H

*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 07:22:33 -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/t1259936588er729b825fjepko.htm/, Retrieved Fri, 04 Dec 2009 15:23:12 +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/t1259936588er729b825fjepko.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:

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7.2 7.4 8.8 9.3 9.3 8.7 8.2 8.3 8.5 8.6 8.5 8.2 8.1 7.9 8.6 8.7 8.7 8.5 8.4 8.5 8.7 8.7 8.6 8.5 8.3 8 8.2 8.1 8.1 8 7.9 7.9 8 8 7.9 8 7.7 7.2 7.5 7.3 7 7 7 7.2 7.3 7.1 6.8 6.4 6.1 6.5 7.7 7.9 7.5 6.9 6.6 6.9 7.7 8 8 7.7 7.3 7.4 8.1 8.3 8.2

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 1 beta 0.946034419946908 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 8.1 8.22384559327192 -0.123845593271925 14 7.9 7.76712331010274 0.132876689897259 15 8.6 8.59220925982812 0.00779074017188108 16 8.7 8.70386313482342 -0.00386313482342437 17 8.7 8.70449187515322 -0.00449187515321725 18 8.5 8.4918825602062 0.00811743979380708 19 8.4 8.23999014603631 0.160009853963686 20 8.5 8.61217005966233 -0.112170059662327 21 8.7 8.75533243442093 -0.0553324344209294 22 8.7 8.8480082867998 -0.148008286799808 23 8.6 8.52159398269485 0.078406017305154 24 8.5 8.27706044924263 0.222939550757374 25 8.3 8.5530156898059 -0.253015689805892 26 8 7.99856163242326 0.00143836757673910 27 8.2 8.60570013405751 -0.405700134057511 28 8.1 7.80855113024075 0.291448869759249 29 8.1 7.89340754464655 0.206592455353447 30 8 7.89514424473911 0.104855755260888 31 7.9 7.8334550088854 0.0665449911145988 32 7.9 8.0983050426575 -0.198305042657497 33 8 8.04695829630531 -0.0469582963053128 34 8 8.04873041837974 -0.0487304183797423 35 7.9 7.83126078561202 0.0687392143879819 36 8 7.5956800512799 0.404319948720105 37 7.7 8.22524514176846 -0.525245141768457 38 7.2 7.32556085376415 -0.125560853764153 39 7.5 7.5093345474902 -0.00933454749020335 40 7.3 7.25073247499328 0.0492675250067167 41 7 7.01443591757384 -0.0144359175738371 42 7 6.54087938112092 0.459120618879081 43 7 6.917643419742 0.0823565802580015 44 7.2 7.26062819528953 -0.060628195289528 45 7.3 7.5329031591577 -0.232903159157704 46 7.1 7.363972770967 -0.263972770966996 47 6.8 6.76011236605954 0.039887633940463 48 6.4 6.33306580227634 0.066934197723656 49 6.1 6.134645545948 -0.0346455459480026 50 6.5 5.72339059684669 0.776609403153308 51 7.7 7.62745500837724 0.072544991622765 52 7.9 8.41854842685904 -0.518548426859036 53 7.5 8.04203908818125 -0.542039088181253 54 6.9 6.95925513133752 -0.0592551313375207 55 6.6 6.27946971497574 0.320530285024256 56 6.9 6.54076500308491 0.359234996915093 57 7.7 7.30736517016234 0.392634829837657 58 8 8.4538790675717 -0.453879067571698 59 8 8.15596012961007 -0.155960129610072 60 7.7 7.80113053625897 -0.101130536258967 61 7.3 7.56383460394904 -0.263834603949042 62 7.4 6.82157845836439 0.578421541635613 63 8.1 8.32565682809922 -0.225656828099220 64 8.3 8.25519000235552 0.0448099976444816 65 8.2 8.4072242969027 -0.207224296902703 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 66 7.91711188480816 7.39548951032475 8.43873425929157 67 7.5841860352756 6.47209967500377 8.69627239554743 68 7.54758634839917 5.68577145830018 9.40940123849816 69 7.63991019529805 4.86148301889184 10.4183373717043 70 7.68069118577456 3.87062856311159 11.4907538084375 71 7.55736030383841 2.69823572605404 12.4164848816228 72 7.24303367546874 1.41872732165626 13.0673400292812 73 7.07913824414066 0.145011670375313 14.0132648179060 74 6.81713212553776 -1.15384525418308 14.7881095052586 75 7.3266164163001 -2.73398447683928 17.3872173094395 76 7.32012762070259 -4.32530740834014 18.9655626497453 77 7.23227551626457 -7.64987985244062 22.1144308849698

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936588er729b825fjepko/13plj1259936552.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936588er729b825fjepko/13plj1259936552.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936588er729b825fjepko/2v7p01259936552.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936588er729b825fjepko/2v7p01259936552.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936588er729b825fjepko/3cpax1259936552.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259936588er729b825fjepko/3cpax1259936552.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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