Sanne Seghers - 2MAR03 - double exp. smoothing

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 18 Aug 2008 09:49:08 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Aug/18/t1219074650pcx5g92a14dsp7u.htm/, Retrieved Mon, 18 Aug 2008 15:50:54 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Afzetprijsindexen van de verwerking en conservering van groenten en fruit

Dataseries X:

» Textbox « » Textfile « » CSV «

115.6 118.5 118.1 117.7 117.9 118.5 117 115.6 113.7 112.1 113.5 113.5 112.2 112.7 111.9 111.5 110.8 111.2 110.9 114.1 121.3 121.5 122.5 122.4 122.5 122.8 122.9 123.6 123.4 122.9 121 119 119 114.3 113.4 113.7 113.5 114.4 114.6 111.6 111.8 110.8 112.6 115.3 115.4 115.3 115.5 115 116.3 117 116.9 117.2 117.1 116.7 117.4 126.7 128.6 129.2 131.1 131.1 131.5 133.2 133.7 135.7 134.9 135.7 131.2 127.4 127.5 124.1 124.1 124.1 124.5 123.7 125.9 126 125.5 125.3

Text written by user:

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.320159117207958 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 118.1 121.4 -3.30000000000001 4 117.7 119.943474913214 -2.24347491321373 5 117.9 118.825205965521 -0.92520596552103 6 118.5 118.728992840364 -0.228992840364285 7 117 119.255678694746 -2.25567869474631 8 115.6 117.033502595132 -1.43350259513154 9 113.7 115.174553669759 -1.47455366975889 10 112.1 112.802461868573 -0.702461868573153 11 113.5 110.977562296859 2.52243770314149 12 113.5 113.185143725108 0.314856274891639 13 112.2 113.285947832125 -1.08594783212504 14 112.7 111.638271732858 1.06172826714200 15 111.9 112.478193717581 -0.578193717580916 16 111.5 111.493079727385 0.00692027261496264 17 110.8 111.095295315756 -0.295295315756277 18 111.2 110.300753828148 0.899246171851914 19 110.9 110.988655688681 -0.0886556886808307 20 114.1 110.660271761657 3.43972823834267 21 121.3 114.961532117880 6.33846788211962 22 121.5 124.190850399471 -2.69085039947079 23 122.5 123.529350111038 -1.02935011103754 24 122.4 124.199794288190 -1.79979428818984 25 122.5 123.523573737727 -1.02357373772708 26 122.8 123.295867273459 -0.495867273459126 27 122.9 123.437110844936 -0.537110844936123 28 123.6 123.365149910979 0.234850089021421 29 123.4 124.140339308156 -0.740339308155853 30 122.9 123.703312928822 -0.803312928822336 31 121 122.946124970689 -1.94612497068884 32 119 120.423055318097 -1.42305531809674 33 119 117.967451183717 1.03254881628320 34 114.3 118.298031101212 -3.99803110121215 35 113.4 112.318024993278 1.08197500672190 36 113.7 111.764429156271 1.93557084372873 37 113.5 112.684119808893 0.815880191107084 38 114.4 112.745331290625 1.65466870937479 39 114.6 114.175088563890 0.42491143610971 40 111.6 114.511127834167 -2.91112783416673 41 111.8 110.579103716700 1.22089628329961 42 110.8 111.169984792964 -0.369984792964075 43 112.6 110.051530788268 2.54846921173167 44 115.3 112.667446441328 2.632553558672 45 115.4 116.210282464675 -0.810282464675083 46 115.3 116.050863146096 -0.75086314609564 47 115.5 115.710467464098 -0.210467464097661 48 115 115.843084386591 -0.843084386591158 49 116.3 115.073163233648 1.22683676635168 50 117 116.765946209722 0.234053790278267 51 116.9 117.540880664596 -0.640880664596395 52 117.2 117.235696876784 -0.0356968767835752 53 117.1 117.524268196225 -0.424268196225469 54 116.7 117.288434865062 -0.588434865062496 55 117.4 116.700042078130 0.699957921870293 56 126.7 117.624139988478 9.07586001152158 57 128.6 129.829859317670 -1.22985931767019 58 129.2 131.336108644235 -2.13610864423492 59 131.1 131.252213986436 -0.152213986436351 60 131.1 133.103481290912 -2.00348129091219 61 131.5 132.462048489471 -0.962048489471073 62 133.2 132.554039894371 0.6459601056292 63 133.7 134.460849911541 -0.76084991154059 64 135.7 134.717256875534 0.982743124465998 65 134.9 137.031891046705 -2.13189104670519 66 135.7 135.549346691209 0.150653308791448 67 131.2 136.397579721556 -5.19757972155566 68 127.4 130.233527186284 -2.83352718628441 69 127.5 125.526347623739 1.97365237626114 70 124.1 126.258230426198 -2.15823042619802 71 124.1 122.167253278215 1.93274672178489 72 124.1 122.786039762448 1.31396023755167 73 124.5 123.206716112149 1.29328388785078 74 123.7 124.020772739983 -0.3207727399828 75 125.9 123.118074422726 2.78192557727446 76 126 126.208733259684 -0.208733259683967 77 125.5 126.241905403532 -0.741905403531604 78 125.3 125.504377624485 -0.204377624485119 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 79 125.238944264653 121.184742062575 129.293146466731 80 125.177888529306 118.463537130918 131.892239927694 81 125.116832793959 115.666571810868 134.567093777049 82 125.055777058612 112.707462826733 137.40409129049 83 124.994721323264 109.568368387637 140.421074258892 84 124.933665587917 106.248069818557 143.619261357278 85 124.872609852570 102.750498911595 146.994720793545 86 124.811554117223 99.081205701149 150.541902533297 87 124.750498381876 95.2460892932217 154.254907470531 88 124.689442646529 91.2509120913367 158.127973201721 89 124.628386911182 87.1011182295478 162.155655592816 90 124.567331175835 82.8017781717002 166.332884179969

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/18/t1219074650pcx5g92a14dsp7u/1cpws1219074545.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/18/t1219074650pcx5g92a14dsp7u/1cpws1219074545.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/18/t1219074650pcx5g92a14dsp7u/240y51219074545.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/18/t1219074650pcx5g92a14dsp7u/240y51219074545.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/18/t1219074650pcx5g92a14dsp7u/3p9re1219074545.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/18/t1219074650pcx5g92a14dsp7u/3p9re1219074545.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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=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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