*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 19 Jan 2010 13:52:57 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/19/t1263934821v5g42pbdoy5gvln.htm/, Retrieved Tue, 19 Jan 2010 22:00:25 +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/Jan/19/t1263934821v5g42pbdoy5gvln.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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

8.55 8.56 8.57 8.59 8.61 8.62 8.62 8.63 8.71 8.72 8.74 8.75 8.79 8.82 8.82 8.84 8.86 8.86 8.85 8.86 8.86 8.87 8.88 8.9 8.91 8.96 8.98 8.99 9 9 9 9.01 9.01 8.99 8.99 8.99 9 9 9.02 9.05 9.05 9.05 9.06 9.06 9.08 9.07 9.06 9.08 9.07 9.11 9.15 9.15 9.17 9.2 9.23 9.26 9.27 9.28 9.29 9.29 9.11 9.06 9.11 9.13 9.13 9.19 9.2 9.23 9.24 9.28 9.32 9.32 9.32 9.36 9.37 9.38 9.41 9.44 9.44 9.44 9.47 9.48 9.56 9.58 9.56 9.58 9.7 9.74 9.76 9.78 9.84 9.88 9.96 9.97 9.96 9.96

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.0405252708246452 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 8.57 8.57 0 4 8.59 8.58 0.00999999999999979 5 8.61 8.60040525270825 0.0095947472917537 6 8.62 8.62079408244074 -0.00079408244073953 7 8.62 8.63076190203477 -0.0107619020347709 8 8.63 8.63032577304022 -0.000325773040222188 9 8.71 8.64031257099954 0.0696874290004601 10 8.72 8.72313667293286 -0.00313667293285746 11 8.74 8.73300955841277 0.00699044158723439 12 8.75 8.75329284795127 -0.00329284795127194 13 8.79 8.76315940439626 0.0268405956037370 14 8.82 8.8042471268022 0.0157528731978029 15 8.82 8.8348855162548 -0.0148855162548056 16 8.84 8.83428227667721 0.00571772332278542 17 8.86 8.85451398896337 0.00548601103662882 18 8.86 8.87473631104638 -0.0147363110463772 19 8.85 8.87413911805027 -0.0241391180502664 20 8.86 8.86316087375381 -0.0031608737538118 21 8.86 8.87303277848889 -0.0130327784888955 22 8.87 8.87250462161104 -0.00250462161103648 23 8.88 8.88240312114193 -0.00240312114193308 24 8.9 8.89230573400683 0.00769426599316603 25 8.91 8.91261754622 -0.00261754622000332 26 8.96 8.92251146945054 0.0374885305494583 27 8.98 8.97403070230388 0.00596929769612231 28 8.99 8.99427260970965 -0.00427260970964483 29 9 9.00409946104404 -0.00409946104403502 30 9 9.01393332927499 -0.0139333292749892 31 9 9.01336867733263 -0.0133686773326307 32 9.01 9.01282690806316 -0.00282690806315955 33 9.01 9.0227123468483 -0.0127123468483035 34 8.99 9.02219717554946 -0.0321971755494594 35 8.99 9.00089237629053 -0.0108923762905277 36 8.99 9.00045095979143 -0.0104509597914308 37 9 9.0000274318155 -2.74318155053521e-05 38 9 9.01002632013375 -0.0100263201337540 39 9.02 9.00962000079496 0.0103799992050408 40 9.05 9.0300406530739 0.0199593469260986 41 9.05 9.06084951101357 -0.0108495110135660 42 9.05 9.06040983164143 -0.0104098316414252 43 9.06 9.05998797039492 1.20296050827307e-05 44 9.06 9.06998845789792 -0.00998845789792213 45 9.08 9.06958367293649 0.0104163270635116 46 9.07 9.09000579741173 -0.0200057974117342 47 9.06 9.07919505705356 -0.0191950570535617 48 9.08 9.06841717216797 0.0115828278320276 49 9.07 9.08888656940278 -0.0188865694027793 50 9.11 9.07812118606278 0.0318788139372153 51 9.15 9.11941308363116 0.0305869163688435 52 9.15 9.1606526267007 -0.0106526267006952 53 9.17 9.16022092611866 0.0097790738813437 54 9.2 9.18061722573611 0.019382774263887 55 9.23 9.21140271791249 0.0185972820875122 56 9.26 9.24215637780569 0.0178436221943112 57 9.27 9.2728794954276 -0.00287949542760479 58 9.28 9.28276280309556 -0.00276280309556221 59 9.29 9.29265083975188 -0.00265083975187963 60 9.29 9.30254341375302 -0.0125434137530220 61 9.11 9.30203508851361 -0.192035088513615 62 9.06 9.11425281454377 -0.0542528145437657 63 9.11 9.06205420454138 0.0479457954586184 64 9.13 9.11399722088724 0.0160027791127568 65 9.13 9.13464573784474 -0.00464573784473643 66 9.19 9.1344574680604 0.0555425319396008 67 9.2 9.19670834420954 0.00329165579046276 68 9.23 9.2068417394519 0.0231582605480938 69 9.24 9.23778023423245 0.00221976576755445 70 9.28 9.24787019084134 0.0321298091586559 71 9.32 9.28917226005904 0.0308277399409587 72 9.32 9.33042156256906 -0.0104215625690607 73 9.32 9.32999922592353 -0.00999922592353464 74 9.36 9.32959400458495 0.0304059954150535 75 9.37 9.37082621578383 -0.000826215783833462 76 9.38 9.38079273316543 -0.000792733165432935 77 9.41 9.39076060743921 0.0192393925607863 78 9.44 9.42154028903324 0.0184597109667592 79 9.44 9.45228837381951 -0.0122883738195139 80 9.44 9.45179038414248 -0.0117903841424827 81 9.47 9.45131257563198 0.0186874243680180 82 9.48 9.48206988856551 -0.00206988856551149 83 9.56 9.49198600577082 0.0680139942291831 84 9.58 9.57474229130682 0.0052577086931791 85 9.56 9.59495536137553 -0.0349553613755287 86 9.58 9.57353878588901 0.00646121411098655 87 9.7 9.59380062834072 0.106199371659283 88 9.74 9.71810438663861 0.0218956133613855 89 9.76 9.75899171229996 0.00100828770004213 90 9.78 9.77903257343207 0.000967426567928698 91 9.84 9.79907177865574 0.0409282213442612 92 9.88 9.86073040591009 0.0192695940899146 93 9.96 9.90151131142926 0.0584886885707387 94 9.97 9.98388158137377 -0.0138815813737683 95 9.96 9.99331902652912 -0.0333190265291226 96 9.96 9.98196876395542 -0.0219687639554156 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 9.98107847384644 9.9197183388674 10.0424386088255 98 10.0021569476929 9.91360483681846 10.0907090585673 99 10.0232354215393 9.91259366972259 10.1338771733561 100 10.0443138953858 9.91401502510289 10.1746127656686 101 10.0653923692322 9.91685806977872 10.2139266686857 102 10.0864708430786 9.92061581145594 10.2523258747013 103 10.1075493169251 9.92499378423336 10.2901048496168 104 10.1286277907715 9.9298045078352 10.3274510737078 105 10.1497062646180 9.93492082703831 10.3644917021976 106 10.1707847384644 9.94025242335316 10.4013170535756 107 10.1918632123108 9.94573284665386 10.4379935779678 108 10.2129416861573 9.9513118394692 10.4745715328454

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/19/t1263934821v5g42pbdoy5gvln/1snn21263934374.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/19/t1263934821v5g42pbdoy5gvln/1snn21263934374.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/19/t1263934821v5g42pbdoy5gvln/2ly281263934374.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/19/t1263934821v5g42pbdoy5gvln/2ly281263934374.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/19/t1263934821v5g42pbdoy5gvln/3xz831263934374.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/19/t1263934821v5g42pbdoy5gvln/3xz831263934374.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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