Opgave 10-oefening2-exponential-veerle van rompay

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 16 Jan 2009 06:48:19 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jan/16/t1232113770orf27siotmr02kt.htm/, Retrieved Fri, 16 Jan 2009 14:49:34 +0100

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/Jan/16/t1232113770orf27siotmr02kt.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 «

113,9000 112,0000 113,8500 113,0800 111,7200 110,6900 113,5300 113,9900 112,7400 112,1500 115,8200 118,3800 118,8100 123,8500 117,9600 120,1600 118,7400 119,8400 124,8100 121,3300 120,2000 118,3200 129,5800 130,2000 127,1900 133,1000 129,1200 123,2800 123,3600 124,1300 126,9700 127,1400 123,7000 123,6700 130,1900 134,0100 124,9600 129,9600 128,3200 132,3800 126,2500 128,9100 131,4200 129,4400 126,8600 126,7100 131,6300 132,7800 126,6100 132,8400 123,1400 128,1300 125,4900 126,4800 130,8600 127,3200 126,5600 126,6400 129,2600 126,4700 135,4000 135,5000 132,2200 122,6200 125,1600 128,5000 133,8600 128,8700 125,0700 125,2500 132,1600 130,2400

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.300229450194369 beta 0.106520029572451 gamma 0.101170257297618 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 118.81 114.909131944444 3.90086805555555 14 123.85 121.158542719392 2.69145728060776 15 117.96 116.360093443741 1.59990655625897 16 120.16 119.423844225748 0.736155774252396 17 118.74 118.369314178234 0.370685821765790 18 119.84 119.501497320513 0.338502679486993 19 124.81 122.089426937 2.72057306299986 20 121.33 123.752446052297 -2.42244605229679 21 120.2 122.117241784959 -1.91724178495919 22 118.32 121.431150462165 -3.11115046216479 23 129.58 124.425866602103 5.15413339789714 24 130.2 128.870645876025 1.32935412397472 25 127.19 130.178292838869 -2.98829283886914 26 133.1 134.417717615868 -1.31771761586847 27 129.12 128.354067754233 0.76593224576726 28 123.28 131.095363119880 -7.81536311987963 29 123.36 127.163138340085 -3.8031383400846 30 124.13 126.622054219994 -2.49205421999356 31 126.97 128.020401894517 -1.05040189451685 32 127.14 127.558154410962 -0.418154410962174 33 123.7 125.995558242714 -2.29555824271407 34 123.67 124.534356825636 -0.864356825636392 35 130.19 128.283624381633 1.90637561836684 36 134.01 130.873536460407 3.13646353959291 37 124.96 131.866835354631 -6.90683535463147 38 129.96 134.371527956692 -4.41152795669197 39 128.32 126.751057379220 1.56894262077978 40 132.38 128.376117897315 4.00388210268454 41 126.25 127.904611612568 -1.65461161256836 42 128.91 127.798292478315 1.11170752168466 43 131.42 130.192803171065 1.22719682893498 44 129.44 130.344101545671 -0.904101545671466 45 126.86 128.372139383371 -1.51213938337112 46 126.71 127.141963020923 -0.431963020923078 47 131.63 131.125529114614 0.504470885386155 48 132.78 133.245124327386 -0.465124327385752 49 126.61 132.194405981146 -5.58440598114551 50 132.84 135.06339096987 -2.22339096986991 51 123.14 128.383836801113 -5.2438368011134 52 128.13 127.778588491292 0.351411508707585 53 125.49 125.335801081501 0.154198918499262 54 126.48 125.552127595202 0.927872404798052 55 130.86 127.477485839017 3.38251416098306 56 127.32 127.771778730716 -0.451778730716228 57 126.56 125.553828167139 1.00617183286083 58 126.64 124.897989447036 1.74201055296376 59 129.26 129.411861148902 -0.151861148902071 60 126.47 131.056091905674 -4.58609190567375 61 135.4 128.064252019138 7.3357479808623 62 135.5 135.121925154186 0.378074845814041 63 132.22 129.16449942158 3.05550057841987 64 122.62 131.867421332597 -9.24742133259656 65 125.16 126.642188477594 -1.48218847759372 66 128.5 126.483032577361 2.0169674226385 67 133.86 129.005014016007 4.85498598399315 68 128.87 129.612890214242 -0.742890214242038 69 125.07 127.544402925246 -2.47440292524621 70 125.25 125.918023721728 -0.668023721728304 71 132.16 129.519515849384 2.64048415061600 72 130.24 131.722727875470 -1.48272787546981 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 130.640437049224 124.500772182621 136.780101915827 74 134.902336491291 128.432739348052 141.371933634530 75 128.908070579365 122.062969181734 135.753171976996 76 129.612045781185 122.347627802425 136.876463759946 77 127.798046806868 120.072643288183 135.523450325553 78 128.464153209514 120.23841360357 136.689892815458 79 130.649537916387 121.886452144992 139.412623687781 80 129.316268671027 119.981087575066 138.651449766989 81 127.284764135178 117.344859724704 137.224668545653 82 126.544819790573 115.969515583432 137.120123997713 83 130.618126892226 119.378518789680 141.857734994772 84 131.689262728196 119.758043200548 143.620482255845

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/16/t1232113770orf27siotmr02kt/1xsou1232113697.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/16/t1232113770orf27siotmr02kt/1xsou1232113697.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/16/t1232113770orf27siotmr02kt/2o6t81232113697.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/16/t1232113770orf27siotmr02kt/2o6t81232113697.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/16/t1232113770orf27siotmr02kt/3asbm1232113697.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/16/t1232113770orf27siotmr02kt/3asbm1232113697.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=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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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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