Opgave 10 - Aantal maandelijkse passagiers - William Baeyaert 202

*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 06:55:53 -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/t1243947385geicaenlp03vl0w.htm/, Retrieved Tue, 02 Jun 2009 14:56:25 +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/t1243947385geicaenlp03vl0w.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 «

112 118 132 129 121 135 148 148 136 119 104 118 115 126 141 135 125 149 170 170 158 133 114 140 145 150 178 163 172 178 199 199 184 162 146 166 171 180 193 181 183 218 230 242 209 191 172 194 196 196 236 235 229 243 264 272 237 211 180 201 204 188 235 227 234 264 302 293 259 229 203 229 242 233 267 269 270 315 364 347 312 274 237 278 284 277 317 313 318 374 413 405 355 306 271 306 315 301 356 348 355 422 465 467 404 347 305 336 340 318 362 348 363 435 491 505 404 359 310 337 360 342 406 396 420 472 548 559 463 407 362 405 417 391 419 461 472 535 622 606 508 461 390 432

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 0.275592931492602 beta 0.0326927269946913 gamma 0.870730972375243 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 115 111.081808708867 3.91819129113324 14 126 122.331453874744 3.66854612525647 15 141 137.439015376159 3.56098462384085 16 135 132.323383220296 2.67661677970437 17 125 123.479682818149 1.52031718185104 18 149 147.66729023319 1.33270976680993 19 170 162.443244801901 7.5567551980989 20 170 165.529592394220 4.47040760577954 21 158 153.887714464935 4.11228553506467 22 133 136.318642929538 -3.31864292953799 23 114 119.090609201624 -5.09060920162445 24 140 133.988714960676 6.01128503932392 25 145 134.830370109667 10.1696298903335 26 150 149.705146015383 0.294853984617163 27 178 166.540824859926 11.459175140074 28 163 161.749729120072 1.25027087992819 29 172 149.757505882892 22.2424941171083 30 178 185.647729927993 -7.64772992799348 31 199 206.262157804506 -7.26215780450633 32 199 203.180877899402 -4.18087789940165 33 184 186.419241979637 -2.41924197963704 34 162 158.147782759529 3.85221724047076 35 146 138.368716981075 7.63128301892533 36 166 169.141347816421 -3.14134781642136 37 171 170.360945870197 0.639054129803043 38 180 177.438178047915 2.56182195208476 39 193 206.247937689474 -13.2479376894740 40 181 185.96072416093 -4.96072416092983 41 183 184.798364145761 -1.7983641457605 42 218 195.68435973355 22.3156402664498 43 230 227.498387941040 2.50161205896046 44 242 229.004769688520 12.9952303114803 45 209 215.630988418272 -6.63098841827184 46 191 186.286598351092 4.71340164890827 47 172 166.037643993561 5.96235600643919 48 194 192.842509510068 1.15749048993183 49 196 198.309952885672 -2.30995288567220 50 196 206.984486038047 -10.9844860380474 51 236 224.192940896220 11.8070591037797 52 235 214.065417855660 20.9345821443404 53 229 222.675252447111 6.32474755288877 54 243 256.738013695478 -13.7380136954783 55 264 268.357973304409 -4.35797330440869 56 272 275.595124348777 -3.59512434877661 57 237 240.950022441516 -3.95002244151587 58 211 216.418700337473 -5.41870033747318 59 180 191.302342357418 -11.3023423574182 60 201 212.165187519306 -11.1651875193057 61 204 211.884585973222 -7.8845859732215 62 188 213.27848237778 -25.2784823777802 63 235 241.844280631674 -6.84428063167385 64 227 231.126644343173 -4.12664434317313 65 234 222.847562357434 11.1524376425660 66 264 244.403573681983 19.5964263180174 67 302 270.925436787527 31.0745632124733 68 293 288.463304382643 4.53669561735745 69 259 253.325573114433 5.67442688556693 70 229 228.457242585486 0.542757414514483 71 203 198.766723711057 4.23327628894268 72 229 226.32537093004 2.67462906995985 73 242 232.507697921117 9.49230207888297 74 233 226.155470683085 6.84452931691496 75 267 284.984135370836 -17.9841353708361 76 269 271.954055875778 -2.95405587577795 77 270 274.414364054023 -4.41436405402328 78 315 301.110875438727 13.8891245612733 79 364 337.48148399703 26.5185160029703 80 347 335.985512136356 11.0144878636440 81 312 297.836655531173 14.163344468827 82 274 267.300437713930 6.69956228607032 83 237 236.992541506196 0.00745849380362529 84 278 266.900682035765 11.0993179642347 85 284 281.633930499988 2.36606950001163 86 277 269.967232749698 7.0327672503015 87 317 320.174971097683 -3.17497109768345 88 313 321.276901514021 -8.27690151402084 89 318 322.045741716532 -4.04574171653167 90 374 367.951193908384 6.04880609161643 91 413 417.203241898467 -4.20324189846684 92 405 394.606219282432 10.3937807175679 93 355 352.306636965003 2.69336303499716 94 306 308.449783989776 -2.44978398977639 95 271 266.696313192658 4.30368680734244 96 306 309.394151440327 -3.39415144032654 97 315 315.103159698907 -0.103159698907064 98 301 304.405343346895 -3.40534334689534 99 356 349.058165450357 6.94183454964292 100 348 349.292530352986 -1.29253035298638 101 355 355.07317102392 -0.0731710239201107 102 422 414.360938373302 7.63906162669832 103 465 462.091156275841 2.90884372415928 104 467 448.97971785273 18.0202821472701 105 404 397.635009922127 6.36499007787268 106 347 345.450966287893 1.54903371210713 107 305 304.243031112076 0.756968887923563 108 336 345.615225431214 -9.6152254312135 109 340 352.616275490588 -12.6162754905881 110 318 334.810864863463 -16.8108648634631 111 362 386.941342201636 -24.9413422016360 112 348 372.19081066778 -24.1908106677798 113 363 372.090086438254 -9.09008643825427 114 435 435.498520155351 -0.498520155351457 115 491 478.418370094784 12.5816299052164 116 505 476.297754928993 28.7022450710072 117 404 417.219149854212 -13.2191498542122 118 359 354.436902962756 4.56309703724361 119 310 311.876475452214 -1.87647545221392 120 337 345.975115388032 -8.97511538803184 121 360 350.643058140311 9.35694185968907 122 342 334.994580207103 7.00541979289682 123 406 390.685875425541 15.3141245744593 124 396 386.498865844795 9.50113415520485 125 420 407.130762273234 12.8692377267661 126 472 491.605011219989 -19.6050112199886 127 548 543.780046558761 4.21995344123911 128 559 549.935327391731 9.06467260826867 129 463 449.63874670941 13.3612532905901 130 407 399.913034211778 7.08696578822219 131 362 348.39721266747 13.6027873325298 132 405 386.652084703312 18.3479152966885 133 417 413.916781467446 3.08321853255381 134 391 392.451160427232 -1.45116042723186 135 419 460.170497130599 -41.1704971305986 136 461 435.421755571338 25.5782444286622 137 472 465.095102857788 6.90489714221167 138 535 534.352674389889 0.647325610110556 139 622 616.735366186234 5.26463381376573 140 606 627.551069242217 -21.5510692422174 141 508 510.133139879421 -2.13313987942115 142 461 446.162791637769 14.8372083622311 143 390 395.452817969961 -5.45281796996073 144 432 434.572452493994 -2.57245249399358 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 145 447.055907793737 427.306081839849 466.805733747625 146 419.712252491671 399.132529133901 440.291975849441 147 464.867062938288 442.962936376511 486.771189500064 148 496.083938082048 472.83286932562 519.335006838475 149 507.532607460904 483.137451881794 531.927763040015 150 575.450839384529 548.708168067459 602.1935107016 151 666.592241551563 636.628745108617 696.555737994509 152 657.91364795573 627.18198410402 688.645311807441 153 550.308727275637 521.63972761337 578.977726937903 154 492.985286976114 465.015260234125 520.955313718102 155 420.2072394493 393.468712587960 446.94576631064 156 465.63445928396 443.300359438503 487.968559129416

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243947385geicaenlp03vl0w/1dkk31243947346.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243947385geicaenlp03vl0w/1dkk31243947346.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243947385geicaenlp03vl0w/2zkgm1243947346.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243947385geicaenlp03vl0w/2zkgm1243947346.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243947385geicaenlp03vl0w/35jx31243947346.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243947385geicaenlp03vl0w/35jx31243947346.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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

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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