Maxime Jonckheere-Exponential Smoothing 2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 27 May 2009 16:07:59 -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/May/28/t1243462120n5nev5knzrzdva7.htm/, Retrieved Thu, 28 May 2009 00:08:40 +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/May/28/t1243462120n5nev5knzrzdva7.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:

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66,2 66,2 66,2 66,08 66,31 66,39 66,37 66,23 66,27 66,27 66,27 66,28 66,28 66,28 66,26 66,13 65,86 65,9 65,94 65,94 65,91 65,95 65,91 66,08 66,47 66,47 66,56 66,78 67,08 67,28 67,27 67,27 67,26 67,37 67,5 67,63 67,64 67,64 67,71 67,87 67,93 68,33 68,39 68,39 68,58 68,44 68,49 68,52 68,54 68,54 68,54 68,62 68,75 68,71 68,72 68,72 68,72 68,92 68,9 69,12 69,09 69,09 69,1 69,16 68,83 68,52 68,53 68,53 68,51 68,38 68,44 68,41 68,42 68,42 68,45 68,63 68,84 68,72 68,37 68,37 68,47 68,69 68,46 68,17 68,17

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.0985808158232413 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 66.2 66.2 0 4 66.08 66.2 -0.120000000000005 5 66.31 66.0681703021012 0.241829697898794 6 66.39 66.3220100710104 0.0679899289896326 7 66.37 66.4087125736779 -0.0387125736779268 8 66.23 66.3848962565821 -0.154896256582134 9 66.27 66.2296264572403 0.0403735427596814 10 66.27 66.2736065140232 -0.00360651402323242 11 66.27 66.2732509809285 -0.00325098092854148 12 66.28 66.2729304965764 0.00706950342362234 13 66.28 66.2836274139913 -0.00362741399133881 14 66.28 66.2832698205607 -0.00326982056074598 15 66.26 66.2829474789823 -0.0229474789822746 16 66.13 66.2606852977831 -0.130685297783131 17 65.86 66.1178022345115 -0.257802234511544 18 65.9 65.8223878799124 0.0776121200876503 19 65.94 65.8700389460284 0.0699610539716247 20 65.94 65.9169357638047 0.0230642361952675 21 65.91 65.9192094550252 -0.0092094550252142 22 65.95 65.8883015794355 0.0616984205644684 23 65.91 65.9343838600698 -0.0243838600697899 24 66.08 65.8919800792512 0.188019920748815 25 66.47 66.0805152364296 0.38948476357038 26 66.47 66.5089109621731 -0.0389109621731194 27 66.56 66.5050750877776 0.0549249122223756 28 66.78 66.6004896304335 0.179510369566472 29 67.08 66.8381859091141 0.241814090885882 30 67.28 67.1620241394712 0.117975860528801 31 67.27 67.3736542960496 -0.103654296049584 32 67.27 67.3534359709814 -0.0834359709814265 33 67.26 67.3452107848931 -0.0852107848930643 34 67.37 67.3268106362014 0.0431893637986178 35 67.5 67.4410682789195 0.0589317210804552 36 67.63 67.5768778160615 0.0531221839384841 37 67.64 67.7121146442925 -0.0721146442924834 38 67.64 67.7150055238253 -0.0750055238253253 39 67.71 67.7076114180954 0.00238858190461144 40 67.87 67.7778468864482 0.0921531135518165 41 67.93 67.9469314155628 -0.0169314155627802 42 68.33 68.0052623028036 0.324737697196426 43 68.39 68.4372752099218 -0.0472752099217502 44 68.39 68.4926147811594 -0.102614781159446 45 68.58 68.4824989323172 0.0975010676827708 46 68.44 68.682110667113 -0.242110667113025 47 68.49 68.5182432000295 -0.0282432000295216 48 68.52 68.5654589623291 -0.0454589623291497 49 68.54 68.5909775807363 -0.0509775807362587 50 68.54 68.6059521692386 -0.0659521692385852 51 68.54 68.5994505505897 -0.0594505505897303 52 68.62 68.5935898668115 0.0264101331885342 53 68.75 68.6761933992872 0.073806600712814 54 68.71 68.8134693141986 -0.103469314198605 55 68.72 68.7632692247922 -0.0432692247922262 56 68.72 68.7690037093122 -0.0490037093121742 57 68.72 68.7641728836698 -0.0441728836698161 58 68.92 68.7598182847604 0.160181715239631 59 68.9 68.9756091289287 -0.0756091289286616 60 69.12 68.9481555193152 0.171844480684811 61 69.09 69.1850960884158 -0.0950960884158292 62 69.09 69.1457214384382 -0.0557214384381837 63 69.1 69.1402283735781 -0.0402283735781168 64 69.16 69.1462626276915 0.0137373723084693 65 68.83 69.207616869061 -0.377616869060972 66 68.52 68.8403910900403 -0.320391090040332 67 68.53 68.4988066750016 0.0311933249983554 68 68.53 68.5118817384282 0.0181182615717717 69 68.51 68.5136678514353 -0.00366785143526727 70 68.38 68.4933062716485 -0.113306271648469 71 68.44 68.3521364469515 0.0878635530485354 72 68.41 68.4207981076921 -0.0107981076921249 73 68.42 68.3897336214265 0.0302663785735149 74 68.42 68.4027173057183 0.0172826942817181 75 68.45 68.4044210478202 0.0455789521798096 76 68.63 68.4389142581104 0.191085741889552 77 68.84 68.6377516464381 0.202248353561899 78 68.72 68.8676894541312 -0.147689454131154 79 68.37 68.7331301072544 -0.363130107254406 80 68.37 68.3473324450313 0.0226675549687059 81 68.47 68.3495670310928 0.120432968907167 82 68.69 68.4614394114197 0.228560588580294 83 68.46 68.703971100707 -0.243971100707 84 68.17 68.449920230562 -0.279920230561999 85 68.17 68.1323254658678 0.037674534132222 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 86 68.1360394521783 67.8658741765095 68.4062047278471 87 68.1020789043566 67.7007329689576 68.5034248397555 88 68.0681183565349 67.5526704964185 68.5835662166512 89 68.0341578087131 67.411075365103 68.6572402523233 90 68.0001972608914 67.2720949944361 68.7282995273468 91 67.9662367130697 67.1338854178875 68.798588008252 92 67.932276165248 66.9954316309181 68.8691206995779 93 67.8983156174263 66.8561263042013 68.9405049306513 94 67.8643550696046 66.7155861749493 69.0131239642599 95 67.8303945217829 66.5735609794505 69.0872280641152 96 67.7964339739612 66.4298839567796 69.1629839911427 97 67.7624734261395 66.2844430449377 69.2405038073412

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/28/t1243462120n5nev5knzrzdva7/1096o1243462074.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/28/t1243462120n5nev5knzrzdva7/1096o1243462074.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/28/t1243462120n5nev5knzrzdva7/270ps1243462074.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/28/t1243462120n5nev5knzrzdva7/270ps1243462074.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/28/t1243462120n5nev5knzrzdva7/3vsbh1243462074.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/28/t1243462120n5nev5knzrzdva7/3vsbh1243462074.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=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')

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Software written by Ed van Stee & Patrick Wessa

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