Exponential smoothing

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 12 Aug 2008 07:12:52 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Aug/12/t12185468305rth8rsdn8ch1kk.htm/, Retrieved Tue, 12 Aug 2008 13:13:54 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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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

Text written by user:

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.280899310506867 beta 0.014993451758652 gamma 0.883505174307315 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 126 116.281375804017 9.7186241959834 14 141 133.552047422618 7.44795257738187 15 135 130.540326650773 4.45967334922665 16 125 123.086708406871 1.91329159312913 17 149 148.248578661967 0.751421338033111 18 170 169.371743991136 0.62825600886444 19 170 169.438075517978 0.561924482021908 20 158 157.209815834283 0.790184165716823 21 133 132.035744423148 0.964255576852054 22 114 112.692620246665 1.30737975333479 23 140 137.965513020114 2.03448697988628 24 145 143.287475924920 1.71252407508027 25 150 157.327613275899 -7.32761327589944 26 178 170.953314482716 7.04668551728417 27 163 163.840823888383 -0.840823888382772 28 172 150.667031895937 21.3329681040634 29 178 186.183939345429 -8.18393934542874 30 199 209.112336697547 -10.1123366975472 31 199 205.608117997012 -6.60811799701239 32 184 188.644928165252 -4.64492816525157 33 162 156.993962936175 5.00603706382546 34 146 134.991668943101 11.0083310568994 35 166 168.489901774244 -2.48990177424432 36 171 172.894857765863 -1.89485776586304 37 180 181.233088070878 -1.23308807087810 38 193 210.229388144907 -17.2293881449072 39 181 188.694053944275 -7.69405394427463 40 183 186.893392341417 -3.89339234141659 41 218 197.097421071782 20.9025789282179 42 230 229.719656828424 0.28034317157622 43 242 231.152522280983 10.8474777190172 44 209 217.558308348151 -8.55830834815114 45 191 186.567220967549 4.43277903245126 46 172 164.596978005659 7.40302199434089 47 194 191.455392863139 2.54460713686089 48 196 198.212886575579 -2.21288657557881 49 196 208.015022257809 -12.0150222578093 50 236 225.805554836701 10.194445163299 51 235 215.809152727707 19.1908472722926 52 229 224.308075022651 4.69192497734937 53 243 258.173038248152 -15.1730382481524 54 264 269.606808068124 -5.60680806812354 55 272 276.989796426739 -4.98979642673891 56 237 242.093421287755 -5.09342128775486 57 211 217.038312353546 -6.03831235354647 58 180 190.937337132638 -10.9373371326384 59 201 211.341411677736 -10.3414116777360 60 204 211.370213527733 -7.37021352773255 61 188 213.326199359853 -25.3261993598532 62 235 242.666972805517 -7.66697280551733 63 227 232.514056296515 -5.51405629651512 64 234 224.505115138515 9.49488486148536 65 264 246.390550342698 17.6094496573021 66 302 273.316122105627 28.6838778943728 67 293 290.944806002852 2.05519399714774 68 259 255.287978076269 3.71202192373082 69 229 229.892913843582 -0.892913843582363 70 203 199.43440871691 3.56559128309021 71 229 226.559440295758 2.44055970424199 72 242 232.437734610037 9.56226538996273 73 233 225.859207165884 7.1407928341163 74 267 284.847268353404 -17.8472683534038 75 269 271.816279104082 -2.81627910408235 76 270 274.497764248186 -4.497764248186 77 315 301.385220728306 13.6147792716945 78 364 338.157915969633 25.8420840303668 79 347 336.757057885315 10.2429421146852 80 312 298.668872923485 13.3311270765146 81 274 267.970413540025 6.02958645997461 82 237 237.336073764774 -0.336073764773971 83 278 266.866601515947 11.1333984840530 84 284 281.284317533078 2.71568246692181 85 277 269.263370526338 7.73662947366165 86 317 319.087689493591 -2.0876894935908 87 313 320.224938768331 -7.22493876833119 88 318 320.927108670734 -2.92710867073379 89 374 366.827773739644 7.17222626035584 90 413 416.153800041502 -3.15380004150177 91 405 393.704825553790 11.2951744462105 92 355 351.872707497962 3.12729250203773 93 306 308.216218194239 -2.21621819423927 94 271 266.532883942527 4.46711605747328 95 306 309.233289147014 -3.23328914701398 96 315 314.736317155828 0.263682844172308 97 301 303.931795754729 -2.93179575472885 98 356 348.281286520358 7.71871347964168 99 348 348.496910117826 -0.496910117826019 100 355 354.215611268775 0.78438873122542 101 422 413.365679896899 8.63432010310055 102 465 460.919374392577 4.08062560742263 103 467 447.937605062674 19.0623949373261 104 404 396.798499239558 7.20150076044183 105 347 344.787663817616 2.21233618238364 106 305 303.746714811714 1.25328518828644 107 336 345.027015350703 -9.02701535070304 108 340 351.992313564864 -11.9923135648640 109 318 334.161008973001 -16.1610089730015 110 362 386.192197615529 -24.1921976155287 111 348 371.450293921487 -23.4502939214871 112 363 371.517324667406 -8.51732466740555 113 435 435.144372189276 -0.144372189276396 114 491 478.241530872724 12.7584691272763 115 505 476.449921743768 28.5500782562323 116 404 417.42838144451 -13.4283814445097 117 359 354.647864114073 4.35213588592723 118 310 312.197102861513 -2.1971028615132 119 337 346.353464954916 -9.35346495491575 120 360 351.088149572442 8.91185042755842 121 342 335.430827635179 6.56917236482116 122 406 391.092492088269 14.9075079117309 123 396 386.720933169789 9.27906683021143 124 420 407.175313193508 12.8246868064923 125 472 491.329832090014 -19.3298320900138 126 548 543.100581486448 4.8994185135524 127 559 549.223047193135 9.77695280686498 128 463 448.846681135598 14.1533188644022 129 407 399.437273747962 7.56272625203832 130 362 347.965997940374 14.0340020596257 131 405 386.158297117203 18.8417028827972 132 417 413.470759506924 3.52924049307609 133 391 391.831406431631 -0.831406431631422 134 419 459.328420854134 -40.3284208541342 135 461 434.434133637605 26.5658663623951 136 472 464.238428785654 7.76157121434602 137 535 533.12690155366 1.87309844634001 138 622 615.416098056033 6.58390194396657 139 606 626.05270305136 -20.0527030513606 140 508 508.720515758472 -0.72051575847189 141 461 444.989239023324 16.0107609766756 142 390 394.565358759392 -4.56535875939153 143 432 433.629003574392 -1.62900357439185 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 144 446.165888018917 426.272188876449 466.059587161386 145 418.776549113291 398.061024816972 439.49207340961 146 463.532987574271 441.537567359875 485.528407788667 147 494.864017931474 471.602976717914 518.125059145034 148 505.864488625518 481.576901417936 530.1520758331 149 573.207351846183 546.787097108086 599.62760658428 150 663.756003594139 634.448819995664 693.063187192614 151 654.658689744205 624.810890191196 684.506489297214 152 547.365267589531 519.539966541438 575.190568637624 153 490.097466150254 462.992972841699 517.201959458808 154 417.412520574714 391.467173654527 443.3578674949 155 462.363954417815 441.514377669981 483.213531165649

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/12/t12185468305rth8rsdn8ch1kk/1tivu1218546766.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/12/t12185468305rth8rsdn8ch1kk/1tivu1218546766.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/12/t12185468305rth8rsdn8ch1kk/2g3py1218546766.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/12/t12185468305rth8rsdn8ch1kk/2g3py1218546766.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/12/t12185468305rth8rsdn8ch1kk/3gsae1218546766.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/12/t12185468305rth8rsdn8ch1kk/3gsae1218546766.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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