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: Sun, 06 Jun 2010 20:20:36 +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/Jun/06/t1275855682rt08dzo768rka1j.htm/, Retrieved Sun, 06 Jun 2010 22:21:22 +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/Jun/06/t1275855682rt08dzo768rka1j.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 «

0,9383 0,9217 0,9095 0,8920 0,8742 0,8607 0,8607 0,9005 0,9111 0,9059 0,8883 0,8924 0,8833 0,8700 0,8758 0,8858 0,9170 0,9554 0,9922 0,9778 0,9808 0,9811 1,0014 1,0183 1,0622 1,0773 1,0807 1,0848 1,1582 1,1663 1,1372 1,1139 1,1222 1,1692 1,1702 1,2286 1,2613 1,2646 1,2262 1,1985 1,2007 1,2138 1,2266 1,2176 1,2218 1,2490 1,2991 1,3408 1,3119 1,3014 1,3201 1,2938 1,2694 1,2165 1,2037 1,2292 1,2256 1,2015 1,1786 1,1856 1,2103 1,1938 1,2020 1,2271 1,2770 1,2650 1,2684 1,2811 1,2727 1,2611 1,2881 1,3213 1,2999 1,3074 1,3242 1,3516 1,3511 1,3419 1,3716 1,3622 1,3896 1,4227 1,4684 1,4570 1,4718 1,4748 1,5527 1,5751 1,5557 1,5553 1,5770 1,4975 1,4370 1,3322 1,2732 1,3449 1,3239 1,2785 1,3050 1,3190 1,3650 1,4016 1,4088 1,4268 1,4562 1,4816 1,4914 1,4614

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 2 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.9999383030001 beta FALSE gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 0.9217 0.9383 -0.0166000000000001 3 0.9095 0.921701024170198 -0.0122010241701983 4 0.892 0.909500752766587 -0.0175007527665869 5 0.8742 0.892001079743942 -0.0178010797439417 6 0.8607 0.874201098273215 -0.0135010982732151 7 0.8607 0.860700832977259 -8.32977258835577e-07 8 0.9005 0.860700000051392 0.0397999999486077 9 0.9111 0.900497544459407 0.0106024555405929 10 0.9059 0.911099345860302 -0.00519934586030157 11 0.8883 0.905900320784041 -0.0176003207840411 12 0.8924 0.88830108588699 0.00409891411301033 13 0.8833 0.892399747109296 -0.0090997471092964 14 0.87 0.883300561427096 -0.0133005614270965 15 0.8758 0.870000820604737 0.00579917939526298 16 0.8858 0.87579964220803 0.0100003577919706 17 0.917 0.885799383007926 0.0312006169920737 18 0.9554 0.916998075015537 0.0384019249844634 19 0.9922 0.955397630716438 0.0368023692835618 20 0.9778 0.992197729404226 -0.014397729404226 21 0.9808 0.97780088829671 0.00299911170329037 22 0.9811 0.980799814963806 0.000300185036194445 23 1.0014 0.981099981479484 0.0203000185205162 24 1.0183 1.00139874754976 0.0169012524502405 25 1.0622 1.01829895724343 0.0439010427565707 26 1.0773 1.06219729143737 0.0151027085626305 27 1.0807 1.07729906820819 0.00340093179180867 28 1.0848 1.08069979017271 0.00410020982728843 29 1.1582 1.08479974702935 0.0734002529706452 30 1.1663 1.1581954714246 0.00810452857540023 31 1.1372 1.16629949997490 -0.0290994999749012 32 1.1139 1.13720179535185 -0.0233017953518471 33 1.1222 1.11390143765087 0.00829856234913473 34 1.1692 1.1221994880036 0.0470005119964003 35 1.1702 1.16919710020942 0.00100289979058377 36 1.2286 1.17019993812409 0.0584000618759082 37 1.2613 1.22859639689139 0.0327036031086119 38 1.2646 1.26129798228580 0.00330201771419758 39 1.2262 1.26459979627541 -0.0383997962754135 40 1.1985 1.22620236915223 -0.0277023691522269 41 1.2007 1.19850170915307 0.00219829084693335 42 1.2138 1.20069986437205 0.0131001356279501 43 1.2266 1.21379919176093 0.0128008082390665 44 1.2176 1.22659921022854 -0.00899921022853523 45 1.2218 1.21760055522427 0.00419944477572742 46 1.249 1.22179974090686 0.0272002590931439 47 1.2991 1.24899832182562 0.0501016781743824 48 1.3408 1.29909690887677 0.0417030911232334 49 1.3119 1.34079742704439 -0.0288974270443911 50 1.3014 1.31190178288455 -0.0105017828845537 51 1.3201 1.30140064792850 0.0186993520715026 52 1.2938 1.32009884630608 -0.0262988463060772 53 1.2694 1.29380162255992 -0.0244016225599180 54 1.2165 1.26940150550690 -0.0529015055069049 55 1.2037 1.21650326386418 -0.0128032638641800 56 1.2292 1.20370078992297 0.0254992100770308 57 1.2256 1.22919842677524 -0.00359842677523847 58 1.2015 1.22560022201214 -0.0241002220121365 59 1.1786 1.20150148691140 -0.0229014869113950 60 1.1856 1.17860141295304 0.00699858704696421 61 1.2103 1.18559956820818 0.0247004317918242 62 1.1938 1.21029847605746 -0.0164984760574622 63 1.202 1.19380101790648 0.00819898209352443 64 1.2271 1.20199949414740 0.0251005058525975 65 1.277 1.22709845137409 0.0499015486259069 66 1.265 1.27699692122416 -0.0119969212241595 67 1.2684 1.26500074017405 0.00339925982595246 68 1.2811 1.26839979027587 0.0127002097241331 69 1.2727 1.28109921643516 -0.00839921643516184 70 1.2611 1.27270051820646 -0.0116005182064554 71 1.2881 1.26110071571717 0.0269992842828293 72 1.3213 1.28809833422516 0.0332016657748395 73 1.2999 1.32129795155683 -0.0213979515568299 74 1.3074 1.29990132018942 0.00749867981058472 75 1.3242 1.30739953735395 0.0168004626460476 76 1.3516 1.32419896346186 0.0274010365381421 77 1.3511 1.35159830943825 -0.000498309438251354 78 1.3419 1.35110003074420 -0.00920003074419729 79 1.3716 1.34190056761430 0.0296994323857038 80 1.3622 1.37159816763412 -0.00939816763412304 81 1.3896 1.36220057983875 0.0273994201612522 82 1.4227 1.38959830953798 0.0331016904620232 83 1.4684 1.42269795772501 0.045702042274993 84 1.457 1.46839718032110 -0.0113971803211022 85 1.4718 1.45700070317183 0.0147992968281667 86 1.4748 1.47179908692779 0.00300091307221506 87 1.5527 1.47479981485267 0.0779001851473333 88 1.5751 1.55269519379228 0.0224048062077151 89 1.5557 1.57509861769067 -0.0193986176906735 90 1.5553 1.55570119683651 -0.000401196836513851 91 1.577 1.55530002475264 0.0216999752473588 92 1.4975 1.57699866117663 -0.0794986611766293 93 1.437 1.49750490482889 -0.0605049048288906 94 1.3322 1.43700373297111 -0.104803732971107 95 1.2732 1.33220646607590 -0.0590064660759024 96 1.3449 1.27320364052193 0.0716963594780684 97 1.3239 1.34489557654972 -0.0209955765497163 98 1.2785 1.32390129536408 -0.0454012953640843 99 1.305 1.27850280112372 0.0264971988762845 100 1.319 1.30499836520232 0.0140016347976764 101 1.365 1.31899913614114 0.0460008638588607 102 1.4016 1.36499716188471 0.0366028381152927 103 1.4088 1.4015977417147 0.00720225828529952 104 1.4268 1.40879955564227 0.0180004443577286 105 1.4562 1.42679888942659 0.0294011105734135 106 1.4816 1.45619818603968 0.0254018139603163 107 1.4914 1.48159843278429 0.00980156721571346 108 1.4614 1.49139939527271 -0.0299993952727085 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 109 1.46140185087269 1.40219697261222 1.52060672913316 110 1.46140185087269 1.37767609193199 1.54512760981338 111 1.46140185087269 1.35886021147408 1.56394349027129 112 1.46140185087269 1.34299757345455 1.57980612829083 113 1.46140185087269 1.32902225270412 1.59378144904125 114 1.46140185087269 1.31638756498461 1.60641613676077 115 1.46140185087269 1.30476875024582 1.61803495149956 116 1.46140185087269 1.29395420737674 1.62884949436864 117 1.46140185087269 1.28379695676021 1.63900674498517 118 1.46140185087269 1.27418998289135 1.64861371885403 119 1.46140185087269 1.26505249738910 1.65775120435627 120 1.46140185087269 1.25632173551827 1.66648196622710

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/06/t1275855682rt08dzo768rka1j/1yxt01275855632.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275855682rt08dzo768rka1j/1yxt01275855632.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275855682rt08dzo768rka1j/296al1275855632.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275855682rt08dzo768rka1j/296al1275855632.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275855682rt08dzo768rka1j/396al1275855632.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275855682rt08dzo768rka1j/396al1275855632.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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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