Exponential smoothing - Eigen reeks: Faxtoestellen - Kirsten Witvrouwen

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 27 May 2008 06:41:58 -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/May/27/t1211892205z5lbz2onfjquyhh.htm/, Retrieved Tue, 27 May 2008 14:43:28 +0200

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Dataseries X:

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77.5 77.7 76.6 77 76.5 77.6 77.8 76.9 76.9 77 77 76.3 76.5 77.1 76.4 75.4 75.4 75.5 75.5 75.8 75.7 75.9 76.1 76 76 75.89 74.87 74.9 74.79 74.64 74.09 74.33 73.93 73.78 72.85 71.51 71.5 71.5 71.31 70.85 70.62 70.07 68.83 68.82 68.4 68.21 67.75 67.7 67.42 66.27 64.8 62.69 62.75 62.31 62.4 61.75 61.69 60.39 59.9 59.62 58.97 58.54 58.32 56.03 53.63 53.61 53.48 53.48 52.81 52.8 52.57 52.36

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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.0938618268174845 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 76.6 77.9 -1.30000000000001 4 77 76.6779796251373 0.322020374862731 5 76.5 77.1082050457943 -0.608205045794335 6 77.6 76.5511178091165 1.04888219088352 7 77.8 77.7495678076691 0.0504321923308737 8 76.9 77.9543014653717 -1.05430146537171 9 76.9 76.9553428038156 -0.0553428038155772 10 77 76.9501482271482 0.0498517728517527 11 77 77.0548274056182 -0.0548274056181981 12 76.3 77.0496812051672 -0.749681205167207 13 76.5 76.2793147577195 0.220685242280524 14 77.1 76.5000286777116 0.599971322288397 15 76.4 77.1563430820597 -0.756343082059672 16 75.4 76.3853513386768 -0.985351338676793 17 75.4 75.2928644619715 0.107135538028459 18 75.5 75.302920399288 0.19707960071203 19 75.5 75.4214186506393 0.0785813493607463 20 75.8 75.428794439644 0.371205560355961 21 75.7 75.7636364716639 -0.0636364716638553 22 75.9 75.6576634361813 0.242336563818739 23 76.1 75.880409588766 0.219590411234023 24 76 76.101020745916 -0.101020745915989 25 76 75.9915387541579 0.0084612458421418 26 75.89 75.9923329421497 -0.102332942149744 27 74.87 75.872727785256 -1.00272778525596 28 74.9 74.7586099235312 0.141390076468809 29 74.79 74.8018810544024 -0.0118810544024228 30 74.64 74.6907658769317 -0.0507658769316919 31 74.09 74.5360008989829 -0.446000898982888 32 74.33 73.9441384398421 0.385861560157878 33 73.93 74.2203561107772 -0.290356110777168 34 73.78 73.793102755792 -0.0131027557920191 35 72.85 73.641872907197 -0.791872907197032 36 71.51 72.6375462695202 -1.12754626952024 37 71.5 71.1917127168418 0.308287283158165 38 71.5 71.2106491244237 0.289350875576346 39 71.31 71.2378081261965 0.0721918738035043 40 70.85 71.054584187353 -0.204584187353078 41 70.62 70.5753815417901 0.0446184582098681 42 70.07 70.3495695117875 -0.279569511787514 43 68.83 69.7733286066886 -0.943328606688638 44 68.82 68.4447860603757 0.375213939624331 45 68.4 68.4700043261962 -0.0700043261961696 46 68.21 68.0434335922543 0.166566407745705 47 67.75 67.8690678195717 -0.119067819571711 48 67.7 67.3978918965116 0.30210810348845 49 67.42 67.3762483150013 0.0437516849986537 50 66.27 67.1003549280817 -0.830354928081661 51 64.8 65.872416297625 -1.07241629762501 52 62.69 64.3017573448211 -1.61175734482109 53 62.75 62.0404748560497 0.709525143950323 54 62.31 62.1670721822338 0.142927817766207 55 62.4 61.7404876483124 0.659512351687631 56 61.75 61.8923906824505 -0.142390682450461 57 61.69 61.2290256328739 0.46097436712612 58 60.39 61.2122935290884 -0.822293529088363 59 59.9 59.8351115562679 0.064888443732059 60 59.62 59.351202104136 0.268797895864026 61 58.97 59.0964319656865 -0.126431965686464 62 58.54 58.434564830419 0.105435169580993 63 58.32 58.0144611680467 0.305538831953314 64 56.03 57.8231396009775 -1.79313960097751 65 53.63 55.364832242291 -1.73483224229098 66 53.61 52.8019977188077 0.808002281192316 67 53.48 52.8578382889931 0.62216171100691 68 53.48 52.7862355237641 0.693764476235913 69 52.81 52.8513535248847 -0.0413535248846557 70 52.8 52.1774720074936 0.622527992506349 71 52.57 52.2259036221153 0.344096377884689 72 52.36 52.0282011367449 0.331798863255145 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 51.8493443841859 50.6437084477191 53.0549803206528 74 51.3386887683719 49.5518510166001 53.1255265201436 75 50.8280331525578 48.5382066885265 53.1178596165892 76 50.3173775367438 47.5550020952489 53.0797529782386 77 49.8067219209297 46.5848219379767 53.0286219038828 78 49.2960663051157 45.6192903652026 52.9728422450287 79 48.7854106893016 44.6537699338516 52.9170514447516 80 48.2747550734876 43.6854660898565 52.8640440571186 81 47.7640994576735 42.712599951816 52.815598963531 82 47.2534438418594 41.7339974207854 52.7728902629335 83 46.7427882260454 40.7488654868559 52.7367109652349 84 46.2321326102313 39.7566618089471 52.7076034115155

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211892205z5lbz2onfjquyhh/19uj21211892113.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211892205z5lbz2onfjquyhh/19uj21211892113.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211892205z5lbz2onfjquyhh/2jkm31211892113.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211892205z5lbz2onfjquyhh/2jkm31211892113.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211892205z5lbz2onfjquyhh/3yp2v1211892113.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211892205z5lbz2onfjquyhh/3yp2v1211892113.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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