Exp sm Multi

*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: Wed, 15 Dec 2010 19:00:17 +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/Dec/15/t1292439494zdqabf0x1a99azb.htm/, Retrieved Wed, 15 Dec 2010 19:58:17 +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/Dec/15/t1292439494zdqabf0x1a99azb.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:

» Textbox « » Textfile « » CSV «

597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516 528 533 536 537 524 536 587 597 581 564 558

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 9 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.844736520425172 beta 0.201418589917053 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 557 582.052496527966 -25.0524965279658 14 561 561.593877817214 -0.59387781721432 15 549 545.131939567328 3.86806043267177 16 532 528.704091295119 3.29590870488096 17 526 523.343217568612 2.65678243138757 18 511 508.065790468832 2.93420953116845 19 499 515.704882590008 -16.7048825900082 20 555 535.010017014547 19.9899829854526 21 565 552.934515429898 12.0654845701021 22 542 556.158169828962 -14.1581698289621 23 527 512.48839064945 14.5116093505502 24 510 504.568207335858 5.43179266414199 25 514 498.94407769568 15.0559223043196 26 517 523.126709865252 -6.12670986525234 27 508 510.2048028684 -2.20480286839967 28 493 495.300399761747 -2.30039976174669 29 490 490.085511028767 -0.0855110287672005 30 469 477.622647624964 -8.62264762496432 31 478 474.134726310683 3.86527368931695 32 528 520.807555531323 7.19244446867651 33 534 530.695609713923 3.30439028607748 34 518 525.596810978296 -7.59681097829628 35 506 496.538262261834 9.46173773816565 36 502 486.518951675203 15.4810483247966 37 516 495.446568160868 20.5534318391322 38 528 526.496822834529 1.50317716547136 39 533 527.296214421762 5.7037855782379 40 536 526.50033096707 9.49966903292977 41 537 541.542046882319 -4.54204688231869 42 524 531.890508591238 -7.89050859123802 43 536 541.466795338661 -5.46679533866097 44 587 595.153791745806 -8.1537917458055 45 597 598.106445768071 -1.10644576807078 46 581 591.8267065732 -10.8267065731999 47 564 565.016013354905 -1.01601335490500 48 558 547.804228463212 10.1957715367879 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 49 554.103642111245 534.106091829984 574.101192392506 50 563.383815128361 534.71561078866 592.052019468062 51 561.106066787084 524.087928956162 598.124204618006 52 552.441223075713 507.314011723428 597.568434427997 53 552.54194866692 498.474733792012 606.609163541827 54 542.030427598852 479.79223351731 604.268621680395 55 556.528351509304 483.029247911721 630.027455106886 56 614.705009288946 522.995857682173 706.414160895719 57 625.646056012605 521.214163332778 730.077948692433 58 618.125743458512 503.66519861243 732.586288304594 59 602.5041392458 479.616217809035 725.392060682565 60 588.552268264309 458.453463761461 718.651072767158

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292439494zdqabf0x1a99azb/1dyk41292439608.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292439494zdqabf0x1a99azb/1dyk41292439608.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292439494zdqabf0x1a99azb/267161292439608.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292439494zdqabf0x1a99azb/267161292439608.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292439494zdqabf0x1a99azb/367161292439608.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292439494zdqabf0x1a99azb/367161292439608.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=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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