werkloosheid voor jongeren -25jaar (additief, triple), Jonas Janssens, MAR 202 B

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 26 May 2008 02:16:39 -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/26/t1211789862bjia1an2o4u5sje.htm/, Retrieved Mon, 26 May 2008 10:17:46 +0200

User-defined keywords:

Dataseries X:

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18.3 15.3 18.6 18.2 16.1 13.1 16.5 16.5 14.7 12.1 15.7 15.7 14 11.7 15.2 15.6 14.3 12.5 16.6 18.1 18.5 17.6 22.6 23.9 23.2 20.6 24.2 24.5 22.9 20.4 23.9 24.1 22.3 19.5 23.3 23.4 21.8 19.8 23.3 23.2 21.2 19 23.8 24.3 23.1 21.6 22.2 17.4 15.6 14.5 20.3 16.1 14.1 15.3 17.8 19.6 17.8 15.7 18.9 18.4 20.8 19 24.5 22.6 19.6 17.5 25 22.3 20.5 19.9 23.4 22.1 20 18.9 23 20 18.6 19.2 20.3 17.8

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 0.859340004640999 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 5 16.1 17.4075892857143 -1.30758928571429 6 13.1 13.7589255028600 -0.658925502860049 7 16.5 16.9801844581742 -0.480184458174222 8 16.5 16.8675427436583 -0.367542743658252 9 14.7 14.8052730577572 -0.105273057757156 10 12.1 12.2810487525014 -0.181048752501376 11 15.7 15.9381080312026 -0.238108031202568 12 15.7 16.0493364576049 -0.349336457604942 13 14 14.0396030144470 -0.0396030144470458 14 11.7 11.5611529956431 0.138847004356897 15 15.2 15.4850855376502 -0.285085537650222 16 15.6 15.5402989235023 0.0597010764977011 17 14.3 13.9256349014756 0.374365098524372 18 12.5 11.8280250216105 0.671974978389455 19 16.6 16.1504654099058 0.449534590094203 20 18.1 16.8854649432890 1.21453505671097 21 18.5 16.3074565990563 2.19254340094367 22 17.6 15.8141418743510 1.78585812564897 23 22.6 21.0624981475965 1.53750185240346 24 23.9 22.8400364353058 1.05996356469418 25 23.2 22.2667652735669 0.93323472643312 26 20.6 20.6340718777277 -0.0340718777277047 27 24.2 24.2835557011831 -0.0835557011831192 28 24.5 24.6008838499370 -0.100883849937041 29 22.9 23.0122243877198 -0.112224387719767 30 20.4 20.3450648094205 0.054935190579517 31 23.9 24.0640755729905 -0.164075572990519 32 24.1 24.3097723974085 -0.209772397408468 33 22.3 22.6259454903099 -0.325945490309859 34 19.5 19.7986394842267 -0.298639484226719 35 23.3 23.1830033321205 0.116996667879508 36 23.4 23.6638090622016 -0.263809062201602 37 21.8 21.9172053806205 -0.117205380620526 38 19.8 19.2731189640555 0.526881035944491 39 23.3 23.4253489988107 -0.125348998810740 40 23.2 23.6443332703276 -0.444333270327633 41 21.2 21.7632191880685 -0.56321918806853 42 19 18.8264524565060 0.173547543493971 43 23.8 22.5833062125573 1.21669378744266 44 24.3 23.9106932120905 0.389306787909518 45 23.1 22.7292368887081 0.370763111291872 46 21.6 20.6987121156549 0.901287884345145 47 22.2 25.2276712054232 -3.02767120542324 48 17.4 22.7913253207745 -5.39132532077448 49 15.6 16.6397322208207 -1.03973222082073 50 14.5 13.4717359946392 1.02826400536079 51 20.3 17.5571633774980 2.74283662250205 52 16.1 19.7471741395838 -3.64717413958384 53 14.1 15.7064949890128 -1.60649498901282 54 15.3 12.3423411825599 2.95765881744011 55 17.8 18.3269464885550 -0.526946488554952 56 19.6 16.8082829326711 2.79171706732891 57 17.8 18.5878425015799 -0.787842501579892 58 15.7 16.5691833807104 -0.869183380710382 59 18.9 18.7750855282172 0.124914471782787 60 18.4 18.2833953733840 0.116604626616027 61 20.8 17.2606229727254 3.53937702727461 62 19 18.9490752941833 0.0509247058166657 63 24.5 22.0854929283546 2.41450707164538 64 22.6 23.5601724261307 -0.960172426130704 65 19.6 22.093529577959 -2.49352957795898 66 17.5 18.1069782219304 -0.606978221930408 67 25 21.0104950357263 3.98950496427371 68 22.3 23.3639508273679 -1.06395082736787 69 20.5 21.5924450375355 -1.09244503753551 70 19.9 19.0752639819604 0.824736018039633 71 23.4 23.8556514210159 -0.455651421015883 72 22.1 21.6783874356935 0.421612564306486 73 20 21.1794777022872 -1.17947770228715 74 18.9 18.8571766745600 0.0428233254400254 75 23 22.7855359654928 0.214464034507188 76 20 21.3075249469337 -1.30752494693371 77 18.6 19.0974888271249 -0.497488827124869 78 19.2 17.5331769794322 1.66682302056783 79 20.3 22.8812471572539 -2.58124715725392 80 17.8 18.786686707126 -0.986686707126008 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 81 16.9662993986555 14.0833877455636 19.8492110517473 82 16.1339316964250 12.3327875440797 19.9350758487702 83 19.4521006405191 14.9148973020865 23.9893039789518 84 17.8 12.6304998886101 22.9695001113899

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211789862bjia1an2o4u5sje/12fdf1211789794.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211789862bjia1an2o4u5sje/12fdf1211789794.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211789862bjia1an2o4u5sje/2kz0w1211789794.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211789862bjia1an2o4u5sje/2kz0w1211789794.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211789862bjia1an2o4u5sje/3gfnn1211789794.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211789862bjia1an2o4u5sje/3gfnn1211789794.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 4 ; 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=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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