Opgave 10 oefening 2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 16 Jan 2010 10:09:08 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/16/t1263661803uldper14cwcef0s.htm/, Retrieved Sat, 16 Jan 2010 18:10:07 +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/Jan/16/t1263661803uldper14cwcef0s.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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

10 15 12 13 12 15 13 13 16 14 12 15 14 19 16 16 11 13 12 11 6 9 6 15 17 13 12 13 10 14 13 10 11 12 7 11 9 13 12 5 13 11 8 8 8 8 0 3 0 -1 -1 -4 1 -1 0 -1 6 0 -3 -3

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.635345371205515 beta 0.281122102631007 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 12 20 -8 4 13 18.4883600171545 -5.4883600171545 5 12 17.5922049379589 -5.5922049379589 6 15 15.6312508328869 -0.631250832886929 7 13 16.7094684796509 -3.70946847965089 8 13 15.1694080127592 -2.16940801275921 9 16 14.2203406796729 1.77965932032705 10 14 16.0981592840101 -2.09815928401006 11 12 15.1374723413373 -3.13747234133733 12 15 12.9560798949468 2.04392010505323 13 14 14.431724962636 -0.431724962636004 14 19 14.2573701614291 4.74262983857086 15 16 18.2175970769512 -2.21759707695120 16 16 17.3595918531815 -1.35959185318151 17 11 16.8038800835107 -5.80388008351069 18 13 12.3878815035589 0.612118496441143 19 12 12.1575881791556 -0.157588179155598 20 11 11.4101185153825 -0.410118515382502 21 6 10.4289537564839 -4.42895375648388 22 9 6.10338685261743 2.89661314738257 23 6 6.94944796538283 -0.94944796538283 24 15 5.18235140615841 9.8176485938416 25 17 12.0096063570887 4.99039364291132 26 13 16.6612195647143 -3.66121956471428 27 12 15.1621413078765 -3.16214130787654 28 13 13.4153612329751 -0.415361232975057 29 10 13.3395476496351 -3.33954764963514 30 14 10.8093904030464 3.19060959695359 31 13 12.9980119252203 0.00198807477968899 32 10 13.1611126120489 -3.1611126120489 33 11 10.7499467754068 0.250053224593248 34 12 10.5507112765769 1.44928872342315 35 7 11.3722614187128 -4.37226141871278 36 11 7.7141886451886 3.28581135481140 37 9 9.50851450000374 -0.508514500003741 38 13 8.80130740112481 4.19869259887519 39 12 11.8347294613283 0.165270538671715 40 5 12.3350543946717 -7.3350543946717 41 13 6.75997127218705 6.24002872781295 42 11 10.9242835766641 0.0757164233358534 43 8 11.1856522739298 -3.18565227392982 44 8 8.80593730230932 -0.805937302309315 45 8 7.79421506202745 0.205784937972554 46 8 7.46204103499584 0.537958965004157 47 0 7.43699688836597 -7.43699688836597 48 3 1.01678221709952 1.98321778290048 49 0 0.935879120754331 -0.935879120754331 50 -1 -1.16681570177592 0.166815701775916 51 -1 -2.5391235827457 1.5391235827457 52 -4 -2.7646397151898 -1.2353602848102 53 1 -4.97355856961831 5.97355856961831 54 -1 -1.53538913259705 0.535389132597048 55 0 -1.45670982213283 1.45670982213283 56 -1 -0.532491278707392 -0.467508721292608 57 6 -0.914317638200897 6.9143176382009 58 0 4.62882890275241 -4.62882890275241 59 -3 2.01133731761596 -5.01133731761596 60 -3 -1.74425230566867 -1.25574769433133 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 -3.33803407250328 -10.5353534755914 3.85928533058483 62 -4.13398235434248 -13.4141233200847 5.14615861139974 63 -4.92993063618169 -16.641248279672 6.78138700730863 64 -5.72587891802089 -20.1553042375247 8.70354640148296 65 -6.52182719986009 -23.9168308879973 10.8731764882772 66 -7.3177754816993 -27.8991639279938 13.2636129645952 67 -8.1137237635385 -32.0831956163983 15.8557480893213 68 -8.9096720453777 -36.4544958703117 18.6351517795563 69 -9.7056203272169 -41.0016878270664 21.5904471726326 70 -10.5015686090561 -45.7154894328372 24.712352214725 71 -11.2975168908953 -50.5881204836736 27.9930867018830 72 -12.0934651727345 -55.6129188493618 31.4259885038928

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/16/t1263661803uldper14cwcef0s/1yplf1263661746.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t1263661803uldper14cwcef0s/1yplf1263661746.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t1263661803uldper14cwcef0s/2gab21263661746.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t1263661803uldper14cwcef0s/2gab21263661746.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t1263661803uldper14cwcef0s/3d9151263661747.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/16/t1263661803uldper14cwcef0s/3d9151263661747.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=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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