Opgave 10 oef 2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 04 Jun 2009 06:15:59 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/04/t1244117791xncdt7g7os52zql.htm/, Retrieved Thu, 04 Jun 2009 14:16:35 +0200

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/2009/Jun/04/t1244117791xncdt7g7os52zql.htm/}, year = {2009}, } @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 = {2009}, 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:

Dataseries X:

» Textbox « » Textfile « » CSV «

65 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

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 0.942505883717753 beta 0.0229525145944379 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 69.75 67.6758012820513 2.07419871794869 14 69.9 69.851796739716 0.0482032602840547 15 70.21 70.2772390001607 -0.0672390001606828 16 70.48 70.5470050110147 -0.0670050110146718 17 71.55 71.5976253799827 -0.0476253799827333 18 72.18 72.2163142244234 -0.0363142244234069 19 72.64 73.1361283182693 -0.496128318269299 20 72.77 72.6289155721832 0.141084427816793 21 72.74 72.7911649843006 -0.0511649843005983 22 73.13 72.9415280150545 0.188471984945451 23 73.44 73.2472441577892 0.192755842210772 24 73.34 73.3615843918819 -0.0215843918818877 25 73.34 73.9801949839464 -0.64019498394643 26 73.81 73.462841817917 0.347158182083007 27 74.26 74.1513470858405 0.108652914159478 28 74.72 74.5786442479861 0.141355752013865 29 75.11 75.8230060543459 -0.713006054345882 30 75.26 75.7970719004046 -0.537071900404555 31 75.89 76.1895013798266 -0.299501379826623 32 75.91 75.8795193172994 0.0304806827006274 33 76.43 75.899350814736 0.530649185264039 34 76.56 76.5973211313606 -0.0373211313605708 35 76.76 76.6710539667104 0.0889460332896022 36 76.76 76.6535655742686 0.106434425731393 37 76.56 77.3383736330767 -0.778373633076654 38 76.82 76.7256695200649 0.0943304799351381 39 77.09 77.1348173952727 -0.044817395272716 40 77.51 77.388674957503 0.121325042497062 41 77.76 78.5339304522478 -0.773930452247839 42 77.86 78.4282654303364 -0.568265430336425 43 77.89 78.7718544823174 -0.881854482317436 44 77.94 77.8862759974699 0.0537240025300889 45 77.99 77.9115768027045 0.0784231972955212 46 78.17 78.0956891589705 0.0743108410295434 47 78.91 78.2293329707253 0.68066702927473 48 78.87 78.7307887740867 0.1392112259133 49 78.88 79.3565651549811 -0.476565154981145 50 79.08 79.045968899175 0.0340311008250183 51 79.41 79.3564558605251 0.0535441394748659 52 79.51 79.6808715937616 -0.170871593761618 53 79.73 80.461236694468 -0.731236694468009 54 80.38 80.370537486443 0.00946251355694017 55 80.56 81.2160090859209 -0.656009085920886 56 80.46 80.5773672471657 -0.117367247165660 57 80.45 80.4194181777817 0.0305818222182666 58 80.58 80.5337529500308 0.0462470499691676 59 80.68 80.6507509159294 0.0292490840706279 60 80.52 80.4679614331267 0.052038566873307 61 81.49 80.935138238323 0.55486176167696 62 81.66 81.6073016225599 0.0526983774401231 63 81.95 81.918185735785 0.0318142642149297 64 82.3 82.1904295186085 0.109570481391501 65 82.4 83.1901731678355 -0.790173167835505 66 83.14 83.0725148065408 0.0674851934592482 67 83.17 83.9216705926155 -0.75167059261554 68 83.11 83.2090246944902 -0.0990246944901827 69 83.21 83.0624553291892 0.147544670810802 70 83.33 83.276044715378 0.0539552846220204 71 83.88 83.3876129886166 0.492387011383414 72 83.8 83.6409455295367 0.159054470463289 73 83.73 84.2385114320388 -0.508511432038773 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 83.8571806631447 82.9663193709516 84.7480419553377 75 84.0936682927977 82.8561841765218 85.3311524090737 76 84.3161819961045 82.7987574549504 85.8336065372587 77 85.1343390575644 83.3713848454469 86.8972932696819 78 85.8012417886438 83.8141834860961 87.7883000911915 79 86.5287437686848 84.3322694389668 88.7252180984027 80 86.5673839495266 84.172170657126 88.9625972419271 81 86.5357732421657 83.9498913394909 89.1216551448405 82 86.6091792657754 83.8388980907884 89.3794604407623 83 86.6981935991035 83.7484805198838 89.6479066783233 84 86.4607240643274 83.3355718424042 89.5858762862506 85 86.8589985141476 83.5616498698864 90.1563471584088

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244117791xncdt7g7os52zql/1typp1244117756.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244117791xncdt7g7os52zql/1typp1244117756.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244117791xncdt7g7os52zql/2yxzr1244117756.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244117791xncdt7g7os52zql/2yxzr1244117756.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244117791xncdt7g7os52zql/30lhg1244117756.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244117791xncdt7g7os52zql/30lhg1244117756.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=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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