Opgave 10 - Superbenzine Loodvrij 98 - Stijn Cappaert

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 15 Aug 2008 07:13:44 -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/Aug/15/t1218806078zc6z1a47mj0sf2v.htm/, Retrieved Fri, 15 Aug 2008 13:14:42 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

0.91 0.9 0.89 0.89 0.89 0.89 0.89 0.89 0.88 0.88 0.88 0.86 0.85 0.85 0.86 0.9 0.92 0.91 0.93 0.96 0.96 0.97 0.98 1.01 0.99 1.03 1.08 1.06 1.1 1.17 1.16 1.12 1.17 1.13 1.12 1.07 1.04 1.08 1.06 1.12 1.18 1.13 1.08 1.06 1.09 1.02 1.01 1.01 1 1.01 1.03 1.09 1.07 1.05 1.06 1.06 1.08 1.07 1.04 1.04 1.06 1.09 1.09 1.05 1.01 1.02 1.03 1.06 1.08 1.05 1.05 1.05 1.04 1.05 1.07 1.1 1.16 1.16 1.17 1.17 1.18 1.21 1.18 1.13 1.12 1.17 1.19 1.26 1.25 1.28 1.35 1.39 1.45 1.41 1.32 1.31

Text written by user:

Triple multiplicative

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' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.799338468046928 beta 0.0091143646723173 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 0.85 0.810376237496724 0.0396237625032760 14 0.85 0.848082474508208 0.00191752549179225 15 0.86 0.864043420959625 -0.0040434209596254 16 0.9 0.904578457094851 -0.00457845709485105 17 0.92 0.92383889187728 -0.00383889187728059 18 0.91 0.9110934864036 -0.00109348640359919 19 0.93 0.928891265433826 0.00110873456617377 20 0.96 0.957157261173913 0.0028427388260871 21 0.96 0.953558433521962 0.00644156647803829 22 0.97 0.963743469551814 0.0062565304481863 23 0.98 0.975492482157564 0.00450751784243641 24 1.01 1.00165189145377 0.00834810854622758 25 0.99 0.990215789475333 -0.000215789475333295 26 1.03 0.986668888745007 0.043331111254993 27 1.08 1.03552324162965 0.0444767583703489 28 1.06 1.12360370959481 -0.0636037095948134 29 1.1 1.09854563340606 0.00145436659393994 30 1.17 1.08713222596386 0.0828677740361419 31 1.16 1.17575854419085 -0.0157585441908548 32 1.12 1.19602409819807 -0.0760240981980698 33 1.17 1.12753730987977 0.0424626901202250 34 1.13 1.16586684933194 -0.0358668493319356 35 1.12 1.14313613719794 -0.0231361371979428 36 1.07 1.14988461978709 -0.0798846197870884 37 1.04 1.06337914250779 -0.0233791425077887 38 1.08 1.04876179235534 0.0312382076446582 39 1.06 1.08723326930132 -0.0272332693013189 40 1.12 1.09411432945624 0.0258856705437613 41 1.18 1.15436112828891 0.0256388717110918 42 1.13 1.17656263174621 -0.0465626317462124 43 1.08 1.14068107677332 -0.0606810767733239 44 1.06 1.10984176849747 -0.0498417684974661 45 1.09 1.08397643545216 0.00602356454783615 46 1.02 1.07700358520965 -0.0570035852096511 47 1.01 1.03807194043097 -0.0280719404309666 48 1.01 1.02630400488978 -0.016304004889782 49 1 1.00145034562005 -0.00145034562005142 50 1.01 1.01357567832863 -0.00357567832863293 51 1.03 1.01126326455766 0.0187367354423402 52 1.09 1.06317204620579 0.0268279537942113 53 1.07 1.12173910695277 -0.0517391069527693 54 1.05 1.06738693496684 -0.0173869349668403 55 1.06 1.05059718530651 0.00940281469348547 56 1.06 1.07619885060324 -0.0161988506032447 57 1.08 1.08751901052413 -0.00751901052413051 58 1.07 1.05581116613567 0.014188833864335 59 1.04 1.07911047634731 -0.0391104763473056 60 1.04 1.06039957127836 -0.020399571278358 61 1.06 1.03405067747473 0.0259493225252680 62 1.09 1.06746737196142 0.0225326280385840 63 1.09 1.08995651674227 4.34832577309585e-05 64 1.05 1.12978866779252 -0.0797886677925153 65 1.01 1.08554664847600 -0.0755466484760015 66 1.02 1.01831003372372 0.00168996627628260 67 1.03 1.02112851919973 0.008871480800267 68 1.06 1.03981359483301 0.0201864051669896 69 1.08 1.08094844970193 -0.00094844970193364 70 1.05 1.05794900976268 -0.0079490097626811 71 1.05 1.05173126496785 -0.00173126496785181 72 1.05 1.06591575877450 -0.0159157587745022 73 1.04 1.05152139264002 -0.0115213926400182 74 1.05 1.05316961574409 -0.00316961574409125 75 1.07 1.04972859585630 0.0202714041437018 76 1.1 1.08739497682481 0.0126050231751886 77 1.16 1.11711128676712 0.0428887132328801 78 1.16 1.16070035651934 -0.000700356519342638 79 1.17 1.16288433106370 0.00711566893629678 80 1.17 1.18367679210897 -0.0136767921089738 81 1.18 1.19509502285563 -0.0150950228556337 82 1.21 1.15650151010083 0.0534984898991733 83 1.18 1.20033971905677 -0.0203397190567707 84 1.13 1.19784906074891 -0.0678490607489077 85 1.12 1.14211693226228 -0.0221169322622847 86 1.17 1.13735668552374 0.0326433144762635 87 1.19 1.16702953169489 0.0229704683051053 88 1.26 1.20687790410827 0.0531220958917287 89 1.25 1.27776750084836 -0.0277675008483582 90 1.28 1.25555176437635 0.0244482356236533 91 1.35 1.27925421769210 0.0707457823078963 92 1.39 1.34780750300696 0.0421924969930394 93 1.45 1.40721656199859 0.0427834380014096 94 1.41 1.42514909362493 -0.0151490936249323 95 1.32 1.39656620503061 -0.0765662050306122 96 1.31 1.33895995103608 -0.0289599510360776 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 1.32431164206200 1.25589880119140 1.39272448293260 98 1.35210173813037 1.26369089605749 1.44051258020325 99 1.35352607068900 1.24932927350651 1.4577228678715 100 1.38398429483692 1.26430761607940 1.50366097359445 101 1.39668848921256 1.26393507286084 1.52944190556429 102 1.40777708666746 1.26298319081396 1.55257098252096 103 1.42133615881860 1.26498163917051 1.57769067846668 104 1.42698430809734 1.26038363625372 1.59358497994095 105 1.45242166478541 1.27396941231930 1.63087391725152 106 1.42355104286842 1.23964489742996 1.60745718830689 107 1.39292104077567 1.20416938956715 1.5816726919842 108 1.40602462566043 -6.65804712080839 9.47009637212924

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/15/t1218806078zc6z1a47mj0sf2v/12cmt1218806022.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/15/t1218806078zc6z1a47mj0sf2v/12cmt1218806022.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/15/t1218806078zc6z1a47mj0sf2v/2jxux1218806022.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/15/t1218806078zc6z1a47mj0sf2v/2jxux1218806022.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/15/t1218806078zc6z1a47mj0sf2v/3a3uu1218806022.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/15/t1218806078zc6z1a47mj0sf2v/3a3uu1218806022.ps (open in new window)

Parameters (Session):

par2 = grey ; par3 = FALSE ; par4 = Unknown ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = Unknown ;

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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