Tijdreeks A stap 32

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 04 Aug 2010 12:41:06 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Aug/04/t12809256508xupzezir6zv8m8.htm/, Retrieved Wed, 04 Aug 2010 14:40:51 +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/2010/Aug/04/t12809256508xupzezir6zv8m8.htm/}, year = {2010}, } @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 = {2010}, 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:

Bogaerts Yannik

Dataseries X:

» Textbox « » Textfile « » CSV «

442 441 440 438 458 457 442 432 433 433 434 436 439 439 441 436 460 453 435 421 412 408 402 409 410 410 416 410 437 431 411 398 394 395 389 404 397 401 402 383 406 400 377 372 362 365 361 372 355 365 367 341 370 366 333 320 298 306 293 313 293 304 304 286 320 313 283 272 251 262 247 268 251 257 261 242 274 272 243 234 217 231 209 226 208 214 222 194 230 226 197 188 175 190 165 176 159 169 170 141 170 164 132 123 113 125 101 99 87 90 89 66 102 97 65 54 33 49 30 34

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 2 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.629530665310154 beta 0.0694788787378497 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 439 439.841079059829 -0.841079059829156 14 439 439.259508768634 -0.259508768634248 15 441 441.616037467087 -0.616037467086699 16 436 437.304508835147 -1.3045088351472 17 460 461.960841675652 -1.96084167565243 18 453 455.201560779497 -2.20156077949667 19 435 432.069445572213 2.93055442778683 20 421 423.171334034321 -2.17133403432086 21 412 421.79978842851 -9.79978842851045 22 408 414.197263075964 -6.19726307596392 23 402 409.549908623796 -7.54990862379606 24 409 404.804129560103 4.19587043989679 25 410 408.699608138046 1.30039186195404 26 410 408.64788673553 1.35211326447023 27 416 410.923662163391 5.07633783660867 28 410 409.226344288174 0.773655711826166 29 437 434.324434737331 2.67556526266924 30 431 429.974167825028 1.02583217497192 31 411 410.495682657533 0.504317342467289 32 398 397.794561758935 0.205438241064542 33 394 394.811591114848 -0.811591114848 34 395 394.313604645821 0.686395354178842 35 389 393.911263366435 -4.9112633664351 36 404 395.706108088484 8.29389191151591 37 397 401.816039262232 -4.81603926223158 38 401 398.372779433713 2.62722056628746 39 402 403.326538370803 -1.32653837080289 40 383 396.21989920926 -13.2198992092598 41 406 412.816649016664 -6.81664901666426 42 400 401.067817981349 -1.06781798134915 43 377 379.174787610289 -2.17478761028889 44 372 363.655857873196 8.34414212680366 45 362 364.755147597983 -2.75514759798318 46 365 362.839056277637 2.16094372236284 47 361 360.606188411535 0.393811588464587 48 372 370.179845612931 1.82015438706895 49 355 366.621377684997 -11.6213776849968 50 365 360.617633542951 4.3823664570491 51 367 364.25451806712 2.74548193288024 52 341 354.526275390355 -13.5262753903546 53 370 372.510019532484 -2.51001953248357 54 366 364.998137159652 1.00186284034771 55 333 343.484489705345 -10.4844897053449 56 320 325.754383490978 -5.75438349097817 57 298 312.372710826702 -14.3727108267021 58 306 302.962564998555 3.03743500144486 59 293 298.663440651037 -5.66344065103664 60 313 302.723983065168 10.2760169348322 61 293 297.650611134798 -4.650611134798 62 304 300.41051635668 3.58948364331957 63 304 301.353602961394 2.64639703860615 64 286 283.94222395927 2.05777604073046 65 320 314.906851255704 5.09314874429617 66 313 312.904056724697 0.0959432753027158 67 283 285.946755177542 -2.94675517754217 68 272 274.425928346298 -2.42592834629761 69 251 259.804062899839 -8.80406289983927 70 262 260.450313041766 1.54968695823391 71 247 252.026961520829 -5.02696152082945 72 268 262.456869783264 5.54313021673596 73 251 248.730732895842 2.26926710415825 74 257 259.058875577938 -2.05887557793773 75 261 256.008967592811 4.99103240718875 76 242 239.870300045455 2.12969995454466 77 274 272.022621664135 1.97737833586484 78 272 266.088665290476 5.91133470952389 79 243 241.801086970221 1.19891302977894 80 234 233.400345966203 0.599654033796867 81 217 218.769920540842 -1.76992054084209 82 231 228.437439169231 2.56256083076934 83 209 219.016891746628 -10.0168917466282 84 226 230.804741308723 -4.80474130872329 85 208 209.48219019738 -1.48219019737974 86 214 215.811900131031 -1.8119001310308 87 222 215.506716766544 6.49328323345583 88 194 199.296904609828 -5.2969046098284 89 230 226.43586589945 3.56413410054984 90 226 222.745979855425 3.25402014457535 91 197 194.711253014663 2.2887469853375 92 188 186.493777373946 1.50622262605393 93 175 171.315050991678 3.68494900832246 94 190 186.019060799601 3.98093920039867 95 165 172.890595232081 -7.89059523208124 96 176 188.100428425627 -12.1004284256267 97 159 163.249288039178 -4.249288039178 98 169 167.427213470512 1.57278652948838 99 170 172.189988866295 -2.18998886629478 100 141 145.626468186535 -4.62646818653459 101 170 175.980137740149 -5.98013774014851 102 164 165.25939932911 -1.25939932910964 103 132 132.920766727966 -0.920766727965685 104 123 121.147555621702 1.85244437829766 105 113 105.763734301818 7.23626569818178 106 125 121.738190038505 3.26180996149512 107 101 102.652644925829 -1.65264492582939 108 99 119.396361086631 -20.3963610866314 109 87 91.0349430096177 -4.03494300961773 110 90 96.3177401187613 -6.31774011876134 111 89 93.1871045294938 -4.18710452949384 112 66 62.8442558164945 3.15574418350549 113 102 96.316518880207 5.68348111979296 114 97 93.9183762803797 3.08162371962034 115 65 63.8589774287454 1.1410225712546 116 54 53.9222699892167 0.0777300107833128 117 33 38.8492822771176 -5.84928227711762 118 49 43.9747504482956 5.02524955170444 119 30 23.1170011651622 6.88299883483781 120 34 37.6018473752156 -3.60184737521563 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 25.920723626213 15.4325544804576 36.4088927719685 122 33.1206487488496 20.4768915456692 45.7644059520299 123 35.2556056019672 20.5444992634858 49.9667119404487 124 10.9511541394199 -5.78439911194383 27.6867073907836 125 43.9173853993292 25.1751399328385 62.6596308658199 126 37.2729754169988 16.5264912009963 58.0194596330013 127 4.71544596563955 -18.0427209059921 27.4736128372712 128 -6.22261549566044 -31.0065883683582 18.5613573770373 129 -23.4328408075865 -50.2613881676179 3.39570655244488 130 -10.2330751233618 -39.1282646152715 18.6621143685479 131 -33.4226193973938 -64.4088948828122 -2.43634391197549 132 -27.3126875305545 -60.4162178805927 5.79084281948378

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/04/t12809256508xupzezir6zv8m8/1gu9d1280925661.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/04/t12809256508xupzezir6zv8m8/1gu9d1280925661.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/04/t12809256508xupzezir6zv8m8/2gu9d1280925661.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/04/t12809256508xupzezir6zv8m8/2gu9d1280925661.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/04/t12809256508xupzezir6zv8m8/3r38g1280925661.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/04/t12809256508xupzezir6zv8m8/3r38g1280925661.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=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) 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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