Thomas Van den Bosch opgave 10 oef 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 13:33:43 -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/t1244403265xhk1l9ag8xtuxuu.htm/, Retrieved Sun, 07 Jun 2009 21:34:29 +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/t1244403265xhk1l9ag8xtuxuu.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

36.80 35.40 33.00 28.73 26.70 26.46 24.60 28.00 31.60 33.50 34.50 35.00 34.76 33.50 32.74 34.40 31.93 29.24 25.75 26.03 26.08 23.80 20.61 19.70 18.18 19.60 20.60 20.03 23.00 23.60 22.56 22.55 23.75 24.92 24.50 30.58 28.07 27.70 27.00 25.23 26.86 25.60 24.55 23.96 23.50 23.64 21.55 21.05 21.89 21.98 21.45 22.15 22.58 23.80 23.30 22.38 23.00 21.96 22.40 20.80 20.40 16.00 12.78 9.75 7.50 11.24 12.24 12.75 12.52 14.49 14.21 14.32 22.15 22.58 23.80 23.30 22.38 23.00 21.96 22.40 20.80 20.40 16.00 12.78 9.75 7.50 11.24 12.24 12.75 12.52 14.49 14.21 14.32

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 0.777924358723283 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 34.76 33.438421474359 1.32157852564102 14 33.5 33.1471375151736 0.352862484826353 15 32.74 32.8801824178193 -0.140182417819275 16 34.4 34.9717590140859 -0.571759014085856 17 31.93 32.9463516634618 -1.01635166346177 18 29.24 30.5884181945122 -1.34841819451218 19 25.75 22.5492454156751 3.20075458432493 20 26.03 28.5098182868696 -2.47981828686955 21 26.08 30.1771684833925 -4.09716848339253 22 23.8 28.5709258987877 -4.77092589878773 23 20.61 25.3118010088766 -4.70180100887656 24 19.7 21.7268667212880 -2.02686672128803 25 18.18 19.946319372578 -1.76631937257799 26 19.6 17.0377561851387 2.56224381486130 27 20.6 18.3800393791937 2.21996062080629 28 20.03 22.2117860859024 -2.18178608590237 29 23 18.8351662601912 4.16483373980877 30 23.6 20.4340592356778 3.16594076432225 31 22.56 16.9169767170775 5.64302328292253 32 22.55 23.5159330362688 -0.96593303626879 33 23.75 26.0017973634841 -2.25179736348414 34 24.92 25.6814888138517 -0.761488813851706 35 24.5 25.5567536513359 -1.05675365133595 36 30.58 25.4014282391675 5.1785717608325 37 28.07 29.2840282205289 -1.21402822052886 38 27.7 27.7663742190333 -0.0663742190332997 39 27 26.9877786549244 0.0122213450756092 40 25.23 28.1245504787021 -2.89455047870205 41 26.86 25.6028835375358 1.25711646246424 42 25.6 24.7179626165974 0.882037383402555 43 24.55 19.9742757138228 4.57572428617723 44 23.96 24.2752659326508 -0.315265932650782 45 23.5 26.9817409041293 -3.4817409041293 46 23.64 26.0355905412344 -2.39559054123443 47 21.55 24.5740767122251 -3.02407671222508 48 21.05 24.2730366589892 -3.22303665898924 49 21.89 20.2001800578303 1.68981994216971 50 21.98 21.1963662744777 0.78363372552229 51 21.45 21.0964667558479 0.353533244152104 52 22.15 21.8532302030287 0.296769796971251 53 22.58 22.7361531391231 -0.15615313912307 54 23.8 20.6685194426547 3.13148055734527 55 23.3 18.495007066063 4.80499293393699 56 22.38 21.8881811613505 0.491818838649493 57 23 24.5193100761003 -1.51931007610035 58 21.96 25.3409899950015 -3.38098999500152 59 22.4 22.9733384583778 -0.57333845837784 60 20.8 24.5346032318987 -3.7346032318987 61 20.4 21.1548123127678 -0.754812312767822 62 16 20.0480176650006 -4.04801766500061 63 12.78 16.0939439966101 -3.3139439966101 64 9.75 13.9850817842050 -4.23508178420502 65 7.5 11.2419838337016 -3.74198383370162 66 11.24 7.11494845508915 4.12505154491085 67 12.24 6.08600548606157 6.15399451393843 68 12.75 9.57074986723929 3.17925013276071 69 12.52 13.8458743046403 -1.32587430464027 70 14.49 14.4045988601667 0.0854011398333014 71 14.21 15.3570484396707 -1.14704843967073 72 14.32 15.7699703420760 -1.44997034207604 73 22.15 14.8291899779151 7.3208100220849 74 22.58 19.2732779658266 3.3067220341734 75 23.8 21.2036553421449 2.59634465785512 76 23.3 23.4879883762498 -0.187988376249788 77 22.38 24.0027280133935 -1.62272801339346 78 23 23.2713902864168 -0.271390286416789 79 21.96 19.2729269360501 2.68707306394987 80 22.4 19.4000504054171 2.99994959458285 81 20.8 22.5352141881701 -1.73521418817014 82 20.4 23.0889131766513 -2.68891317665128 83 16 21.6094590398976 -5.60945903989764 84 12.78 18.4836914620280 -5.70369146202803 85 9.75 16.1816144973090 -6.43161449730903 86 7.5 9.03592529602405 -1.53592529602405 87 11.24 7.0413318420811 4.1986681579189 88 12.24 9.95381881336358 2.28618118663642 89 12.75 12.0746544961044 0.675345503895638 90 12.52 13.4311433286635 -0.911143328663542 91 14.49 9.59200314889215 4.89799685110785 92 14.21 11.5085403437508 2.70145965624916 93 14.32 13.3599369990351 0.960063000964904 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 94 15.7985644520037 9.8798777311776 21.7172511728298 95 15.7622992784006 8.2636097816492 23.260988775152 96 16.9793398013542 8.17991732950435 25.7787622732041 97 18.9526493847287 9.02141947562364 28.8838792938338 98 17.8974830856851 6.950848023854 28.8441181475162 99 18.3712368514442 6.495702722559 30.2467709803293 100 17.5927608179048 4.85589297232663 30.3296286634830 101 17.5773930998701 4.03385980219888 31.1209263975414 102 18.0561936895257 3.75141176687703 32.3609756121744 103 16.2159226300990 1.18840528610821 31.2434399740897 104 13.8343913593945 -1.88266209197955 29.5514448107686 105 13.1975349650350 -3.18004913222299 29.5751190622929

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244403265xhk1l9ag8xtuxuu/1gume1244403221.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244403265xhk1l9ag8xtuxuu/1gume1244403221.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244403265xhk1l9ag8xtuxuu/2pkzt1244403221.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244403265xhk1l9ag8xtuxuu/2pkzt1244403221.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244403265xhk1l9ag8xtuxuu/3z8pt1244403221.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244403265xhk1l9ag8xtuxuu/3z8pt1244403221.ps (open in new window)

Parameters (Session):

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')

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Software written by Ed van Stee & Patrick Wessa

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