exponentiol smoothing - sigaretten - caroline thys

*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 09:44:56 -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/t12439575339kyaz6ceny42vfj.htm/, Retrieved Tue, 02 Jun 2009 17:45:33 +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/t12439575339kyaz6ceny42vfj.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 «

106.07 106.07 106.07 106.07 106.07 106.2 107.5 108.31 108.53 108.61 108.62 108.62 108.62 108.62 110.1 110.74 110.77 110.77 110.78 110.78 110.78 110.84 110.84 110.84 110.84 110.84 111.01 112.66 114.04 114.16 114.2 114.2 114.23 114.23 114.23 114.23 114.23 114.23 115.97 116.96 117.08 117.08 117.08 117.63 119.12 119.47 119.5 119.52 119.49 119.49 119.5 119.5 119.56 122.35 122.92 122.92 123.04 123.04 123.04 123.06 123.33 128.21 129.57 129.79 131.66 135.01 136.01 136.31 136.37 136.4 136.4 136.4 137.34 142.18 143.79 144.08 144.08 144.09 144.09 144.11 144.11 144.15 144.15 144.16 144.2 144.38 144.38 144.28 144.46 144.53 144.53 145.34 147.98 150.42 150.53 150.64

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 R Framework error message Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.912394349585859 beta 0.0280522073302993 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 108.62 106.516988420335 2.10301157966508 14 108.62 108.532103268903 0.0878967310965066 15 110.1 110.234617744641 -0.134617744641417 16 110.74 110.901450987309 -0.161450987309451 17 110.77 110.930653037448 -0.160653037448185 18 110.77 110.926647260655 -0.156647260654680 19 110.78 110.787947354488 -0.00794735448762651 20 110.78 111.719939359441 -0.939939359441027 21 110.78 111.105905222161 -0.325905222160614 22 110.84 110.810404221686 0.029595778314075 23 110.84 110.740495558946 0.0995044410535684 24 110.84 110.731380271562 0.108619728438001 25 110.84 110.981899150867 -0.141899150866962 26 110.84 110.720798473541 0.119201526458681 27 111.01 112.415447209349 -1.40544720934903 28 112.66 111.849183401653 0.810816598347444 29 114.04 112.712422206809 1.32757779319113 30 114.16 114.048940279579 0.111059720421025 31 114.2 114.152661325118 0.0473386748822264 32 114.2 115.065099160724 -0.865099160723517 33 114.23 114.570732180148 -0.34073218014764 34 114.23 114.282120240736 -0.0521202407359311 35 114.23 114.127390085190 0.102609914809790 36 114.23 114.105359340524 0.124640659475560 37 114.23 114.339315024196 -0.10931502419551 38 114.23 114.115240337951 0.114759662049394 39 115.97 115.702575789328 0.267424210672488 40 116.96 116.924650096031 0.035349903969248 41 117.08 117.139651691333 -0.0596516913332152 42 117.08 117.080106413129 -0.000106413129444149 43 117.08 117.049968510364 0.0300314896364142 44 117.63 117.858802189427 -0.228802189426958 45 119.12 117.989239896285 1.13076010371493 46 119.47 119.093061254196 0.376938745804239 47 119.5 119.371538435794 0.128461564205878 48 119.52 119.402529079566 0.117470920433689 49 119.49 119.646361181752 -0.156361181752075 50 119.49 119.425293980728 0.0647060192721369 51 119.5 121.079187694063 -1.57918769406268 52 119.5 120.613136997018 -1.11313699701826 53 119.56 119.735993557495 -0.175993557494678 54 122.35 119.533174521743 2.8168254782574 55 122.92 122.097863266039 0.82213673396123 56 122.92 123.685780969789 -0.765780969789162 57 123.04 123.494749552160 -0.454749552159853 58 123.04 123.077507473430 -0.0375074734297982 59 123.04 122.935185346174 0.104814653826082 60 123.06 122.922263726376 0.137736273624370 61 123.33 123.145590358459 0.184409641541293 62 128.21 123.242646606609 4.96735339339098 63 129.57 129.428153568954 0.141846431046389 64 129.79 130.804727386048 -1.01472738604818 65 131.66 130.269664908033 1.39033509196744 66 135.01 131.962392383415 3.04760761658491 67 136.01 134.729465493354 1.28053450664638 68 136.31 136.863746972248 -0.553746972247865 69 136.37 137.152179022137 -0.782179022136518 70 136.4 136.669465768531 -0.269465768530750 71 136.4 136.504127863033 -0.104127863033256 72 136.4 136.472284947038 -0.0722849470375877 73 137.34 136.693402494146 0.646597505854146 74 142.18 137.837406978883 4.34259302111724 75 143.79 143.318005592303 0.471994407697025 76 144.08 145.183920713335 -1.10392071333521 77 144.08 145.008404497298 -0.928404497297578 78 144.09 144.887975793587 -0.797975793586716 79 144.09 143.997421144278 0.0925788557218539 80 144.11 144.925313799889 -0.815313799889253 81 144.11 144.985009562717 -0.875009562716826 82 144.15 144.462951067344 -0.312951067344301 83 144.15 144.261999563211 -0.111999563210901 84 144.16 144.213755672225 -0.0537556722247245 85 144.2 144.519250742944 -0.319250742944433 86 144.38 145.101504902410 -0.721504902409691 87 144.38 145.490871864122 -1.11087186412220 88 144.28 145.595826178109 -1.31582617810915 89 144.46 145.055643725257 -0.595643725257219 90 144.53 145.07194655305 -0.541946553050053 91 144.53 144.319762952464 0.210237047535742 92 145.34 145.107487726942 0.232512273057523 93 147.98 145.977827997950 2.00217200205046 94 150.42 148.056088905561 2.36391109443937 95 150.53 150.296597408776 0.233402591223864 96 150.64 150.556276792780 0.083723207220146 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 150.967001580134 148.798316128932 153.135687031336 98 151.839994870281 148.863773277691 154.816216462871 99 152.917718259413 149.273165210047 156.562271308780 100 154.121148005582 149.878767475583 158.363528535581 101 154.964054812409 150.177147464209 159.750962160608 102 155.653990657130 150.357425393060 160.950555921199 103 155.544544249315 149.785820313667 161.303268184963 104 156.279732299861 150.047437889816 162.512026709906 105 157.237873790305 150.53597825365 163.939769326959 106 157.572832559082 150.436017864066 164.709647254098 107 157.446350755637 149.903141624874 164.9895598864 108 157.457640068931 148.927131069726 165.988149068137

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439575339kyaz6ceny42vfj/1jltv1243957491.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439575339kyaz6ceny42vfj/1jltv1243957491.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439575339kyaz6ceny42vfj/2162o1243957491.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439575339kyaz6ceny42vfj/2162o1243957491.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439575339kyaz6ceny42vfj/3uk1l1243957491.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439575339kyaz6ceny42vfj/3uk1l1243957491.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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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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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