Opgave 10 Eigen reeks

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 19 May 2011 14:47:31 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/19/t1305816251pwmovhiymncxehy.htm/, Retrieved Thu, 19 May 2011 16:44:13 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

0,8833 0,87 0,8758 0,8858 0,917 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 1,249 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 1,202 1,2271 1,277 1,265 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 1,457 1,4718 1,4748 1,5527 1,575 1,5557 1,5553 1,577 1,4975 1,4369 1,3322 1,2732 1,3449 1,3239 1,2785 1,305 1,319 1,365 1,4016 1,4088 1,4268 1,4562 1,4816 1,4914 1,4614 1,4272

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 'Gwilym Jenkins' @ www.wessa.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.026516277171168 gamma 0.0783163830565602 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1.0622 0.95641920405983 0.10578079594017 14 1.0773 1.08369586570174 -0.00639586570173889 15 1.0807 1.08707627115404 -0.00637627115404249 16 1.0848 1.08884052951414 -0.00404052951413636 17 1.1582 1.16099172304695 -0.00279172304695452 18 1.1663 1.16809269694486 -0.00179269694485651 19 1.1372 1.17951599462912 -0.0423159946291161 20 1.1139 1.12312726532009 -0.00922726532009022 21 1.1222 1.115899259262 0.0063007407380029 22 1.1692 1.12201216478312 0.0471878352168769 23 1.1702 1.18875091050084 -0.0185509105008419 24 1.2286 1.18536317608289 0.0432368239171099 25 1.2613 1.27591798902321 -0.0146179890232103 26 1.2646 1.28254704104125 -0.0179470410412526 27 1.2262 1.2738211523266 -0.0476211523266008 28 1.1985 1.23269174998563 -0.0341917499856312 29 1.2007 1.27224344539938 -0.071543445399378 30 1.2138 1.20632137957139 0.0074786204286117 31 1.2266 1.22299051807686 0.00360948192313537 32 1.2176 1.20971956143332 0.00788043856668397 33 1.2218 1.21724518799325 0.0045548120067529 34 1.249 1.21921179798421 0.0297882020157862 35 1.2991 1.2656891702053 0.033410829794704 36 1.3408 1.31277926769532 0.028020732304683 37 1.3119 1.38623060653298 -0.0743306065329805 38 1.3014 1.32967630223452 -0.0282763022345176 39 1.3201 1.30687651996709 0.0132234800329083 40 1.2938 1.32446049076214 -0.0306604907621448 41 1.2694 1.36550582202423 -0.096105822024225 42 1.2165 1.27233245340967 -0.0558324534096681 43 1.2037 1.22132281793324 -0.0176228179332441 44 1.2292 1.18188885974172 0.0473111402582775 45 1.2256 1.22496004171676 0.000639958283238373 46 1.2015 1.21902284436131 -0.0175228443613111 47 1.1786 1.2129457037634 -0.0343457037633998 48 1.1856 1.18523915022944 0.000360849770562943 49 1.2103 1.2232570519553 -0.0129570519553039 50 1.1938 1.221930145841 -0.0281301458410022 51 1.202 1.19313423909702 0.00886576090298252 52 1.2271 1.20010265940379 0.0269973405962129 53 1.277 1.29407686170325 -0.0170768617032542 54 1.265 1.27729904690512 -0.012299046905117 55 1.2684 1.26834375530177 5.62446982270703e-05 56 1.2811 1.24557858003511 0.0355214199648859 57 1.2727 1.27553714251908 -0.00283714251908296 58 1.2611 1.26470774539501 -0.00360774539500586 59 1.2881 1.27149958141815 0.0166004185818502 60 1.3213 1.29504392938509 0.0262560706149104 61 1.2999 1.35994847596427 -0.0600484759642737 62 1.3074 1.31127288059857 -0.00387288059856528 63 1.3242 1.30712018622316 0.0170798137768366 64 1.3516 1.32290641263263 0.028693587367365 65 1.3511 1.41922559308164 -0.0681255930816362 66 1.3419 1.35069415597303 -0.00879415597303357 67 1.3716 1.3446318010291 0.0269681989709003 68 1.3622 1.34888023060115 0.0133197693988476 69 1.3896 1.35615008796505 0.033449912034945 70 1.4227 1.38208288843726 0.0406171115627423 71 1.4684 1.43474740302535 0.0336525969746515 72 1.457 1.47744391128092 -0.0204439112809238 73 1.4718 1.49651014819627 -0.0247101481962699 74 1.4748 1.48497159372442 -0.0101715937244231 75 1.5527 1.47615188092595 0.0765481190740454 76 1.575 1.55461498540159 0.0203850145984137 77 1.5557 1.64561385343215 -0.0899138534321493 78 1.5553 1.55770467277302 -0.00240467277301515 79 1.577 1.56061174313659 0.0163882568634068 80 1.4975 1.55657963203127 -0.0590796320312688 81 1.4369 1.49182972679982 -0.0549297267998237 82 1.3322 1.4274190282724 -0.0952190282723961 83 1.2732 1.33868167412676 -0.0654816741267565 84 1.3449 1.27404951057265 0.0708504894273543 85 1.3239 1.37863653512135 -0.0547365351213476 86 1.2785 1.33050179265135 -0.0520017926513472 87 1.305 1.27217289870401 0.0328271012959929 88 1.319 1.29807668455403 0.0209233154459696 89 1.365 1.38078982631907 -0.0157898263190688 90 1.4016 1.36014613890791 0.041453861092092 91 1.4088 1.40121617431177 0.00758382568822569 92 1.4268 1.38245060246907 0.0443493975309255 93 1.4562 1.41794325005305 0.0382567499469544 94 1.4816 1.44600350997164 0.0355964900283601 95 1.4914 1.49083489636755 0.000565103632446551 96 1.4614 1.49675404747877 -0.0353540474787679 97 1.4272 1.49682492309003 -0.0696249230900319 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 98 1.43509539599802 1.35770461579907 1.51248617619698 99 1.43144079199604 1.32053314339824 1.54234844059385 100 1.4263195213274 1.28868978860906 1.56394925404574 101 1.48935658399209 1.32835327456417 1.65035989342 102 1.48616864665678 1.30382475224733 1.66851254106622 103 1.4863515426548 1.28403482009298 1.68866826521662 104 1.46036777198615 1.23905629645663 1.68167924751567 105 1.45070066798417 1.21112216915311 1.69027916681524 106 1.43867939731553 1.18139017817395 1.69596861645711 107 1.44514562664689 1.17057897333822 1.71971227995555 108 1.44771602264491 1.15621371746516 1.73921832782465 109 1.48129475197626 1.17312855478797 1.78946094916455

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t1305816251pwmovhiymncxehy/1oc4t1305816448.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305816251pwmovhiymncxehy/1oc4t1305816448.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305816251pwmovhiymncxehy/2liik1305816448.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305816251pwmovhiymncxehy/2liik1305816448.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305816251pwmovhiymncxehy/3x9t41305816448.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305816251pwmovhiymncxehy/3x9t41305816448.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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