*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: Fri, 04 Dec 2009 05:40:04 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/04/t1259930479zwsv42b9mo4x423.htm/, Retrieved Fri, 04 Dec 2009 13:41:27 +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/2009/Dec/04/t1259930479zwsv42b9mo4x423.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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111,5 108,1 124,5 106,3 111,1 121,3 116,5 117,4 123,6 98,4 107,2 118,9 111,9 115,2 124,4 104,6 117 126,2 117,5 122,2 124,1 105,8 107,5 125,6 112,1 120,1 130,6 109,8 122,1 129,5 132,1 133,3 128,4 114,7 114,1 136,9 123,4 134 137 127,8 140,1 140,4 157,8 151,8 141,1 138,8 141,1 139,5 150,7 144,4 146 143,6 143,1 156,4 164,8 145,1 153,4 133,2 131,4 145,9

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 0.242037573055879 beta 0.0101587425110497 gamma 0.717611294485236 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 111.9 110.438328940193 1.46167105980669 14 115.2 114.073692087286 1.12630791271364 15 124.4 123.518076924008 0.881923075992404 16 104.6 103.975631334110 0.624368665890216 17 117 116.410936657466 0.589063342533578 18 126.2 125.686928425276 0.513071574723739 19 117.5 119.273110540321 -1.77311054032124 20 122.2 119.699896783751 2.50010321624943 21 124.1 126.621122340376 -2.52112234037564 22 105.8 100.607901317585 5.19209868241461 23 107.5 111.060870035117 -3.56087003511709 24 125.6 122.020939428539 3.57906057146074 25 112.1 116.500522579400 -4.40052257939954 26 120.1 118.639229606241 1.46077039375942 27 130.6 128.347752818404 2.25224718159564 28 109.8 108.248451316425 1.55154868357509 29 122.1 121.380809125568 0.719190874432385 30 129.5 131.015464401879 -1.51546440187894 31 132.1 122.582891110496 9.51710888950375 32 133.3 128.271404622036 5.02859537796377 33 128.4 133.325090785582 -4.92509078558169 34 114.7 109.633111314929 5.0668886850713 35 114.1 115.559455822279 -1.45945582227927 36 136.9 131.931296740266 4.96870325973364 37 123.4 121.6964892601 1.70351073990007 38 134 129.051256535917 4.94874346408287 39 137 140.933981246858 -3.93398124685757 40 127.8 117.391129362678 10.4088706373225 41 140.1 133.441453626264 6.65854637373647 42 140.4 144.250866206381 -3.85086620638086 43 157.8 140.997365590964 16.8026344090358 44 151.8 146.162700720502 5.63729927949754 45 141.1 145.813404297501 -4.71340429750072 46 138.8 125.631680795489 13.1683192045113 47 141.1 130.198692249186 10.9013077508142 48 139.5 156.406201564472 -16.9062015644722 49 150.7 137.563697081524 13.1363029184757 50 144.4 150.771557707329 -6.37155770732926 51 146 155.860073575039 -9.86007357503885 52 143.6 136.933446521625 6.6665534783752 53 143.1 151.230741679164 -8.13074167916437 54 156.4 153.020812030909 3.37918796909065 55 164.8 163.309139876017 1.49086012398320 56 145.1 158.368963278440 -13.2689632784403 57 153.4 147.546911975748 5.85308802425214 58 133.2 139.009553343902 -5.80955334390234 59 131.4 137.593586961383 -6.19358696138255 60 145.9 144.060884092591 1.83911590740883 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 145.906121532797 135.633822365746 156.178420699848 62 145.230696020751 134.479774555819 155.981617485683 63 149.807106366999 138.529242890176 161.084969843821 64 142.089414786972 130.494727458478 153.684102115467 65 146.612770546764 134.465015576610 158.760525516919 66 156.704697380373 143.826304605133 169.583090155613 67 165.154461975807 151.561106373660 178.747817577954 68 151.574886863623 138.091958023462 165.057815703785 69 154.379437870814 140.368882101399 168.389993640228 70 137.779560322295 124.107217052926 151.451903591664 71 137.497419182399 123.431445489261 151.563392875537 72 150.263722440696 121.371130616217 179.156314265175

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259930479zwsv42b9mo4x423/1jksy1259930400.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259930479zwsv42b9mo4x423/1jksy1259930400.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259930479zwsv42b9mo4x423/2ty421259930400.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259930479zwsv42b9mo4x423/2ty421259930400.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259930479zwsv42b9mo4x423/31tyj1259930400.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259930479zwsv42b9mo4x423/31tyj1259930400.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')

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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