*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 20 Jan 2010 08:07:04 -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/20/t1264000054fy1fhc4d76ptv20.htm/, Retrieved Wed, 20 Jan 2010 16:07:38 +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/20/t1264000054fy1fhc4d76ptv20.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 «

23.98 24.24 24.92 25.46 25.84 26.08 26.18 26.34 26.42 26.38 26.04 25.58 25.65 25.56 25.62 25.62 25.69 25.68 25.68 25.83 25.93 26.11 24.72 24.62 24.65 25.24 25.56 25.9 25.87 25.78 25.78 25.74 25.78 25.73 24.67 24.31 24.56 25 25.38 25.99 26.22 26.19 26.22 26.22 26.61 26.72 25.46 25.48 25.59 25.88 26 26.97 27.2 27.19 27.19 27.19 27.26 26.9 26.11 25.87 26.02 26.31 26.37 26.52 26.86 26.92 26.98 26.98 27.03 26.75 26.39 26.3 26.3 26.52 26.53 26.98 27.22 27.34 27.41 27.47 27.46 27.53 27.21 26.91 26.95 26.91 27.39 27.62 27.79 27.88 27.9 28.09 28.46 28.73 27.93 27.61 27.65 28.19 28.98 28.99 29.02 29 29.04 29.19 29.23 29.26 29.02 28.47 28.53 28.48 28.68 28.89 29.2 29.21 29.15 29.22 29.34 29.13 28.84 28.76

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 0.843623991338351 beta 0.0118408398755793 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 25.65 25.5819364316239 0.0680635683760684 14 25.56 25.5776136070211 -0.0176136070211399 15 25.62 25.6504188489409 -0.0304188489409185 16 25.62 25.6421174210916 -0.0221174210915933 17 25.69 25.7451816745618 -0.0551816745618048 18 25.68 25.7685509088495 -0.0885509088494842 19 25.68 26.0858011689778 -0.405801168977835 20 25.83 25.7588578626315 0.0711421373685077 21 25.93 25.7954026929132 0.134597307086846 22 26.11 25.8151576817308 0.294842318269218 23 24.72 25.7084611169199 -0.988461116919861 24 24.62 24.4125983671556 0.207401632844416 25 24.65 24.6828927457645 -0.0328927457645385 26 25.24 24.5706824182867 0.66931758171328 27 25.56 25.2185382837644 0.341461716235578 28 25.9 25.5265185872417 0.373481412758295 29 25.87 25.9633569948208 -0.093356994820791 30 25.78 25.9541290667629 -0.17412906676293 31 25.78 26.1535449529318 -0.373544952931844 32 25.74 25.9326902118613 -0.192690211861329 33 25.78 25.7582410872747 0.0217589127253106 34 25.73 25.7083926860234 0.0216073139765776 35 24.67 25.1683125548834 -0.49831255488343 36 24.31 24.4756532429014 -0.165653242901371 37 24.56 24.3926248842715 0.167375115728522 38 25 24.5601462785977 0.439853721402251 39 25.38 24.9618320714130 0.418167928586954 40 25.99 25.3389768599257 0.651023140074287 41 26.22 25.9391723964979 0.280827603502068 42 26.19 26.2389411656517 -0.0489411656517156 43 26.22 26.5199916444388 -0.299991644438823 44 26.22 26.3974112576997 -0.177411257699710 45 26.61 26.2774808244409 0.332519175559057 46 26.72 26.5009720825094 0.219027917490610 47 25.46 26.0593083445771 -0.599308344577054 48 25.48 25.3456282576335 0.134371742366490 49 25.59 25.5829445954288 0.00705540457121145 50 25.88 25.6713828589784 0.208617141021605 51 26 25.8858482219371 0.114151778062944 52 26.97 26.0511412122580 0.918858787742032 53 27.2 26.8302856463779 0.369714353622147 54 27.19 27.1652474154161 0.0247525845839505 55 27.19 27.4817195097738 -0.291719509773802 56 27.19 27.3978790297665 -0.207879029766502 57 27.26 27.3442744935536 -0.0842744935536395 58 26.9 27.2065262154050 -0.306526215405043 59 26.11 26.196399282182 -0.0863992821820183 60 25.87 26.0381501473715 -0.168150147371531 61 26.02 26.0053191817461 0.0146808182538791 62 26.31 26.1367626603854 0.173237339614595 63 26.37 26.3113080544708 0.0586919455292438 64 26.52 26.5597960663654 -0.0397960663653905 65 26.86 26.4388924369209 0.421107563079147 66 26.92 26.7583495693267 0.161650430673344 67 26.98 27.1372733937366 -0.157273393736567 68 26.98 27.1777585994591 -0.197758599459089 69 27.03 27.1499148573228 -0.119914857322790 70 26.75 26.9448828289851 -0.194882828985058 71 26.39 26.0620168891329 0.327983110867081 72 26.3 26.2433595470583 0.0566404529417461 73 26.3 26.4337959219185 -0.13379592191853 74 26.52 26.468330350403 0.0516696495970237 75 26.53 26.5247468611462 0.00525313885380996 76 26.98 26.7145583277112 0.265441672288802 77 27.22 26.9280908097437 0.291909190256341 78 27.34 27.1015455960160 0.238454403983958 79 27.41 27.4997236433436 -0.0897236433436355 80 27.47 27.5958718764446 -0.125871876444609 81 27.46 27.646571836462 -0.186571836461987 82 27.53 27.3786427824094 0.151357217590608 83 27.21 26.8781552014326 0.331844798567420 84 26.91 27.0288810252406 -0.118881025240622 85 26.95 27.0482671031612 -0.098267103161163 86 26.91 27.1489352796717 -0.238935279671708 87 27.39 26.9571875741348 0.432812425865190 88 27.62 27.5569120423643 0.0630879576357088 89 27.79 27.6103780907772 0.179621909222831 90 27.88 27.6861290547344 0.193870945265640 91 27.9 28.0003143676811 -0.100314367681083 92 28.09 28.0867076163757 0.00329238362428441 93 28.46 28.2430041984505 0.216995801549508 94 28.73 28.3785323780964 0.351467621903563 95 27.93 28.0872395042733 -0.157239504273267 96 27.61 27.7621466436877 -0.152146643687651 97 27.65 27.7636275457869 -0.113627545786905 98 28.19 27.8361216927336 0.35387830726636 99 28.98 28.2622342562111 0.717765743788853 100 28.99 29.0600858832815 -0.0700858832815179 101 29.02 29.0336458364341 -0.0136458364340761 102 29 28.9608685451477 0.0391314548522708 103 29.04 29.1092515046038 -0.0692515046038444 104 29.19 29.2491051518121 -0.0591051518120835 105 29.23 29.3966098727707 -0.166609872770746 106 29.26 29.2361454579684 0.0238545420315681 107 29.02 28.5922463311824 0.427753668817598 108 28.47 28.7706333619727 -0.300633361972665 109 28.53 28.6605567175041 -0.130556717504103 110 28.48 28.7993925477856 -0.319392547785629 111 28.68 28.7152123212211 -0.0352123212210564 112 28.89 28.7479022248779 0.142097775122053 113 29.2 28.9046805506457 0.295319449354302 114 29.21 29.0992824888224 0.110717511177633 115 29.15 29.290299356577 -0.140299356577003 116 29.22 29.3702829534414 -0.150282953441426 117 29.34 29.4216269154447 -0.0816269154447475 118 29.13 29.3610593215966 -0.231059321596614 119 28.84 28.5611415816008 0.278858418399228 120 28.76 28.4944001079222 0.265599892077816 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 28.888648912328 28.3472545041805 29.4300433204755 122 29.1094418718592 28.3976254664993 29.821258277219 123 29.3436840557357 28.4920473069582 30.1953208045131 124 29.4386949319342 28.4645419299981 30.4128479338703 125 29.5030248823037 28.4177563219468 30.5882934426606 126 29.4201394466219 28.2319286160688 30.6083502771749 127 29.4779118816082 28.1929434167673 30.7628803464491 128 29.6755081990905 28.2986410026273 31.0523753955537 129 29.8666858447412 28.4018440661703 31.3315276233122 130 29.8547436422436 28.3051640445757 31.4043232399115 131 29.3349307022865 27.7033277322897 30.9665336722833 132 29.0335173960828 27.3221980518196 30.7448367403461

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/20/t1264000054fy1fhc4d76ptv20/1w2yk1264000021.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1264000054fy1fhc4d76ptv20/1w2yk1264000021.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1264000054fy1fhc4d76ptv20/26vz91264000021.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1264000054fy1fhc4d76ptv20/26vz91264000021.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1264000054fy1fhc4d76ptv20/3x9v01264000021.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1264000054fy1fhc4d76ptv20/3x9v01264000021.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')

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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