Opgave 10: Extra oefening: hotelkamers: Exponential smoothing: Vincent Van Gestel - 2MAR04B

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 28 May 2008 03:09:32 -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/28/t12119660940w2z8esze8n9784.htm/, Retrieved Wed, 28 May 2008 11:14:54 +0200

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Dataseries X:

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65.05 65.84 66.6 67.55 68.07 69.06 69.06 69.11 69.29 69.38 69.28 69.75 69.9 70.21 70.48 71.55 72.18 72.64 72.77 72.74 73.13 73.44 73.34 73.34 73.81 74.26 74.72 75.11 75.26 75.89 75.91 76.43 76.56 76.76 76.76 76.56 76.82 77.09 77.51 77.76 77.86 77.89 77.94 77.99 78.17 78.91 78.87 78.88 79.08 79.41 79.51 79.73 80.38 80.56 80.46 80.45 80.58 80.68 80.52 81.49 81.66 81.95 82.3 82.4 83.14 83.17 83.11 83.21 83.33 83.88 83.8 83.73

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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.91765681329827 beta 0.0281982947013472 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 69.9 68.0280291666667 1.87197083333332 14 70.21 70.1097524451255 0.100247554874514 15 70.48 70.5228191607047 -0.0428191607047381 16 71.55 71.58557505941 -0.0355750594100357 17 72.18 72.2048913374113 -0.0248913374112476 18 72.64 72.68295084189 -0.0429508418899331 19 72.77 72.8195765077098 -0.0495765077097872 20 72.74 72.7696725600557 -0.0296725600557295 21 73.13 73.1435157878132 -0.0135157878132333 22 73.44 73.4722523150126 -0.0322523150125988 23 73.34 73.4212939012777 -0.081293901277661 24 73.34 73.436145218406 -0.0961452184060647 25 73.81 73.8711076123279 -0.061107612327902 26 74.26 74.0224412105834 0.237558789416610 27 74.72 74.5426873281708 0.177312671829171 28 75.11 75.8066967965121 -0.696696796512128 29 75.26 75.8017541088003 -0.541754108800276 30 75.89 75.7721935357428 0.117806464257242 31 75.91 76.028123117202 -0.118123117201989 32 76.43 75.8875115810444 0.542488418955642 33 76.56 76.7730937917569 -0.21309379175689 34 76.76 76.8973401889136 -0.137340188913640 35 76.76 76.7233864502541 0.0366135497458657 36 76.56 76.8257419727494 -0.265741972749396 37 76.82 77.0840978458444 -0.264097845844390 38 77.09 77.0446365569296 0.0453634430704284 39 77.51 77.3494664730734 0.160533526926628 40 77.76 78.4915895617186 -0.731589561718593 41 77.86 78.4319627090602 -0.571962709060188 42 77.89 78.3927865831474 -0.50278658314744 43 77.94 78.0075341009755 -0.067534100975493 44 77.99 77.9167884069322 0.0732115930677537 45 78.17 78.2464209468388 -0.0764209468388088 46 78.91 78.4427629525903 0.467237047409682 47 78.87 78.7940108439444 0.0759891560555985 48 78.88 78.864704944621 0.0152950553789708 49 79.08 79.3454661605704 -0.265466160570440 50 79.41 79.2945702665686 0.115429733431441 51 79.51 79.639332533077 -0.129332533077033 52 79.73 80.4006491909566 -0.670649190956595 53 80.38 80.370317175459 0.00968282454105918 54 80.56 80.8458673936501 -0.285867393650108 55 80.46 80.6764046131194 -0.216404613119437 56 80.45 80.437676354775 0.0123236452249529 57 80.58 80.6745779025397 -0.0945779025396547 58 80.68 80.8740192182473 -0.194019218247334 59 80.52 80.5441279228942 -0.0241279228942375 60 81.49 80.4732442219525 1.01675577804747 61 81.66 81.8310911391947 -0.171091139194701 62 81.95 81.8818126091552 0.0681873908447699 63 82.3 82.145494954248 0.154505045752032 64 82.4 83.1124748853218 -0.712474885321768 65 83.14 83.0884711697166 0.0515288302834165 66 83.17 83.567857162711 -0.397857162710949 67 83.11 83.2882201563354 -0.178220156335357 68 83.21 83.0912285752946 0.118771424705429 69 83.33 83.4076267565173 -0.077626756517347 70 83.88 83.6054904434145 0.274509556585457 71 83.8 83.7227163305017 0.0772836694982715 72 83.73 83.836406681119 -0.106406681118941 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 84.0425047936678 83.2831187344802 84.8018908528553 74 84.2510993642003 83.207045752859 85.2951529755416 75 84.4387195093133 83.1612322416505 85.7162067769761 76 85.1679316674074 83.6836079930224 86.6522553417923 77 85.8544868651597 84.1798079844048 87.5291657459145 78 86.2420908027627 84.3882451443125 88.0959364612128 79 86.3484384390919 84.323451490527 88.3734253876569 80 86.3468614160224 84.1567000385088 88.537022793536 81 86.5424371502539 84.1916457654581 88.8932285350496 82 86.846881295241 84.3389769461708 89.3547856443113 83 86.6952078119162 84.0329397217883 89.3574759020442 84 86.7200992105304 83.9056269917818 89.534571429279

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t12119660940w2z8esze8n9784/1vvf81211965765.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t12119660940w2z8esze8n9784/1vvf81211965765.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t12119660940w2z8esze8n9784/2lvc41211965765.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t12119660940w2z8esze8n9784/2lvc41211965765.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t12119660940w2z8esze8n9784/3chqz1211965765.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t12119660940w2z8esze8n9784/3chqz1211965765.ps (open in new window)

Parameters (Session):

par1 = additive ; par2 = 12 ;

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=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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