Opgave 10 Oefening 2 - Wisselkoers Euro in Dollar - Anthony Van Trier

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 02 Jun 2009 12:55:35 -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/02/t1243968976omuucx36j8ovaql.htm/, Retrieved Tue, 02 Jun 2009 20:56:16 +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/02/t1243968976omuucx36j8ovaql.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:

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1.1608 1.1208 1.0883 1.0704 1.0628 1.0378 1.0353 1.0604 1.0501 1.0706 1.0338 1.0110 1.0137 0.9834 0.9643 0.9470 0.9060 0.9492 0.9397 0.9041 0.8721 0.8552 0.8564 0.8973 0.9383 0.9217 0.9095 0.8920 0.8742 0.8532 0.8607 0.9005 0.9111 0.9059 0.8883 0.8924 0.8833 0.8700 0.8758 0.8858 0.9170 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 1.2490 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 1.2020 1.2271 1.2770 1.2650 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 1.4570 1.4718 1.4748 1.5527 1.5750 1.5557 1.5553 1.5770 1.4975 1.4369 1.3322 1.2732 1.3449 1.3239

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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.859998440553193 beta 0.0713194296639774 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1.0137 1.07518811431624 -0.0614881143162398 14 0.9834 0.987017021911577 -0.00361702191157653 15 0.9643 0.963026463475407 0.0012735365245935 16 0.947 0.947582389518923 -0.00058238951892331 17 0.906 0.90678150143204 -0.000781501432040699 18 0.9492 0.945723944333983 0.00347605566601727 19 0.9397 0.887370248845404 0.0523297511545964 20 0.9041 0.957036112891393 -0.0529361128913926 21 0.8721 0.896564182795004 -0.0244641827950045 22 0.8552 0.889294234023439 -0.0340942340234387 23 0.8564 0.815717966731732 0.0406820332682678 24 0.8973 0.8214943888695 0.0758056111305005 25 0.9383 0.8764681080107 0.0618318919893 26 0.9217 0.909748193147141 0.0119518068528588 27 0.9095 0.908080518081188 0.00141948191881203 28 0.892 0.900760105001888 -0.0087601050018884 29 0.8742 0.860654922085992 0.0135450779140076 30 0.8532 0.921149384218215 -0.0679493842182153 31 0.8607 0.812463783404426 0.0482362165955741 32 0.9005 0.867875021730493 0.0326249782695065 33 0.9111 0.894222659114398 0.0168773408856017 34 0.9059 0.932944847692385 -0.0270448476923846 35 0.8883 0.888118920605185 0.000181079394815264 36 0.8924 0.873716916431145 0.0186830835688550 37 0.8833 0.883840396382622 -0.000540396382622488 38 0.87 0.858902929733969 0.0110970702660314 39 0.8758 0.857379024348628 0.0184209756513719 40 0.8858 0.866650874839171 0.0191491251608291 41 0.917 0.858778311669086 0.0582216883309142 42 0.9554 0.9541334241941 0.00126657580590062 43 0.9922 0.933333126354961 0.058866873645039 44 0.9778 1.00844666252811 -0.0306466625281139 45 0.9808 0.9870409001049 -0.00624090010490086 46 0.9811 1.00717912096454 -0.02607912096454 47 1.0014 0.974501480444845 0.0268985195551548 48 1.0183 0.994811536879122 0.0234884631208777 49 1.0622 1.01581584890246 0.0463841510975367 50 1.0773 1.04518031198103 0.0321196880189711 51 1.0807 1.07636822566147 0.00433177433852650 52 1.0848 1.08636821396511 -0.00156821396510587 53 1.1582 1.07762118846067 0.0805788115393287 54 1.1663 1.19707304991013 -0.0307730499101331 55 1.1372 1.16766118027058 -0.0304611802705801 56 1.1139 1.15882011924888 -0.0449201192488764 57 1.1222 1.1330800188951 -0.0108800188951006 58 1.1692 1.15069065227706 0.0185093477229406 59 1.1702 1.17075022270366 -0.000550222703664005 60 1.2286 1.17226767792138 0.0563323220786183 61 1.2613 1.23202824188678 0.0292717581132225 62 1.2646 1.25093459729483 0.0136654027051726 63 1.2262 1.26748518764415 -0.041285187644154 64 1.1985 1.23975443868747 -0.0412544386874714 65 1.2007 1.20826968130461 -0.00756968130460822 66 1.2138 1.23080963754201 -0.0170096375420106 67 1.2266 1.20860721210141 0.0179927878985868 68 1.2176 1.23771338760201 -0.0201133876020145 69 1.2218 1.23789538929663 -0.0160953892966329 70 1.249 1.25463817115914 -0.00563817115914067 71 1.2991 1.24928426678652 0.0498157332134752 72 1.3408 1.30319090956326 0.037609090436737 73 1.3119 1.34302351950686 -0.0311235195068611 74 1.3014 1.30406331330588 -0.00266331330588421 75 1.3201 1.29413474682630 0.0259652531736971 76 1.2938 1.32362503759217 -0.0298250375921731 77 1.2694 1.30676794420661 -0.0373679442066110 78 1.2165 1.30061464605355 -0.0841146460535516 79 1.2037 1.21974136717618 -0.0160413671761772 80 1.2292 1.20629478225293 0.0229052177470728 81 1.2256 1.23872525622995 -0.0131252562299464 82 1.2015 1.25435855940209 -0.0528585594020885 83 1.1786 1.20813476898104 -0.0295347689810443 84 1.1856 1.17920016452589 0.00639983547410972 85 1.2103 1.16776499411458 0.0425350058854206 86 1.1938 1.18584809702119 0.00795190297881443 87 1.202 1.17942034285751 0.022579657142487 88 1.2271 1.18834434334750 0.0387556566525016 89 1.277 1.22377293544824 0.0532270645517645 90 1.265 1.28890561493379 -0.0239056149337915 91 1.2684 1.27295429340549 -0.00455429340548652 92 1.2811 1.27915563097058 0.00194436902942252 93 1.2727 1.29154633429204 -0.0188463342920409 94 1.2611 1.29937674392037 -0.0382767439203742 95 1.2881 1.27253297797409 0.0155670220259145 96 1.3213 1.29375736321546 0.0275426367845437 97 1.2999 1.31320135349621 -0.0133013534962094 98 1.3074 1.28263628972595 0.0247637102740519 99 1.3242 1.29795842111513 0.0262415788848662 100 1.3516 1.31776478535101 0.0338352146489931 101 1.3511 1.35615448294248 -0.00505448294247746 102 1.3419 1.36195841002156 -0.0200584100215606 103 1.3716 1.35385284364131 0.0177471563586877 104 1.3622 1.38333901629522 -0.0211390162952225 105 1.3896 1.37474730337604 0.0148526966239597 106 1.4227 1.41268544594394 0.0100145540560628 107 1.4684 1.44171916606334 0.0266808339366584 108 1.457 1.48166851206183 -0.0246685120618342 109 1.4718 1.45478091868475 0.0170190813152504 110 1.4748 1.46176838680960 0.0130316131904047 111 1.5527 1.47263609040293 0.0800639095970745 112 1.575 1.54852212049079 0.0264778795092062 113 1.5557 1.58341806835461 -0.0277180683546092 114 1.5553 1.57451887755431 -0.0192188775543141 115 1.577 1.57936774184362 -0.00236774184362409 116 1.4975 1.59181686520620 -0.0943168652061963 117 1.4369 1.52654873491655 -0.0896487349165489 118 1.3322 1.46874643113537 -0.13654643113537 119 1.2732 1.35988994788131 -0.0866899478813117 120 1.3449 1.27401676859847 0.0708832314015333 121 1.3239 1.31986564027861 0.00403435972139055 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 122 1.29905739024732 1.22415693785220 1.37395784264244 123 1.29123263801043 1.18938855171837 1.39307672430249 124 1.26898110035171 1.14332478653317 1.39463741417026 125 1.25011398323685 1.10211343894329 1.39811452753041 126 1.24453765187573 1.07495468365181 1.41412062009966 127 1.24774815221630 1.05697502864644 1.43852127578615 128 1.22897997975374 1.01719146429816 1.44076849520932 129 1.23088210956139 0.998114920311562 1.46364929881121 130 1.23451475412627 0.98071333276193 1.4883161754906 131 1.24934592134310 0.974390695828924 1.52430114685728 132 1.26468149323295 0.9684072663467 1.56095572011921 133 1.24045939599681 0.922667804859097 1.55825098713451

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243968976omuucx36j8ovaql/1d72c1243968930.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243968976omuucx36j8ovaql/1d72c1243968930.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243968976omuucx36j8ovaql/25r1d1243968930.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243968976omuucx36j8ovaql/25r1d1243968930.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243968976omuucx36j8ovaql/3u9211243968930.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243968976omuucx36j8ovaql/3u9211243968930.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')

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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