Paper : Opgave 10 (oef 2) - Ishia Opgenhaffen

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 30 May 2010 15:34:20 +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/May/30/t1275233741nfvx06s1fzdf6v3.htm/, Retrieved Sun, 30 May 2010 17:35:42 +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/2010/May/30/t1275233741nfvx06s1fzdf6v3.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 «

121,67 121,65 121,61 121,5 121,41 121,41 121,4 121,38 121,34 121,19 120,96 120,96 120,96 120,9 120,86 120,73 120,53 120,53 120,53 120,52 120,51 120,43 120,29 120,27 120,27 120,24 120,21 120,06 119,86 119,85 119,85 119,83 119,71 119,57 119,2 119,13 119,13 119,09 118,9 118,54 118,12 118,11 118,1 118,08 117,91 117,63 117,28 117,2 117,17 117,14 116,96 116,34 115,99 115,99 115,97 115,92 115,63 115,31 115,13 115,09 115,07 115,01 114,64 113,86 113,34 113,33 113,32 113,26 113,2 112,61 112,28 112,16

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.0943679107239916 gamma 0.561964915342722 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 120.96 121.369898504274 -0.409898504273542 14 120.9 120.865566986291 0.0344330137089486 15 120.86 120.827149691188 0.0328503088119732 16 120.73 120.696083039531 0.0339169604693836 17 120.53 120.492617045562 0.0373829544384705 18 120.53 120.493228130202 0.0367718697980735 19 120.53 120.583364881395 -0.0533648813948702 20 120.52 120.475828949032 0.0441710509684299 21 120.51 120.451663945493 0.0583360545073788 22 120.43 120.33800233041 0.0919976695903131 23 120.29 120.192100624947 0.0978993750529327 24 120.27 120.295922517765 -0.0259225177653661 25 120.27 120.273059597256 -0.00305959725645266 26 120.24 120.211937536122 0.0280624638776175 27 120.21 120.202919065542 0.00708093445842906 28 120.06 120.079420611866 -0.0194206118657547 29 119.86 119.850921262632 0.00907873736767328 30 119.85 119.848861337443 0.00113866255692585 31 119.85 119.925635457316 -0.075635457316281 32 119.83 119.815997897233 0.014002102767364 33 119.71 119.778985913083 -0.0689859130832389 34 119.57 119.543309189929 0.0266908100705052 35 119.2 119.331244612578 -0.131244612578044 36 119.13 119.183442666029 -0.0534426660286442 37 119.13 119.107982726625 0.0220172733746864 38 119.09 119.04922711738 0.0407728826198195 39 118.9 119.031408102461 -0.131408102460512 40 118.54 118.734840727712 -0.194840727712489 41 118.12 118.279787348648 -0.159787348647626 42 118.11 118.041791883729 0.0682081162710233 43 118.1 118.124895207823 -0.0248952078225813 44 118.08 118.010045899073 0.0699541009267364 45 117.91 117.978313988091 -0.0683139880910062 46 117.63 117.692700673095 -0.0627006730949518 47 117.28 117.332200408241 -0.0522004082406511 48 117.2 117.211857698109 -0.0118576981094094 49 117.17 117.130322045246 0.0396779547538557 50 117.14 117.043233037605 0.0967669623952645 51 116.96 117.040698067006 -0.080698067006395 52 116.34 116.758916092357 -0.418916092356895 53 115.99 116.022717189286 -0.0327171892858331 54 115.99 115.866713069822 0.12328693017848 55 115.97 115.965014066509 0.00498593349128384 56 115.92 115.842984578635 0.0770154213647487 57 115.63 115.78191902971 -0.151919029709674 58 115.31 115.36841608161 -0.0584160816100621 59 115.13 114.968320144703 0.161679855297479 60 115.09 115.038160868186 0.0518391318135514 61 115.07 115.002636152083 0.0673638479172212 62 115.01 114.928159804336 0.0818401956643129 63 114.64 114.894216225947 -0.25421622594709 64 113.86 114.406059705166 -0.546059705165703 65 113.34 113.497862524992 -0.157862524991955 66 113.33 113.16004870166 0.169951298339782 67 113.32 113.252753317276 0.0672466827239475 68 113.26 113.146599246228 0.113400753772225 69 113.2 113.078967305102 0.121032694897508 70 112.61 112.921222240983 -0.311222240982588 71 112.28 112.227269514997 0.0527304850031243 72 112.16 112.136828914031 0.0231710859685421 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 112.018598854337 111.747497781139 112.289699927535 74 111.81636437534 111.414472132695 112.218256617985 75 111.632463229677 111.117318829575 112.147607629779 76 111.354395417347 110.732805575737 111.975985258958 77 110.999660938351 110.274521700729 111.724800175973 78 110.842009792688 110.014337329861 111.669682255514 79 110.771025313691 109.840795604924 111.701255022458 80 110.597540834695 109.564103495269 111.63097817412 81 110.405723022365 109.268029311126 111.543416733603 82 110.104738543368 108.861477085018 111.348000001718 83 109.729170731038 108.378853005934 111.079488456143 84 109.588186252042 108.129202804617 111.047169699466

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/30/t1275233741nfvx06s1fzdf6v3/1t2z61275233655.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/30/t1275233741nfvx06s1fzdf6v3/1t2z61275233655.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/30/t1275233741nfvx06s1fzdf6v3/2t2z61275233655.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/30/t1275233741nfvx06s1fzdf6v3/2t2z61275233655.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/30/t1275233741nfvx06s1fzdf6v3/34cg91275233655.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/30/t1275233741nfvx06s1fzdf6v3/34cg91275233655.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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