opdracht 10

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 20 Dec 2010 16:11:23 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/20/t1292861461djavx4pet6ay1v4.htm/, Retrieved Mon, 20 Dec 2010 17:11:02 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/20/t1292861461djavx4pet6ay1v4.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

108 106,6 122,2 115,8 115,6 124,5 121,7 118,7 113,7 113,4 115,1 143,9 101 103,4 121,5 111,9 117,4 124,3 122 119,7 115 112,2 115,3 142,6 104,1 105,3 124,4 113,9 124,8 131,8 125,6 125 119,7 116,1 120 148,1 109,2 109,4 135,1 114,9 129 138,5 125,6 130,4 120,3 126,2 127,6 150,9 114,6 118,6 131,4 124,5 136,8 136,8 136,6 131 125,8 129,4 124,8 157,1 116,6 114,2 128,4 127,3 133,5 137,2 137,7 131,2 127,7 133,9 124,3 160,6

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 0.127863990701472 beta 0.243685602085768 gamma 0.106601253861168 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 101 101.507665598291 -0.507665598290629 14 103.4 103.738925385997 -0.338925385996987 15 121.5 121.639533858845 -0.139533858844715 16 111.9 111.952956313147 -0.0529563131466801 17 117.4 117.421632205983 -0.0216322059831953 18 124.3 124.297805961287 0.00219403871319912 19 122 120.902094598525 1.09790540147485 20 119.7 118.434861140059 1.26513885994113 21 115 113.765930791807 1.23406920819349 22 112.2 113.860646306122 -1.66064630612205 23 115.3 115.429321839654 -0.129321839654168 24 142.6 144.135602474634 -1.53560247463443 25 104.1 100.929525138683 3.1704748613173 26 105.3 103.736859216469 1.56314078353115 27 124.4 122.048561454647 2.35143854535306 28 113.9 112.915504416903 0.984495583096873 29 124.8 118.779036491753 6.0209635082467 30 131.8 126.877625914214 4.92237408578575 31 125.6 124.813773669407 0.786226330592768 32 125 122.913400129326 2.08659987067446 33 119.7 118.963376701266 0.736623298733889 34 116.1 119.326623284516 -3.22662328451649 35 120 121.389902011815 -1.38990201181525 36 148.1 150.317445691267 -2.21744569126702 37 109.2 107.953656489524 1.24634351047625 38 109.4 110.79751865771 -1.39751865770988 39 135.1 129.143688114542 5.95631188545761 40 114.9 120.796541935946 -5.89654193594566 41 129 126.486141054938 2.51385894506188 42 138.5 134.162544396478 4.33745560352173 43 125.6 131.749518991346 -6.14951899134553 44 130.4 128.977259709978 1.42274029002158 45 120.3 124.690208787274 -4.39020878727382 46 126.2 123.743071638205 2.45692836179498 47 127.6 126.594544633493 1.00545536650689 48 150.9 155.716778131472 -4.81677813147218 49 114.6 113.22701479798 1.37298520202017 50 118.6 115.72956955907 2.87043044092972 51 131.4 135.326432488089 -3.92643248808852 52 124.5 124.327022370751 0.172977629248834 53 136.8 131.477086334344 5.32291366565605 54 136.8 139.672204318251 -2.87220431825071 55 136.6 135.127694151238 1.47230584876195 56 131 134.036829711193 -3.03682971119269 57 125.8 128.503010829938 -2.70301082993775 58 129.4 128.324644997448 1.07535500255199 59 124.8 130.737927693135 -5.93792769313471 60 157.1 158.088116452009 -0.988116452008597 61 116.6 116.439725657956 0.160274342043635 62 114.2 118.665008027763 -4.46500802776306 63 128.4 136.202031686404 -7.80203168640415 64 127.3 124.477447993625 2.82255200637461 65 133.5 131.916898406113 1.58310159388662 66 137.2 138.227202787029 -1.02720278702856 67 137.7 133.735282423544 3.96471757645551 68 131.2 132.03431787576 -0.834317875759893 69 127.7 126.37221165542 1.32778834458045 70 133.9 126.745166971563 7.15483302843691 71 124.3 129.157843063896 -4.85784306389552 72 160.6 157.014055087823 3.58594491217741 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 116.107541707836 109.77325483888 122.441828576792 74 117.927573541166 111.513695389819 124.341451692512 75 135.909647617774 129.383619391048 142.4356758445 76 126.597921690166 119.922988544297 133.272854836035 77 133.900772741499 127.036895911734 140.764649571263 78 140.056182207149 132.961031028382 147.151333385917 79 136.481921934605 129.111865233028 143.851978636183 80 134.026522598103 126.337542842938 141.715502353268 81 128.896784457177 120.845256660625 136.94831225373 82 129.825012511221 121.368316095308 138.281708927133 83 130.166384504849 121.2633422805 139.069426729198 84 159.540498457592 150.151656807631 168.929340107554

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292861461djavx4pet6ay1v4/152l01292861478.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292861461djavx4pet6ay1v4/152l01292861478.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292861461djavx4pet6ay1v4/284nf1292861479.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292861461djavx4pet6ay1v4/284nf1292861479.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292861461djavx4pet6ay1v4/384nf1292861479.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292861461djavx4pet6ay1v4/384nf1292861479.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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