580 577.431277379238 2.56872262076172 50 575 580.329550136699 -5.32955013669914 51 563 570.390452011206 -7.39045201120621 52 552 565.454248257545 -13.4542482575455 53 537 543.793666842844 -6.79366684284389 54 545 538.730361394393 6.2696386056067 55 601 602.81928739912 -1.81928739911973 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 56 616.066721566197 594.375387966704 637.758055165689 57 610.107391376034 580.214397633983 640.000385118085 58 594.592617835598 556.766733498366 632.41850217283 59 580.069080071788 534.289764069337 625.848396074238 60 580.235881449481 526.365218882813 634.106544016149 61 579.988095513466 517.832504226068 642.143686800864 62 575.970964077483 505.308626374654 646.633301780313 63 567.301215091592 487.895887331841 646.706542851343 64 565.541030219201 477.149569565278 653.932490873125 65 555.884204839193 458.260892272141 653.507517406245 66 559.228333371631 452.127441386747 666.329225356516 67 616.515853963662 499.693199885146 733.338508042177

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291031908a89acssmtqceg6m/1qbg51291031979.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291031908a89acssmtqceg6m/1qbg51291031979.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291031908a89acssmtqceg6m/20kfp1291031979.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291031908a89acssmtqceg6m/20kfp1291031979.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291031908a89acssmtqceg6m/30kfp1291031979.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291031908a89acssmtqceg6m/30kfp1291031979.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=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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