*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 20 Dec 2010 19:50:00 +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/20/t1292874550jj984ixm1hfq209.htm/, Retrieved Mon, 20 Dec 2010 20:49:11 +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/20/t1292874550jj984ixm1hfq209.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:

KDGP2W102 - Sofie Baert

Dataseries X:

» Textbox « » Textfile « » CSV «

6,59 6,59 6,59 6,59 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,79 6,79 6,79 6,81 6,80 6,80 6,85 6,85 6,85 6,85 6,85 6,85 6,86 6,86 6,88 6,88 6,88 6,91 6,91 6,91 6,91 6,99 6,99 6,99 7,02 7,02 7,05 7,05 7,05 7,05 7,10 7,10 7,10 7,10 7,12 7,13 7,18 7,24 7,24 7,24 7,27 7,27 7,27 7,27 7,30 7,30 7,57 7,76 7,94 7,94 7,96

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.153603670908544 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 6.59 6.59 0 4 6.59 6.59 0 5 6.63 6.59 0.04 6 6.63 6.63614414683634 -0.00614414683634212 7 6.63 6.63520038332768 -0.00520038332767836 8 6.63 6.63440158535842 -0.00440158535841562 9 6.63 6.63372548568955 -0.00372548568954567 10 6.63 6.63315323741171 -0.00315323741171447 11 6.63 6.63266888857003 -0.002668888570029 12 6.63 6.63225893748843 -0.00225893748842676 13 6.63 6.63191195639785 -0.00191195639785136 14 6.63 6.63161827287652 -0.00161827287652461 15 6.63 6.63136970022216 -0.00136970022215799 16 6.63 6.63115930923999 -0.00115930923999041 17 6.63 6.63098123508501 -0.00098123508500958 18 6.63 6.63083051377393 -0.000830513773927954 19 6.63 6.63070294380951 -0.000702943809512746 20 6.63 6.63059496905993 -0.000594969059928729 21 6.63 6.63050357962825 -0.000503579628246875 22 6.79 6.63042622794875 0.159573772051247 23 6.79 6.81493734511655 -0.0249373451165482 24 6.79 6.81110687736393 -0.0211068773639331 25 6.81 6.80786478351942 0.00213521648058279 26 6.8 6.82819276060902 -0.0281927606090182 27 6.8 6.81386224908643 -0.0138622490864275 28 6.85 6.8117329567397 0.0382670432602961 29 6.85 6.8676109150593 -0.0176109150593016 30 6.85 6.86490581385813 -0.0149058138581344 31 6.85 6.86261622613165 -0.0126162261316454 32 6.85 6.86067832748481 -0.0106783274848121 33 6.85 6.85903809718398 -0.00903809718398119 34 6.86 6.8576498122785 0.00235018772150664 35 6.86 6.86801080973984 -0.00801080973984103 36 6.88 6.86678031995685 0.0132196800431474 37 6.88 6.88881091133972 -0.00881091133971612 38 6.88 6.88745752301389 -0.00745752301388602 39 6.91 6.88631202010307 0.0236879798969323 40 6.91 6.91995058077165 -0.0099505807716449 41 6.91 6.91842213503745 -0.00842213503744826 42 6.91 6.91712846417881 -0.00712846417880808 43 6.99 6.916033505913 0.0739664940869966 44 6.99 7.007395030929 -0.0173950309290012 45 6.99 7.00472309032274 -0.0147230903227387 46 7.02 7.00246156960205 0.0175384303979511 47 7.02 7.03515553689315 -0.0151555368931477 48 7.05 7.03282759079177 0.0171724092082304 49 7.05 7.0654653358845 -0.0154653358844978 50 7.05 7.0630898035208 -0.0130898035208054 51 7.05 7.06107916164854 -0.0110791616485377 52 7.1 7.05937736174873 0.040622638251266 53 7.1 7.11561714810612 -0.0156171481061183 54 7.1 7.1132182968279 -0.0132182968278958 55 7.1 7.11118791791197 -0.0111879179119718 56 7.12 7.10946941265087 0.0105305873491304 57 7.13 7.13108694952452 -0.00108694952451938 58 7.18 7.14091999008746 0.0390800099125386 59 7.24 7.19692282306917 0.0430771769308311 60 7.24 7.26353963557812 -0.0235396355781221 61 7.24 7.25992386114147 -0.0199238611414732 62 7.27 7.25686348293147 0.0131365170685287 63 7.27 7.28888130017615 -0.0188813001761492 64 7.27 7.28598106315757 -0.0159810631575663 65 7.27 7.28352631319154 -0.0135263131915435 66 7.3 7.28144862183146 0.0185513781685369 67 7.3 7.31429818161856 -0.014298181618563 68 7.57 7.31210192843464 0.257898071565365 69 7.76 7.62171601894731 0.13828398105269 70 7.94 7.83295694606485 0.107043053935151 71 7.94 8.02939915209455 -0.0893991520945514 72 7.96 8.01566711415672 -0.0556671141567167 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 8.02711644107336 7.9346022450535 8.11963063709323 74 8.09423288214672 7.9529918063214 8.23547395797205 75 8.16134932322008 7.97540746975661 8.34729117668355 76 8.22846576429344 7.99859895864992 8.45833256993696 77 8.2955822053668 8.02145441460777 8.56970999612583 78 8.36269864644016 8.04348062905613 8.68191666382419 79 8.42981508751352 8.06443184081302 8.79519833421402 80 8.49693152858688 8.08417948865127 8.90968356852248 81 8.56404796966024 8.1026565860264 9.02543935329408 82 8.6311644107336 8.11983077992569 9.1424980415415 83 8.69828085180696 8.1356901093075 9.26087159430641 84 8.76539729288032 8.15023497990236 9.38055960585827

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292874550jj984ixm1hfq209/1dv5v1292874594.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292874550jj984ixm1hfq209/1dv5v1292874594.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292874550jj984ixm1hfq209/264my1292874594.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292874550jj984ixm1hfq209/264my1292874594.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292874550jj984ixm1hfq209/364my1292874594.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292874550jj984ixm1hfq209/364my1292874594.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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