Oefening 10; Eigen reeks; Weuts Koen

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 19 May 2011 06:44:06 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/19/t13057873493bb371fsdtvrjf1.htm/, Retrieved Thu, 19 May 2011 08:42:33 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

190,2 180,7 193,6 192,8 195,5 197,2 196,9 178,9 172,4 156,4 143,7 153,6 168,8 185,8 199,9 205,4 197,5 199,6 200,5 193,7 179,6 169,1 169,8 195,5 194,8 204,5 203,8 204,8 204,9 240 248,3 258,4 254,9 288,3 333,6 346,3 357,5 490,7 468,2 471,2 517,1 609,2 682 614 554,2 406,8 348,6 298,8 313,7 282,1 232,9 239,3 241,9 265,7 276 271,5 254,6 269,9 293,5 306,1 365,4 347,9 352,1 377,9 377,4 372,2 362,5 341,9 354,8 369,2 406,7 454,7

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 168.8 166.527911324786 2.27208867521364 14 185.8 185.733435314685 0.0665646853146598 15 199.9 199.683435314685 0.216564685314694 16 205.4 205.270935314685 0.12906468531466 17 197.5 196.583435314685 0.916564685314682 18 199.6 197.466768648019 2.13323135198135 19 200.5 206.187601981352 -5.68760198135203 20 193.7 183.879268648019 9.82073135198132 21 179.6 187.425101981352 -7.82510198135199 22 169.1 163.512601981352 5.58739801864803 23 169.8 156.491768648019 13.3082313519814 24 195.5 180.216768648019 15.2832313519813 25 194.8 211.150101981352 -16.350101981352 26 204.5 211.733435314685 -7.23343531468535 27 203.8 218.383435314685 -14.5834353146853 28 204.8 209.170935314685 -4.37093531468534 29 204.9 195.983435314685 8.91656468531468 30 240 204.866768648019 35.1332313519814 31 248.3 246.587601981352 1.71239801864797 32 258.4 231.679268648019 26.7207313519813 33 254.9 252.125101981352 2.77489801864806 34 288.3 238.812601981352 49.4873980186481 35 333.6 275.691768648019 57.9082313519814 36 346.3 344.016768648019 2.28323135198133 37 357.5 361.950101981352 -4.45010198135196 38 490.7 374.433435314685 116.266564685315 39 468.2 504.583435314685 -36.3834353146853 40 471.2 473.570935314685 -2.37093531468537 41 517.1 462.383435314685 54.7165646853147 42 609.2 517.066768648019 92.1332313519814 43 682 615.787601981352 66.212398018648 44 614 665.379268648019 -51.3792686480188 45 554.2 607.725101981352 -53.5251019813519 46 406.8 538.112601981352 -131.312601981352 47 348.6 394.191768648019 -45.5917686480186 48 298.8 359.016768648019 -60.2167686480187 49 313.7 314.450101981352 -0.750101981351975 50 282.1 330.633435314685 -48.5334353146853 51 232.9 295.983435314685 -63.0834353146853 52 239.3 238.270935314685 1.02906468531467 53 241.9 230.483435314685 11.4165646853147 54 265.7 241.866768648019 23.8332313519813 55 276 272.287601981352 3.71239801864795 56 271.5 259.379268648019 12.1207313519814 57 254.6 265.225101981352 -10.6251019813519 58 269.9 238.512601981352 31.387398018648 59 293.5 257.291768648019 36.2082313519815 60 306.1 303.916768648019 2.18323135198136 61 365.4 321.750101981352 43.649898018648 62 347.9 382.333435314685 -34.4334353146853 63 352.1 361.783435314685 -9.6834353146852 64 377.9 357.470935314685 20.4290646853146 65 377.4 369.083435314685 8.31656468531475 66 372.2 377.366768648019 -5.1667686480186 67 362.5 378.787601981352 -16.287601981352 68 341.9 345.879268648019 -3.97926864801866 69 354.8 335.625101981352 19.1748980186481 70 369.2 338.712601981352 30.487398018648 71 406.7 356.591768648019 50.1082313519814 72 454.7 417.116768648019 37.5832313519813 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 470.350101981352 395.567542889567 545.132661073137 74 487.283537296037 381.525027999468 593.042046592607 75 501.166972610723 371.639780743729 630.694164477716 76 506.537907925408 356.972789741838 656.103026108978 77 497.721343240093 330.502457579467 664.94022890072 78 497.688111888112 314.509000453708 680.867223322516 79 504.275713869464 306.419660107608 702.131767631319 80 487.654982517482 276.137963924343 699.172001110622 81 481.380084498834 257.032407223479 705.72776177419 82 465.292686480186 228.809470494013 701.77590246636 83 452.684455128205 204.658765758173 700.710144498237 84 463.101223776224 204.046840042237 722.155607510211

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t13057873493bb371fsdtvrjf1/1ryrd1305787440.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t13057873493bb371fsdtvrjf1/1ryrd1305787440.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t13057873493bb371fsdtvrjf1/2zr2x1305787440.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t13057873493bb371fsdtvrjf1/2zr2x1305787440.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t13057873493bb371fsdtvrjf1/34ou31305787440.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t13057873493bb371fsdtvrjf1/34ou31305787440.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) 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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