*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 09:39:07 -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/t1243957174kxe9zsnjodthlfs.htm/, Retrieved Tue, 02 Jun 2009 17:39:38 +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/t1243957174kxe9zsnjodthlfs.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 «

98.8 100.5 110.4 96.4 101.9 106.2 81.0 94.7 101.0 109.4 102.3 90.7 96.2 96.1 106.0 103.1 102.0 104.7 86.0 92.1 106.9 112.6 101.7 92.0 97.4 97.0 105.4 102.7 98.1 104.5 87.4 89.9 109.8 111.7 98.6 96.9 95.1 97.0 112.7 102.9 97.4 111.4 87.4 96.8 114.1 110.3 103.9 101.6

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 0.096080656622426 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 96.2 96.1709668803419 0.0290331196581519 14 96.1 96.0609795950156 0.0390204049844129 15 106 105.914451894621 0.0855481053786491 16 103.1 102.730727939565 0.369272060434525 17 102 101.645097701744 0.354902298255823 18 104.7 104.437253474404 0.262746525596071 19 86 81.4122215265816 4.58777847341835 20 92.1 95.9319081548858 -3.83190815488577 21 106.9 102.317625763387 4.58237423661264 22 112.6 111.149293149071 1.45070685092934 23 101.7 103.992567876014 -2.29256787601446 24 92 92.317852975942 -0.317852975942031 25 97.4 97.7549469119016 -0.354946911901592 26 97 97.6170942734074 -0.617094273407403 27 105.4 107.449583932283 -2.0495839322829 28 102.7 104.317178660228 -1.61717866022752 29 98.1 103.027699826824 -4.92769982682388 30 104.5 105.228998333120 -0.72899833311989 31 87.4 86.0181589264328 1.38184107356720 32 89.9 92.6190993757672 -2.71909937576724 33 109.8 106.717568996778 3.08243100322152 34 111.7 112.574346124757 -0.874346124757366 35 98.6 101.810609801854 -3.21060980185437 36 96.9 91.8326718265717 5.06732817342831 37 95.1 97.7536475771576 -2.65364757715763 38 97 97.1579741984867 -0.157974198486713 39 112.7 105.739721303783 6.96027869621678 40 102.9 103.863849038741 -0.963849038741245 41 97.4 99.6446984252135 -2.24469842521354 42 111.4 105.899068965123 5.50093103487747 43 87.4 89.1948338332921 -1.79483383329207 44 96.8 91.7836378735066 5.01636212649342 45 114.1 111.869451245693 2.23054875430692 46 110.3 114.067771584417 -3.76777158441718 47 103.9 100.914239114504 2.98576088549640 48 101.6 99.0142407626754 2.58575923732464 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 49 97.7176464097228 91.9462690226163 103.489023796829 50 99.6328246744428 93.8348692713593 105.430780077526 51 114.664076527035 108.839664387781 120.488488666289 52 104.956683775562 99.105934534685 110.807433016440 53 99.6723558741762 93.7953875578274 105.549324190525 54 113.143822808311 107.240751869968 119.046893746654 55 89.3162716215414 83.3872129766256 95.2453302664572 56 98.234296254572 92.27936331401 104.189229195134 57 115.319983665630 109.339288368398 121.300678962862 58 111.881993633464 105.875646478156 117.888340788772 59 105.195119767068 99.163229842524 111.227009691612 60 102.646678321678 96.5893533367072 108.704003306649

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243957174kxe9zsnjodthlfs/1rh1j1243957146.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243957174kxe9zsnjodthlfs/1rh1j1243957146.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243957174kxe9zsnjodthlfs/2oh4x1243957146.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243957174kxe9zsnjodthlfs/2oh4x1243957146.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243957174kxe9zsnjodthlfs/31q421243957146.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243957174kxe9zsnjodthlfs/31q421243957146.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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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