Opdracht 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, 07 Jun 2009 10:45:35 -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/07/t1244393185g0uq1v1qn2kr4ig.htm/, Retrieved Sun, 07 Jun 2009 18:46:29 +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/07/t1244393185g0uq1v1qn2kr4ig.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:

Thomas Cammaert

Dataseries X:

» Textbox « » Textfile « » CSV «

8.9722 8.8284 8.7446 8.7519 8.6337 8.7272 8.6330 8.5865 8.5968 8.5114 8.3884 8.2671 8.2410 8.3177 8.4070 8.3917 8.4145 8.5245 8.6289 8.6622 8.9055 8.9770 9.1264 9.1120 9.0576 9.2106 9.2637 9.3107 9.6744 9.5780 9.4166 9.4359 9.2275 9.1828 9.0594 9.1358 9.2208 9.1137 9.2689 9.2489 9.1679 9.1051 9.0818 9.0961 9.1733 9.1455 9.2265 9.1541 9.1559 9.1182 9.1856 9.2378 9.0682 9.0105 8.9939 9.0228 9.1368 9.1763 9.2346 9.1653 9.1277 9.1430 9.1962 9.1861 9.0920 9.0620 8.9981 8.9819 9.0476 9.0852 9.0884 9.1670 9.1931 9.2628 9.4276 9.3398 9.3342 9.4223 9.5614 9.4316 9.3111 9.3414 9.4017 9.3346 9.3310 9.2349 9.2170 9.2098 9.2665 9.2533 9.1008 9.0377 9.0795 9.1896 9.2992 9.2372 9.2061 9.3290 9.1842 9.3231 9.2835 9.1735 9.2889 9.4319 9.4314 9.3642 9.4020 9.3699 9.3106 9.3739 9.4566 9.3984 9.5637 9.8506

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.00424858042342793 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 8.241 8.38257243589744 -0.141572435897436 14 8.3177 8.31221792371475 0.00548207628524544 15 8.407 8.3885078814234 0.0184921185765941 16 8.3917 8.35704061334305 0.0346593866569531 17 8.4145 8.36210036653468 0.0523996334653187 18 8.5245 8.45651882392495 0.0679811760750475 19 8.6289 8.63212431408545 -0.00322431408545398 20 8.6622 8.63239394866108 0.029806051338916 21 8.9055 8.7062205820673 0.199279417932695 22 8.977 8.84839640336779 0.128603596632209 23 9.1264 8.8779094527575 0.248490547242508 24 9.112 9.02350268483191 0.0884973151680892 25 9.0576 9.09571617279266 -0.0381161727926607 26 9.2106 9.13235423316712 0.0782457668328789 27 9.2637 9.28525333326697 -0.0215533332669668 28 9.3107 9.21741592886386 0.0932840711361411 29 9.6744 9.2850247537423 0.389375246257698 30 9.578 9.72177487912425 -0.143774879124253 31 9.4166 9.6900807066541 -0.273480706654091 32 9.4359 9.42340213521095 0.0124978647890490 33 9.2275 9.48315523339463 -0.255655233394631 34 9.1828 9.17169822824155 0.0111017717584527 35 9.0594 9.08451206167837 -0.0251120616783744 36 9.1358 8.95614287106473 0.179657128935268 37 9.2208 9.11954365882566 0.101256341174343 38 9.1137 9.29617385453452 -0.182473854534521 39 9.2689 9.18786526635502 0.0810347336449784 40 9.2489 9.22256371560467 0.0263362843953274 41 9.1679 9.22288810742698 -0.0549881074269774 42 9.1051 9.21305031936357 -0.107950319363574 43 9.0818 9.21510835041669 -0.133308350416693 44 9.0961 9.08712531250216 0.00897468749783492 45 9.1733 9.14186344218378 0.0314365578162228 46 9.1455 9.11722616959456 0.0282738304054408 47 9.2265 9.04701295990358 0.179487040096417 48 9.1541 9.1239130250284 0.0301869749716062 49 9.1559 9.1378787768193 0.018021223180698 50 9.1182 9.23095534143532 -0.112755341435316 51 9.1856 9.19234295796572 -0.00674295796572011 52 9.2378 9.13886847663318 0.0989315233668187 53 9.0682 9.21170129516661 -0.143501295166613 54 9.0105 9.11288745170656 -0.102387451706564 55 8.9939 9.12006911705031 -0.126169117050308 56 9.0228 8.9988164107429 0.0239835892570994 57 9.1368 9.0682183069507 0.0685816930492944 58 9.1763 9.08053884845586 0.0957611515441368 59 9.2346 9.0779123640763 0.156687635923694 60 9.1653 9.13201556409888 0.033284435901118 61 9.1277 9.14909447570166 -0.0213944757016584 62 9.143 9.20260357955103 -0.059603579551025 63 9.1962 9.21721701561644 -0.0210170156164438 64 9.1861 9.149481889802 0.0366181101979954 65 9.092 9.15974996478813 -0.0677499647881294 66 9.062 9.13675795694738 -0.0747579569473782 67 8.9981 9.17175700842166 -0.173657008421662 68 8.9819 9.00300254598863 -0.0211025459886276 69 9.0476 9.02711289012486 0.0204871098751429 70 9.0852 8.99092909792547 0.0942709020745323 71 9.0884 8.98639628210119 0.102003717898810 72 9.167 8.98516715310017 0.181832846899832 73 9.1931 9.15077718457385 0.0423228154261537 74 9.2628 9.26825699645893 -0.00545699645892839 75 9.4276 9.33750047863727 0.0900995213627311 76 9.3398 9.38183744036656 -0.0420374403665598 77 9.3342 9.31407134092036 0.020128659079635 78 9.4223 9.37995269248061 0.0423473075193872 79 9.5614 9.533549275089 0.0278507249110085 80 9.4316 9.56865093446696 -0.137050934466963 81 9.3111 9.47866866254977 -0.167568662549774 82 9.3414 9.25548590027715 0.0859140997228494 83 9.4017 9.243617579906 0.158082420094003 84 9.3346 9.2997267057813 0.0348732942187073 85 9.331 9.31901236777641 0.011987632223585 86 9.2349 9.406663298196 -0.171763298196003 87 9.217 9.30940021467649 -0.0924002146764877 88 9.2098 9.17026181159996 0.0395381884000354 89 9.2665 9.18344229277317 0.0830577072268284 90 9.2533 9.31189100345545 -0.0585910034554473 91 9.1008 9.36375874153184 -0.262958741531843 92 9.0377 9.10602487350374 -0.0683248735037374 93 9.0795 9.08303458978374 -0.00353458978373666 94 9.1896 9.02284873946144 0.166751260538559 95 9.2992 9.09112386226922 0.208076137730785 96 9.2372 9.19674539047456 0.0404546095254421 97 9.2061 9.22115476513663 -0.0150547651366271 98 9.329 9.28119080375619 0.0478091962438114 99 9.1842 9.40386059163808 -0.219660591638075 100 9.3231 9.13728151261531 0.185818487384687 101 9.2835 9.29718347740312 -0.0136834774031218 102 9.1735 9.32892117538224 -0.155421175382235 103 9.2889 9.28357752268579 0.00532247731420910 104 9.4319 9.29488346899204 0.137016531007957 105 9.4314 9.47886559474337 -0.0474655947433735 106 9.3642 9.37619310001343 -0.0119931000134255 107 9.402 9.26640881303016 0.135591186969840 108 9.3699 9.2999223830927 0.0699776169072948 109 9.3106 9.35435718862598 -0.0437571886259764 110 9.3739 9.386071282691 -0.0121712826909981 111 9.4566 9.4488862386843 0.00771376131570456 112 9.3984 9.41077317788628 -0.0123731778862801 113 9.5637 9.37273310944493 0.190966890555067 114 9.8506 9.610240280971 0.240359719028998 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 115 9.96347813523452 9.73503014254196 10.1919261279271 116 9.97223960380237 9.64847832336582 10.2960008842389 117 10.0214010723702 9.62403407816492 10.4187680665755 118 9.96859170760474 9.50877886139819 10.4284045538113 119 9.87324900950592 9.35807406143667 10.3884239575752 120 9.7730438114071 9.20750465902391 10.3385829637903 121 9.7590761133083 9.14693425485816 10.3712179717584 122 9.83630841520948 9.18052150078269 10.4920953296363 123 9.91310738377733 9.21607590405209 10.6101388635026 124 9.86906051901185 9.13278016568152 10.6053408723422 125 9.84522615424636 9.07138767878782 10.6190646297049 126 9.89278762281421 9.08284537180056 10.7027298738279

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244393185g0uq1v1qn2kr4ig/1v1eg1244393132.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244393185g0uq1v1qn2kr4ig/1v1eg1244393132.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244393185g0uq1v1qn2kr4ig/2hpwj1244393132.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244393185g0uq1v1qn2kr4ig/2hpwj1244393132.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244393185g0uq1v1qn2kr4ig/3xm6y1244393132.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244393185g0uq1v1qn2kr4ig/3xm6y1244393132.ps (open in new window)

Parameters (Session):

par1 = additive ; par2 = 12 ;

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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