Robbe Leys_2MAR03A_opgave 10.2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 27 Jan 2009 10:56:21 -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/27/t123307902345o7lp3v4bdpryn.htm/, Retrieved Tue, 27 Jan 2009 18:57:07 +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/27/t123307902345o7lp3v4bdpryn.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 «

284.4 212.8 226.9 308.4 262 227.9 236.1 320.4 271.9 232.8 237 313.4 261.4 226.8 249.9 314.3 286.1 226.5 260.4 311.4 294.7 232.6 257.2 339.2 279.1 249.8 269.8 345.7 293.8 254.7 277.5 363.4 313.4 272.8 300.1 369.5 330.8 287.8 305.9 386.1 335.2 288 308.3 402.3 352.8 316.1 324.9 404.8 393 318.9 327 442.3 383.1 331.6 361.4 445.9 386.6 357.2 373.6 466.2 409.6 369.8 378.6 487 419.2 376.7 392.8 506.1 458.4 387.4 426.9 565 464.8 444.5 449.5 556.1 499.6 451.9 434.9 553.8 510 432.9 453.2 547.6 485.8 452.6 456.6 565.7 514.8 464.3 430.9 588.3 503.1 442.6 448 554.5 504.5 427.3 473.1 526.2 547.5 440.2 468.7 574.5 492.6 432.6 479.8 575.7 474.6 405.3 434.6 535.1 452.6 429.5 417.2 551.8 464 416.6 422.9 553.6 458.6 427.6 429.2 534.2 481.7 416 440.2 538.7 473.8 439.9 446.8 597.5 467.2 439.4 447.4 568.5 485.9 442.1 430.5 600 464.5 423.6 437 574 443 410 420 532 432 420 411 512

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 0.229158941249302 beta 0.612253088934732 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 226.9 141.2 85.7 4 308.4 101.262911472947 207.137088527052 5 262 118.216228364565 143.783771635435 6 227.9 140.824899513845 87.0751004861552 7 236.1 162.655192925070 73.4448070749303 8 320.4 191.666529299725 128.733470700275 9 271.9 251.409484144807 20.4905158551927 10 232.8 289.222484430925 -56.4224844309248 11 237 301.493923956473 -64.4939239564725 12 313.4 302.867012543181 10.5329874568185 13 261.4 322.911001293801 -61.5110012938015 14 226.8 317.815271258793 -91.0152712587929 15 249.9 293.188633811775 -43.2886338117754 16 314.3 273.425445209599 40.8745547904006 17 286.1 278.683837481709 7.41616251829095 18 226.5 277.315451854313 -50.8154518543131 19 260.4 255.473197086817 4.92680291318294 20 311.4 247.096024962265 64.3039750377346 21 294.7 261.347720684597 33.3522793154027 22 232.6 273.185992423123 -40.5859924231231 23 257.2 262.386300653823 -5.18630065382257 24 339.2 258.971109831875 80.2288901681247 25 279.1 286.38594931522 -7.28594931522008 26 249.8 292.723738327625 -42.9237383276248 27 269.8 284.872468509077 -15.0724685090765 28 345.7 281.288849581273 64.4111504187272 29 293.8 304.956707618449 -11.1567076184491 30 254.7 309.742192758097 -55.0421927580972 31 277.5 296.748326974986 -19.2483269749861 32 363.4 289.256342368322 74.1436576316783 33 313.4 313.568563663855 -0.168563663854911 34 272.8 320.827824972239 -48.027824972239 35 300.1 310.381247753066 -10.2812477530664 36 369.5 307.142143529522 62.3578564704778 37 330.8 329.297950673500 1.50204932650047 38 287.8 337.718847915155 -49.9188479151552 39 305.9 327.352409207821 -21.4524092078206 40 386.1 320.499466302351 65.6005336976491 41 335.2 342.79945299344 -7.59945299344042 42 288 347.258780132505 -59.2587801325051 43 308.3 331.565709951446 -23.265709951446 44 402.3 320.856518448779 81.4434815512215 45 352.8 345.569161162182 7.23083883781845 46 316.1 354.289823575232 -38.1898235752318 47 324.9 347.243777964404 -22.3437779644042 48 404.8 340.694090284295 64.1059097157049 49 393 362.949390240454 30.0506097595460 50 318.9 381.616812518579 -62.7168125185789 51 327 370.226376667461 -43.2263766674607 52 442.3 357.237546479471 85.0624535205287 53 383.1 385.58178914374 -2.48178914374 54 331.6 393.516282715177 -61.9162827151768 55 361.4 379.143773757393 -17.7437737573928 56 445.9 372.40428071084 73.4957192891596 57 386.6 396.884823011544 -10.2848230115436 58 357.2 400.723310645169 -43.523310645169 59 373.6 390.838438855005 -17.2384388550051 60 466.2 384.558371120356 81.641628879644 61 409.6 412.392142488735 -2.7921424887345 62 369.8 420.485413484188 -50.6854134841882 63 378.6 410.492183970628 -31.892183970628 64 487 400.33101334811 86.66898665189 65 419.2 429.499137262103 -10.2991372621029 66 376.7 435.001145932722 -58.3011459327217 67 392.8 421.323223720603 -28.523223720603 68 506.1 410.467277086632 95.6327229133678 69 458.4 441.480359442132 16.9196405578679 70 387.4 456.829516073926 -69.4295160739264 71 426.9 442.649803279729 -15.7498032797291 72 565 438.561527739733 126.438472260267 73 464.8 484.796697946556 -19.9966979465557 74 444.5 494.669337483279 -50.1693374832786 75 449.5 490.588724804648 -41.0887248046483 76 556.1 482.824133278045 73.275866721955 77 499.6 511.548054148655 -11.948054148655 78 451.9 519.065800480587 -67.1658004805867 79 434.9 504.506325109714 -69.6063251097144 80 553.8 479.621586698437 74.1784133015634 81 510 498.093880631982 11.9061193680185 82 432.9 503.96638909457 -71.0663890945702 83 453.2 480.854158613817 -27.654158613817 84 547.6 463.810260034728 83.789739965272 85 485.8 484.060701741871 1.73929825812917 86 452.6 485.752580330857 -33.1525803308565 87 456.6 474.797257546872 -18.197257546872 88 565.7 464.715945965856 100.984054034144 89 514.8 496.114490525629 18.6855094743713 90 464.3 511.275225821811 -46.9752258218107 91 430.9 504.798438761137 -73.8984387611374 92 588.3 481.783764149009 106.516235850991 93 503.1 515.057301516142 -11.9573015161418 94 442.6 519.503919995414 -76.9039199954141 95 448 498.277568723003 -50.277568723003 96 554.5 476.098776636279 78.4012233637215 97 504.5 494.40782828685 10.0921717131503 98 427.3 498.479214672524 -71.1792146725242 99 473.1 473.939859651453 -0.839859651452684 100 526.2 465.401561700034 60.7984382999663 101 547.5 479.518450529874 67.9815494701264 102 440.2 504.819447175985 -64.6194471759846 103 468.7 490.667420101151 -21.9674201011511 104 574.5 483.207385527244 91.2926144727558 105 492.6 514.510552866382 -21.9105528663816 106 432.6 516.798080025309 -84.1980800253092 107 479.8 492.99859748276 -13.1985974827598 108 575.7 483.617474807457 92.0825251925433 109 474.6 511.2819420989 -36.6819420989 110 405.3 504.292283982199 -98.9922839821986 111 434.6 469.134712779112 -34.5347127791117 112 535.1 443.902837229545 91.1971627704548 113 452.6 460.278805280510 -7.67880528050949 114 429.5 452.919099690154 -23.4190996901544 115 417.2 438.666588639452 -21.4665886394517 116 551.8 421.84968037984 129.950319620160 117 464 457.963765237312 6.03623476268757 118 416.6 466.528733076471 -49.928733076471 119 422.9 455.2636636391 -32.3636636391 120 553.6 443.483059090973 110.116940909027 121 458.6 479.802925881605 -21.2029258816047 122 427.6 483.054831206438 -55.454831206438 123 429.2 470.677112035836 -41.4771120358357 124 534.2 455.683137757725 78.5168622422751 125 481.7 479.203028075703 2.49697192429682 126 416 485.652614139696 -69.6526141396959 127 440.2 465.795987947132 -25.5959879471321 128 538.7 452.444130769303 86.255869230697 129 473.8 476.826107237553 -3.02610723755322 130 439.9 480.323747765993 -40.4237477659934 131 446.8 469.579800603168 -22.7798006031681 132 597.5 459.683041185333 137.816958814667 133 467.2 505.92463505687 -38.7246350568701 134 439.4 506.276951276367 -66.8769512763666 135 447.4 490.794857589866 -43.3948575898659 136 568.5 474.605455225595 93.894544774405 137 485.9 503.050858584787 -17.1508585847869 138 442.1 503.642893343059 -61.542893343059 139 430.5 485.427427257277 -54.9274272572773 140 600 461.021456738645 138.978543261355 141 464.5 500.549917154922 -36.0499171549222 142 423.6 494.911119646735 -71.3111196467349 143 437 471.186719060442 -34.1867190604417 144 574 451.173198344680 122.826801655320 145 443 484.373731669252 -41.3737316692524 146 410 474.141374794319 -64.141374794319 147 420 449.692364323455 -29.6923643234546 148 532 428.971716821349 103.028283178651 149 432 453.120397377789 -21.1203973777889 150 420 445.856036932283 -25.8560369322827 151 411 433.878775818879 -22.8787758188788 152 512 419.373813657367 92.626186342633 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 153 444.333603131696 321.879193558692 566.788012704699 154 448.067273811786 317.522469080267 578.612078543306 155 451.800944491877 307.099248462092 596.502640521662 156 455.534615171968 290.382129821402 620.687100522533

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/27/t123307902345o7lp3v4bdpryn/1pwx21233078978.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/27/t123307902345o7lp3v4bdpryn/1pwx21233078978.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/27/t123307902345o7lp3v4bdpryn/2pnb81233078979.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/27/t123307902345o7lp3v4bdpryn/2pnb81233078979.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/27/t123307902345o7lp3v4bdpryn/30uxf1233078979.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/27/t123307902345o7lp3v4bdpryn/30uxf1233078979.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 4 ; par2 = Double ; 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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