workshop 8: minitutorial link 4

*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: Wed, 08 Dec 2010 20:25:33 +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/08/t12918398350nbw28lh46a8ryc.htm/, Retrieved Wed, 08 Dec 2010 21:23:58 +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/08/t12918398350nbw28lh46a8ryc.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:

Dataseries X:

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33 24 24 31 25 28 24 25 16 17 11 12 39 19 14 15 7 12 12 14 9 8 4 7 3 5 0 -2 6 11 9 17 21 21 41 57 65 68 73 71 71 70 69 65 57 57 57 55 65 65 64 60 43 47 40 31 27 24 23 17

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.623322017241314 beta 0.395355498337461 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 39 45.8392094017094 -6.83920940170941 14 19 19.8960120850976 -0.89601208509757 15 14 12.2281995243007 1.77180047569934 16 15 12.5765914377821 2.42340856221786 17 7 4.92835476703561 2.07164523296439 18 12 10.404712981205 1.59528701879499 19 12 13.2689459200521 -1.26894592005214 20 14 12.2017949240138 1.79820507598615 21 9 4.15627182690693 4.84372817309307 22 8 9.6610819392656 -1.6610819392656 23 4 4.03528731155333 -0.0352873115533328 24 7 6.41419028499641 0.585809715003589 25 3 32.4984204152193 -29.4984204152193 26 5 -9.83240206845518 14.8324020684552 27 0 -7.31774050320634 7.31774050320634 28 -2 -2.52658760856032 0.52658760856032 29 6 -11.2166887780162 17.2166887780162 30 11 7.5256925757385 3.4743074242615 31 9 14.9505386295644 -5.95053862956441 32 17 15.4351452634647 1.56485473653527 33 21 11.6484150424500 9.35158495754996 34 21 21.8808047890448 -0.880804789044824 35 41 21.9140137834714 19.0859862165286 36 57 45.7179476168615 11.2820523831385 37 65 79.0455962674453 -14.0455962674453 38 68 78.761684143413 -10.7616841434130 39 73 71.9015131710862 1.09848682891376 40 71 78.13448878202 -7.1344887820201 41 71 76.9444138328207 -5.94441383282071 42 70 76.3543894470259 -6.35438944702591 43 69 71.961409300004 -2.96140930000405 44 65 75.7354606891368 -10.7354606891368 45 57 62.778920986599 -5.77892098659897 46 57 51.5613075527530 5.43869244724695 47 57 56.4474767399983 0.552523260001699 48 55 54.5850814143248 0.414918585675196 49 65 57.7461661814892 7.25383381851085 50 65 63.3720618694555 1.6279381305445 51 64 63.1517287464996 0.848271253500378 52 60 60.515545486921 -0.515545486920971 53 43 59.9185965680545 -16.9185965680545 54 47 45.6484021793069 1.35159782069307 55 40 42.5505186056832 -2.55051860568317 56 31 38.9673546934143 -7.9673546934143 57 27 25.6003921006072 1.39960789939278 58 24 20.8489101490319 3.15108985096805 59 23 19.6710797246676 3.32892027533239 60 17 17.3740649723405 -0.374064972340499 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 20.3116193410594 4.07038736605725 36.5528513160616 62 15.2014915555701 -6.3233506043323 36.7263337154726 63 9.17616834254956 -18.9655067310144 37.3178434161135 64 0.79189943412365 -35.0092315262165 36.5930303944638 65 -10.2409387589134 -54.5654055966592 34.0835280788325 66 -7.4926775549548 -61.0912246186639 46.1058695087543 67 -13.6452206377149 -77.1920290774127 49.9015878019829 68 -17.7927965650271 -91.9067252910435 56.3211321609893 69 -20.8155811236241 -106.073279758424 64.4421175111759 70 -24.2750136200530 -121.219520029263 72.6694927891567 71 -26.6218267396906 -135.768512876446 82.5248593970644 72 -32.4808460541769 -154.321720623404 89.36002851505

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/08/t12918398350nbw28lh46a8ryc/18ubs1291839929.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/08/t12918398350nbw28lh46a8ryc/18ubs1291839929.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/08/t12918398350nbw28lh46a8ryc/2jlsv1291839929.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/08/t12918398350nbw28lh46a8ryc/2jlsv1291839929.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/08/t12918398350nbw28lh46a8ryc/3jlsv1291839929.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/08/t12918398350nbw28lh46a8ryc/3jlsv1291839929.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=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')

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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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