*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 02 Jun 2009 09:41:52 -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/02/t1243957372qyd3gj2wykn53bt.htm/, Retrieved Tue, 02 Jun 2009 17:42:55 +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/02/t1243957372qyd3gj2wykn53bt.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 «

4.43 4.44 4.44 4.44 4.45 4.47 4.48 4.48 4.5 4.52 4.52 4.53 4.53 4.63 4.66 4.67 4.68 4.69 4.69 4.7 4.71 4.72 4.72 4.72 4.73 4.74 4.76 4.81 4.82 4.83 4.83 4.84 4.89 4.92 4.95 4.95 5.01 5.05 5.08 5.11 5.14 5.17 5.18 5.2 5.22 5.24 5.28 5.29 5.33 5.4 5.43 5.46 5.46 5.46 5.47 5.49 5.5 5.54 5.55 5.55 5.56 5.6 5.61 5.63 5.64 5.66 5.67 5.69 5.77 5.77 5.78 5.8 5.82 5.85 5.87 5.88 5.9 5.91 5.94 5.97 5.98 6 6.01 6.02

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.793999311610606 beta 0.0134193323937087 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 4.53 4.42301587278106 0.106984127218944 14 4.63 4.60852587409124 0.0214741259087559 15 4.66 4.65676026637629 0.00323973362370555 16 4.67 4.6714010798474 -0.00140107984740201 17 4.68 4.68275686774525 -0.00275686774524875 18 4.69 4.69342170442019 -0.00342170442019096 19 4.69 4.68937928867316 0.000620711326839718 20 4.7 4.69626861670553 0.00373138329446832 21 4.71 4.72139034061084 -0.0113903406108378 22 4.72 4.73263663761863 -0.0126366376186278 23 4.72 4.72142954082522 -0.00142954082522362 24 4.72 4.72999254138796 -0.00999254138796157 25 4.73 4.74519011869151 -0.0151901186915113 26 4.74 4.81861215888169 -0.0786121588816897 27 4.76 4.78245801993673 -0.0224580199367317 28 4.81 4.77389894447478 0.0361010555252168 29 4.82 4.81329686965032 0.00670313034968029 30 4.83 4.82999158479271 8.415207288337e-06 31 4.83 4.82781029196342 0.00218970803657914 32 4.84 4.83513728283315 0.00486271716684783 33 4.89 4.85695726757439 0.0330427324256100 34 4.92 4.90265445070686 0.0173455492931449 35 4.95 4.91654311115185 0.0334568888481543 36 4.95 4.95061577380595 -0.000615773805945352 37 5.01 4.97253420928564 0.0374657907143590 38 5.05 5.07832615284318 -0.0283261528431797 39 5.08 5.09627139944495 -0.0162713994449462 40 5.11 5.10625070981115 0.00374929018884895 41 5.14 5.11408777720027 0.0259122227997324 42 5.17 5.14534547348452 0.0246545265154818 43 5.18 5.16328800257754 0.0167119974224645 44 5.2 5.18347115235441 0.0165288476455903 45 5.22 5.22249238500372 -0.00249238500372240 46 5.24 5.23795544450701 0.00204455549299443 47 5.28 5.24319914961394 0.0368008503860553 48 5.29 5.27294965702446 0.0170503429755353 49 5.33 5.31889283735148 0.0111071626485151 50 5.4 5.39406203097145 0.00593796902855104 51 5.43 5.44485234825027 -0.0148523482502698 52 5.46 5.46218031798748 -0.00218031798747997 53 5.46 5.47066968608911 -0.0106696860891091 54 5.46 5.47313146498262 -0.0131314649826244 55 5.47 5.45881851498091 0.0111814850190921 56 5.49 5.47447581893316 0.0155241810668363 57 5.5 5.50951006943973 -0.00951006943972654 58 5.54 5.52079455688484 0.0192054431151565 59 5.55 5.54698821631941 0.00301178368058519 60 5.55 5.5449817232243 0.00501827677569988 61 5.56 5.58090218580957 -0.0209021858095735 62 5.6 5.63143873107618 -0.0314387310761832 63 5.61 5.6485507245144 -0.038550724514403 64 5.63 5.64928596073528 -0.0192859607352833 65 5.64 5.64110475250088 -0.00110475250088182 66 5.66 5.64947139550498 0.0105286044950210 67 5.67 5.65766457555686 0.0123354244431413 68 5.69 5.67409072126757 0.0159092787324298 69 5.77 5.70359233727328 0.066407662726724 70 5.77 5.78149934471408 -0.0114993447140765 71 5.78 5.77934351192316 0.000656488076837825 72 5.8 5.77475016790168 0.0252498320983214 73 5.82 5.82174776315338 -0.00174776315338043 74 5.85 5.8876809894394 -0.0376809894394032 75 5.87 5.89950454879958 -0.0295045487995811 76 5.88 5.91244902444505 -0.0324490244450510 77 5.9 5.89735838093163 0.00264161906837401 78 5.91 5.91096243344079 -0.000962433440787613 79 5.94 5.90965281855829 0.0303471814417087 80 5.97 5.94083790310244 0.0291620968975597 81 5.98 5.99193331108579 -0.0119333110857864 82 6 5.99077180815508 0.0092281918449233 83 6.01 6.00697514595099 0.00302485404900654 84 6.02 6.00835582446629 0.0116441755337133 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 6.03872769907324 5.98977037594607 6.08768502220042 86 6.09980441808209 6.03679906429614 6.16280977186804 87 6.14431686850492 6.06956061664446 6.21907312036539 88 6.18122429041336 6.09607335751191 6.26637522331481 89 6.1998188275379 6.10534036207723 6.29429729299858 90 6.2108839491733 6.1078130305737 6.31395486777289 91 6.21682567427785 6.10572911312519 6.32792223543051 92 6.22347603767031 6.10473736008383 6.34221471525679 93 6.24304285184837 6.11676166687579 6.36932403682094 94 6.2556421582667 6.12220578703057 6.38907852950283 95 6.26286203233476 6.12259749960473 6.4031265650648 96 6.26292209369048 3.87035203178801 8.65549215559295

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243957372qyd3gj2wykn53bt/102fl1243957311.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243957372qyd3gj2wykn53bt/102fl1243957311.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243957372qyd3gj2wykn53bt/22ws31243957311.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243957372qyd3gj2wykn53bt/22ws31243957311.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243957372qyd3gj2wykn53bt/3fwv31243957311.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243957372qyd3gj2wykn53bt/3fwv31243957311.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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