cijferreeks - oliezaden - tim deelstra

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 01 Jun 2008 14:44:19 -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/Jun/01/t1212353115fhr8odz2asweioo.htm/, Retrieved Sun, 01 Jun 2008 20:45:19 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

90.2 94.3 96 99 103.3 113.1 112.8 112.1 107.4 111 110.5 110.8 112.4 111.5 116.2 122.5 121.3 113.9 110.7 120.8 141.1 147.4 148 158.1 165 187 190.3 182.4 168.8 151.2 120.1 112.5 106.2 107.1 108.5 106.5 108.3 125.6 124 127.2 136.9 135.8 124.3 115.4 113.6 114.4 118.4 117 116.5 115.4 113.6 117.4 116.9 116.4 111.1 110.2 118.9 131.8 130.6 138.3 148.4 148.7 144.3 152.5 162.9 167.2 166.5 185.6 193.2 207.8 223.4 246.4

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 0.572958262964854 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 96 98.4 -2.39999999999999 4 99 98.7249001688843 0.275099831115654 5 103.3 101.882520890262 1.4174791097377 6 113.1 106.994677258767 6.10532274123342 7 112.8 120.292772371423 -7.4927723714235 8 112.1 115.699726528702 -3.59972652870165 9 107.4 112.937233469668 -5.53723346966824 10 111 105.064629799256 5.9353702007437 11 110.5 112.065349199528 -1.56534919952776 12 110.8 110.668469441233 0.131530558767082 13 112.4 111.043830961711 1.35616903828911 14 111.5 113.420859218176 -1.92085921817575 15 116.2 111.420287057130 4.77971294287026 16 122.5 118.858863082347 3.64113691765269 17 121.3 127.245082565903 -5.94508256590279 18 113.9 122.638798385760 -8.73879838576049 19 110.7 110.231831642255 0.468168357744901 20 120.8 107.300072571284 13.4999274287163 21 141.1 125.134967540993 15.9650324590074 22 147.4 154.582264806883 -7.18226480688296 23 148 156.767126838978 -8.76712683897773 24 158.1 152.343929074125 5.75607092587549 25 165 165.741917473317 -0.741917473316619 26 187 172.216829726542 14.7831702734582 27 190.3 202.686969287536 -12.3869692875361 28 182.4 198.889752881150 -16.4897528811504 29 168.8 181.541812713647 -12.7418127136468 30 151.2 160.641285834212 -9.44128583421227 31 120.1 137.631823102487 -17.5318231024873 32 112.5 96.486820191079 16.0131798089209 33 106.2 98.0617038789423 8.13829612105772 34 107.1 96.4246078879571 10.6753921120429 35 108.5 103.441162008942 5.0588379910581 36 106.5 107.739665036919 -1.23966503691916 37 108.3 105.029388710708 3.27061128929230 38 125.6 108.703312473854 16.8966875261461 39 124 135.684409208694 -11.6844092086945 40 127.2 127.389730404710 -0.189730404710346 41 136.9 130.481022801596 6.41897719840412 42 135.8 143.858828827205 -8.0588288272045 43 124.3 138.141456260838 -13.8414562608383 44 115.4 118.710879524724 -3.31087952472438 45 113.6 107.913883743352 5.68611625664758 46 114.4 109.371791036777 5.0282089632226 47 118.4 113.052744910170 5.34725508983026 48 117 120.116498898069 -3.11649889806887 49 116.5 116.930875102899 -0.430875102899449 50 115.4 116.184001652387 -0.784001652387374 51 113.6 114.634801427474 -1.03480142747395 52 117.4 112.241903399075 5.1580966009251 53 116.9 118.997277467746 -2.09727746774587 54 116.4 117.295625012871 -0.895625012870866 55 111.1 116.282469261229 -5.18246926122852 56 110.2 108.013130675446 2.18686932455374 57 118.9 108.366115524974 10.5338844750263 58 131.8 123.101591676057 8.6984083239428 59 130.6 140.985416599903 -10.3854165999025 60 138.3 133.835006344656 4.46499365534402 61 148.4 144.093261353571 4.30673864642898 62 148.7 156.660842847473 -7.96084284747258 63 144.3 152.399612157848 -8.09961215784847 64 152.5 143.358872445199 9.14112755480136 65 162.9 156.796357010538 6.10364298946223 66 167.2 170.693489695538 -3.49348969553768 67 166.5 172.991865907897 -6.49186590789677 68 185.6 168.572297693908 17.0277023060925 69 193.2 197.428460429489 -4.22846042948890 70 207.8 202.605729086793 5.19427091320671 71 223.4 220.181829526593 3.2181704734069 72 246.4 237.625706890961 8.7742931090389 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 265.653010629461 249.730452954411 281.57556830451 74 284.906021258921 255.227647853542 314.5843946643 75 304.159031888382 258.900984542316 349.417079234447 76 323.412042517842 260.782658982306 386.041426053378 77 342.665053147303 260.996765668416 424.333340626189 78 361.918063776763 259.660759993541 464.175367559985 79 381.171074406224 256.875308153954 505.466840658494 80 400.424085035684 252.725709933703 548.122460137666 81 419.677095665145 247.284721965055 592.069469365234 82 438.930106294605 240.615064381105 637.245148208105 83 458.183116924066 232.771398373923 683.594835474209 84 477.436127553526 223.801846794724 731.070408312329

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212353115fhr8odz2asweioo/1j8nv1212353054.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212353115fhr8odz2asweioo/1j8nv1212353054.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212353115fhr8odz2asweioo/2eqjh1212353054.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212353115fhr8odz2asweioo/2eqjh1212353054.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212353115fhr8odz2asweioo/3vn9f1212353054.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212353115fhr8odz2asweioo/3vn9f1212353054.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')

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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