*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 15 Mar 2009 04:13:52 -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/Mar/15/t1237112069opdzrat1i19b7h8.htm/, Retrieved Sun, 15 Mar 2009 11:14:33 +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/Mar/15/t1237112069opdzrat1i19b7h8.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 6 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.275592931492333 beta 0.0326927269947438 gamma 0.870730972374008 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 115 111.081808708867 3.91819129113328 14 126 122.331453874742 3.66854612525761 15 141 137.439015376157 3.56098462384284 16 135 132.323383220293 2.67661677970653 17 125 123.479682818147 1.52031718185303 18 149 147.667290233188 1.33270976681194 19 170 162.443244801899 7.55675519810066 20 170 165.529592394217 4.47040760578255 21 158 153.887714464933 4.11228553506743 22 133 136.318642929536 -3.3186429295356 23 114 119.090609201624 -5.09060920162396 24 140 133.988714960677 6.0112850393225 25 145 134.830370109663 10.1696298903367 26 150 149.705146015379 0.294853984620914 27 178 166.540824859924 11.4591751400757 28 163 161.749729120069 1.25027087993098 29 172 149.757505882891 22.2424941171092 30 178 185.647729927987 -7.64772992798655 31 199 206.262157804499 -7.26215780449877 32 199 203.180877899402 -4.18087789940233 33 184 186.419241979639 -2.41924197963931 34 162 158.147782759537 3.85221724046292 35 146 138.368716981080 7.63128301892016 36 166 169.141347816413 -3.14134781641266 37 171 170.360945870189 0.639054129810944 38 180 177.438178047919 2.56182195208055 39 193 206.247937689468 -13.2479376894684 40 181 185.960724160939 -4.96072416093864 41 183 184.798364145754 -1.79836414575391 42 218 195.684359733572 22.3156402664278 43 230 227.498387941045 2.5016120589554 44 242 229.004769688519 12.9952303114810 45 209 215.630988418267 -6.63098841826653 46 191 186.286598351088 4.71340164891208 47 172 166.037643993557 5.96235600644326 48 194 192.842509510071 1.15749048992947 49 196 198.309952885667 -2.30995288566717 50 196 206.984486038046 -10.9844860380456 51 236 224.192940896233 11.8070591037674 52 235 214.065417855659 20.9345821443406 53 229 222.675252447097 6.32474755290255 54 243 256.738013695458 -13.7380136954578 55 264 268.357973304421 -4.35797330442080 56 272 275.595124348779 -3.59512434877928 57 237 240.950022441534 -3.95002244153355 58 211 216.418700337475 -5.41870033747466 59 180 191.302342357419 -11.3023423574190 60 201 212.165187519317 -11.1651875193170 61 204 211.884585973233 -7.88458597323302 62 188 213.278482377796 -25.2784823777957 63 235 241.844280631679 -6.84428063167888 64 227 231.126644343174 -4.12664434317369 65 234 222.847562357444 11.1524376425561 66 264 244.403573681996 19.5964263180045 67 302 270.925436787525 31.0745632124749 68 293 288.463304382630 4.53669561737041 69 259 253.325573114429 5.67442688557071 70 229 228.457242585480 0.542757414519542 71 203 198.766723711057 4.23327628894256 72 229 226.325370930038 2.67462906996178 73 242 232.507697921112 9.49230207888777 74 233 226.155470683096 6.84452931690356 75 267 284.984135370815 -17.984135370815 76 269 271.954055875764 -2.95405587576425 77 270 274.414364054006 -4.41436405400611 78 315 301.110875438719 13.8891245612812 79 364 337.481483997019 26.5185160029808 80 347 335.985512136366 11.0144878636339 81 312 297.836655531177 14.1633444688228 82 274 267.300437713933 6.69956228606708 83 237 236.992541506195 0.00745849380476216 84 278 266.900682035767 11.0993179642327 85 284 281.633930499981 2.36606950001874 86 277 269.967232749704 7.03276725029627 87 317 320.174971097699 -3.17497109769943 88 313 321.276901514013 -8.2769015140127 89 318 322.045741716523 -4.04574171652263 90 374 367.95119390836 6.04880609163985 91 413 417.20324189844 -4.20324189843973 92 405 394.606219282439 10.3937807175610 93 355 352.306636965006 2.69336303499392 94 306 308.449783989787 -2.44978398978702 95 271 266.69631319267 4.30368680732988 96 306 309.394151440329 -3.39415144032859 97 315 315.103159698916 -0.103159698916272 98 301 304.405343346902 -3.4053433469017 99 356 349.058165450379 6.94183454962058 100 348 349.292530352998 -1.29253035299848 101 355 355.07317102392 -0.0731710239203949 102 422 414.360938373284 7.6390616267164 103 465 462.091156275825 2.90884372417509 104 467 448.979717852711 18.0202821472888 105 404 397.635009922119 6.36499007788103 106 347 345.450966287894 1.54903371210571 107 305 304.243031112076 0.756968887924245 108 336 345.615225431220 -9.61522543121976 109 340 352.616275490595 -12.6162754905953 110 318 334.810864863475 -16.8108648634752 111 362 386.941342201651 -24.9413422016506 112 348 372.190810667806 -24.1908106678064 113 363 372.090086438278 -9.09008643827758 114 435 435.498520155361 -0.498520155360723 115 491 478.418370094791 12.5816299052085 116 505 476.297754928979 28.7022450710215 117 404 417.219149854204 -13.2191498542045 118 359 354.436902962759 4.56309703724105 119 310 311.876475452214 -1.87647545221381 120 337 345.975115388041 -8.97511538804093 121 360 350.64305814032 9.35694185967964 122 342 334.994580207110 7.0054197928896 123 406 390.685875425546 15.3141245744536 124 396 386.498865844796 9.50113415520354 125 420 407.130762273219 12.8692377267807 126 472 491.605011219962 -19.6050112199623 127 548 543.780046558739 4.2199534412614 128 559 549.9353273917 9.0646726082997 129 463 449.638746709422 13.3612532905782 130 407 399.913034211769 7.08696578823083 131 362 348.397212667469 13.6027873325311 132 405 386.652084703316 18.3479152966844 133 417 413.916781467431 3.08321853256905 134 391 392.451160427228 -1.45116042722816 135 419 460.170497130596 -41.1704971305962 136 461 435.421755571356 25.5782444286439 137 472 465.095102857791 6.90489714220945 138 535 534.352674389911 0.647325610088842 139 622 616.73536618622 5.26463381378016 140 606 627.551069242193 -21.5510692421930 141 508 510.133139879417 -2.1331398794174 142 461 446.162791637769 14.8372083622306 143 390 395.452817969955 -5.45281796995471 144 432 434.572452493995 -2.57245249399460 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 145 447.055907793748 427.306081839881 466.805733747616 146 419.712252491685 399.132529133936 440.291975849435 147 464.867062938332 442.962936376578 486.771189500086 148 496.08393808204 472.832869325636 519.335006838444 149 507.532607460917 483.13745188183 531.927763040004 150 575.45083938456 548.708168067514 602.193510701605 151 666.592241551587 636.628745108668 696.555737994505 152 657.913647955767 627.181984104084 688.64531180745 153 550.308727275651 521.63972761341 578.977726937891 154 492.985286976115 465.015260234151 520.955313718078 155 420.207239449315 393.468712587999 446.945766310631 156 465.634459283973 443.300359438534 487.968559129412

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/15/t1237112069opdzrat1i19b7h8/172r91237112025.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/15/t1237112069opdzrat1i19b7h8/172r91237112025.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/15/t1237112069opdzrat1i19b7h8/2ygze1237112025.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/15/t1237112069opdzrat1i19b7h8/2ygze1237112025.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/15/t1237112069opdzrat1i19b7h8/3g55u1237112025.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/15/t1237112069opdzrat1i19b7h8/3g55u1237112025.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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