Opgave 10-prijzen dieselbrandstof-Messelis Peter

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 01 Jun 2008 08:10:44 -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/Jun/01/t1212329504ivvqggarusmuyjh.htm/, Retrieved Sun, 01 Jun 2008 14:11:48 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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0,76 0,77 0,76 0,77 0,78 0,79 0,78 0,76 0,78 0,76 0,74 0,73 0,72 0,71 0,73 0,75 0,75 0,72 0,72 0,72 0,74 0,78 0,74 0,74 0,75 0,78 0,81 0,75 0,7 0,71 0,71 0,73 0,74 0,74 0,75 0,74 0,74 0,73 0,76 0,8 0,83 0,81 0,83 0,88 0,89 0,93 0,91 0,9 0,86 0,88 0,93 0,98 0,97 1,03 1,06 1,06 1,08 1,09 1,04 1

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 5 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.0157312826556434 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 0.76 0.78 -0.02 4 0.77 0.769685374346887 0.00031462565311291 5 0.78 0.779690323811967 0.000309676188033015 6 0.79 0.789695195415613 0.000304804584387419 7 0.78 0.799699990382684 -0.0196999903826844 8 0.76 0.789390084265661 -0.0293900842656609 9 0.78 0.768927740542805 0.0110722594571954 10 0.76 0.789101921385962 -0.0291019213859625 11 0.74 0.768644110834818 -0.0286441108348175 12 0.73 0.748193502230855 -0.0181935022308554 13 0.72 0.737907295104766 -0.0179072951047657 14 0.71 0.727625590383875 -0.0176255903838747 15 0.73 0.717348317239573 0.0126516827604267 16 0.75 0.737547344437147 0.0124526555628529 17 0.75 0.75774324068162 -0.00774324068161969 18 0.72 0.757621429573787 -0.0376214295737866 19 0.72 0.727029596231252 -0.00702959623125188 20 0.72 0.726919011665983 -0.00691901166598297 21 0.74 0.726810166737768 0.0131898332622322 22 0.78 0.747017659732997 0.0329823402670033 23 0.74 0.787536514250382 -0.0475365142503816 24 0.74 0.746788703908245 -0.00678870390824482 25 0.75 0.746681908888199 0.00331809111180126 26 0.78 0.756734106717356 0.0232658932826444 27 0.81 0.787100109060821 0.0228998909391791 28 0.75 0.817460353717969 -0.0674603537179687 29 0.7 0.756399115825582 -0.0563991158255815 30 0.71 0.705511885393001 0.00448811460699905 31 0.71 0.715582489192475 -0.00558248919247462 32 0.73 0.715494669477066 0.0145053305229343 33 0.74 0.735722856931535 0.00427714306846450 34 0.74 0.745790141878104 -0.00579014187810412 35 0.75 0.745699055519603 0.00430094448039664 36 0.74 0.755766714892911 -0.0157667148929108 37 0.74 0.74551868424438 -0.0055186842443794 38 0.73 0.745431868262644 -0.0154318682626439 39 0.76 0.735189105181099 0.0248108948189005 40 0.8 0.765579412380435 0.0344205876195649 41 0.83 0.806120892373452 0.0238791076265481 42 0.81 0.83649654136509 -0.0264965413650895 43 0.83 0.816079716783478 0.0139202832165215 44 0.88 0.836298700693404 0.0437012993065959 45 0.89 0.886986178185215 0.00301382181478493 46 0.93 0.897033589468057 0.0329664105319428 47 0.91 0.937552193390277 -0.0275521933902771 48 0.9 0.917118762048272 -0.0171187620482718 49 0.86 0.906849461963776 -0.0468494619637757 50 0.88 0.866112459835359 0.0138875401646413 51 0.93 0.88633092865508 0.0436690713449197 52 0.98 0.937017899159717 0.0429821008402832 53 0.97 0.987694062737169 -0.0176940627371686 54 1.03 0.977415712434923 0.0525842875650766 55 1.06 1.03824293072586 0.0217570692741447 56 1.06 1.06858519733237 -0.0085851973323654 57 1.08 1.06845014116648 0.0115498588335246 58 1.09 1.08863183526042 0.00136816473958157 59 1.04 1.09865335824666 -0.0586533582466562 60 1 1.04773066568938 -0.0477306656893755 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 1.00697980109607 0.953886294755929 1.06007330743622 62 1.01395960219215 0.938281144847473 1.08963805953682 63 1.02093940328822 0.927524625621345 1.11435418095510 64 1.02791920438429 0.919210460615664 1.13662794815293 65 1.03489900548037 0.912414577994704 1.15738343296603 66 1.04187880657644 0.906666943503783 1.17709066964910 67 1.04885860767252 0.901690591433132 1.1960266239119 68 1.05583840876859 0.897306514639759 1.21437030289742 69 1.06281820986466 0.893391374661048 1.23224504506828 70 1.06979801096074 0.88985609446609 1.24973992745539 71 1.07677781205681 0.886633974016102 1.26692165009752 72 1.08375761315288 0.883673617787981 1.28384160851779

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212329504ivvqggarusmuyjh/14eax1212329438.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212329504ivvqggarusmuyjh/14eax1212329438.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212329504ivvqggarusmuyjh/20kyp1212329438.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212329504ivvqggarusmuyjh/20kyp1212329438.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212329504ivvqggarusmuyjh/3k6p41212329438.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212329504ivvqggarusmuyjh/3k6p41212329438.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=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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