*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 07:57:32 -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/t12599386844ywpxzftsroyeqa.htm/, Retrieved Fri, 04 Dec 2009 15:58:08 +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/t12599386844ywpxzftsroyeqa.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 «

611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516 528 533 536 537 524 536 587 597 581

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.69080418869719 beta 0.352314670027524 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 612 612.089400000477 -0.0894000004768714 14 595 594.790095339327 0.209904660672578 15 597 596.623735021542 0.376264978457925 16 593 592.956058399974 0.0439416000259598 17 590 590.356680910183 -0.356680910182945 18 580 580.67094089129 -0.670940891289547 19 574 573.599740618945 0.400259381055207 20 573 567.838500065108 5.16149993489239 21 573 574.610761589671 -1.61076158967148 22 620 626.737257475476 -6.73725747547621 23 626 629.320333110901 -3.32033311090072 24 620 624.710194311144 -4.71019431114405 25 588 603.191287814961 -15.1912878149610 26 566 569.986732423449 -3.98673242344898 27 557 561.747652815059 -4.7476528150587 28 561 546.373942618191 14.6260573818089 29 549 549.142751099696 -0.14275109969617 30 532 535.543173268248 -3.54317326824810 31 526 522.046631410014 3.95336858998564 32 511 516.222920374891 -5.22292037489058 33 499 506.843186145951 -7.84318614595105 34 555 537.572357413325 17.4276425866749 35 565 553.54969026782 11.4503097321800 36 542 559.096056446606 -17.0960564466064 37 527 525.2578716831 1.74212831690045 38 510 509.975618584074 0.0243814159264275 39 514 506.498364352349 7.5016356476512 40 517 510.690867908184 6.30913209181563 41 508 507.013581662415 0.986418337584666 42 493 497.367925723622 -4.36792572362214 43 490 489.104822359732 0.895177640268116 44 469 481.279505899806 -12.2795058998058 45 478 467.014058531009 10.9859414689914 46 528 521.775769913937 6.22423008606313 47 534 530.942569439009 3.05743056099061 48 518 523.385386140949 -5.38538614094898 49 506 507.70786057647 -1.70786057647018 50 502 492.875650165955 9.12434983404512 51 516 503.033175760213 12.9668242397867 52 528 517.084311693514 10.9156883064862 53 533 522.285856660578 10.7141433394219 54 536 526.850207267779 9.14979273222082 55 537 542.295806022562 -5.29580602256215 56 524 536.096310404435 -12.0963104044349 57 536 541.154767022147 -5.15476702214653 58 587 597.340633201987 -10.3406332019869 59 597 598.710239866005 -1.71023986600528 60 581 586.630095682546 -5.63009568254608 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 573.468638679858 558.290906496002 588.646370863714 62 565.078142844615 544.470844444672 585.685441244558 63 571.481702111999 544.107572778173 598.855831445825 64 573.654937785177 538.766432850576 608.543442719777 65 565.546262902462 523.077712615336 608.014813189589 66 554.093135344403 503.931279072496 604.25499161631 67 549.038307628732 490.32242553036 607.754189727104 68 536.024972635493 469.333113677823 602.716831593163 69 546.621595847538 468.66320942911 624.579982265965 70 601.46993997143 504.447779178355 698.492100764505 71 611.030188362045 500.509429594391 721.5509471297 72 597.19299396077 477.409265719101 716.976722202439

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599386844ywpxzftsroyeqa/1vh171259938650.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599386844ywpxzftsroyeqa/1vh171259938650.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599386844ywpxzftsroyeqa/2bxhh1259938650.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599386844ywpxzftsroyeqa/2bxhh1259938650.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599386844ywpxzftsroyeqa/36j1i1259938650.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t12599386844ywpxzftsroyeqa/36j1i1259938650.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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