opgave 10-oefening 2- elke torfs mar 201

*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 08:16:46 -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/t1243952266jl5dr8qx9plle5i.htm/, Retrieved Tue, 02 Jun 2009 16:17:50 +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/t1243952266jl5dr8qx9plle5i.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 «

356445 291705 310900 332340 257166 334551 317365 270863 317904 423141 317684 411063 371161 299023 326964 327146 303447 351994 320317 257151 320274 476982 301723 363567 338831 265802 307691 334207 303127 318863 292123 245155 284794 391604 304982 369552 356021 247577 277885 294032 310845 311023 298462 234188 297478 371017 291128 316374 326001 222302 227424 255428 278250 280335 241894 255075 255115 319482 270694 300209 283531 218924 236466 267980 219994 256052 230444 200778 240960 277837 209776 232065

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.147667823524466 beta 0.124242853591504 gamma 0.292533149520714 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 371161 361157.915090309 10003.0849096908 14 299023 293480.223209457 5542.77679054317 15 326964 323388.042746108 3575.95725389244 16 327146 323045.450720606 4100.54927939392 17 303447 299982.360968186 3464.63903181400 18 351994 352748.677695795 -754.67769579502 19 320317 326917.034848067 -6600.03484806692 20 257151 278431.175896412 -21280.1758964119 21 320274 322885.822104651 -2611.82210465142 22 476982 429590.000615249 47391.9993847507 23 301723 327430.411907507 -25707.411907507 24 363567 416559.126517708 -52992.1265177078 25 338831 370781.708270665 -31950.7082706649 26 265802 294297.353265327 -28495.3532653265 27 307691 316049.58595791 -8358.5859579101 28 334207 311809.858004804 22397.1419951958 29 303127 290189.700722495 12937.2992775055 30 318863 339838.660850376 -20975.6608503757 31 292123 308708.708341529 -16585.7083415294 32 245155 255999.928903402 -10844.9289034021 33 284794 301593.359756330 -16799.3597563303 34 391604 406909.956302716 -15305.9563027158 35 304982 286634.188985718 18347.8110142816 36 369552 364816.467473492 4735.53252650757 37 356021 333449.319457376 22571.6805426237 38 247577 269362.671005350 -21785.6710053502 39 277885 294653.697907713 -16768.6979077131 40 294032 295671.763292971 -1639.76329297089 41 310845 269139.195544959 41705.8044550411 42 311023 311206.657278730 -183.657278730476 43 298462 285577.402795548 12884.5972044519 44 234188 241210.153113655 -7022.15311365537 45 297478 284077.499066064 13400.5009339358 46 371017 392163.73739877 -21146.7373987695 47 291128 283399.997402719 7728.00259728072 48 316374 355076.83749303 -38702.8374930298 49 326001 322936.120528219 3064.87947178097 50 222302 248886.550308959 -26584.5503089590 51 227424 272390.39427674 -44966.39427674 52 255428 271352.536469898 -15924.5364698984 53 278250 253349.06131997 24900.9386800301 54 280335 278183.884870883 2151.11512911710 55 241894 256885.912955354 -14991.9129553536 56 255075 208045.478801176 47029.5211988241 57 255115 258255.514490803 -3140.51449080318 58 319482 343012.819417679 -23530.8194176793 59 270694 251177.374004127 19516.6259958728 60 300209 304969.700391699 -4760.70039169939 61 283531 289256.273223095 -5725.27322309453 62 218924 214825.659061911 4098.34093808889 63 236466 235713.103595418 752.896404582309 64 267980 248404.329910087 19575.6700899135 65 219994 247414.126846901 -27420.1268469013 66 256052 258092.299543123 -2040.29954312256 67 230444 234149.675240082 -3705.67524008173 68 200778 204689.920864555 -3911.92086455479 69 240960 231211.159005087 9748.84099491325 70 277837 304676.136356123 -26839.1363561229 71 209776 230253.009807971 -20477.0098079710 72 232065 265177.70131122 -33112.7013112198 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 245284.756237227 229107.042437408 261462.470037046 74 183101.802187382 166130.785475117 200072.818899648 75 197950.651322263 179082.590229975 216818.712414552 76 210632.287350266 189419.6395728 231844.935127732 77 195738.26560289 173250.808965976 218225.722239804 78 211446.175941396 185578.812880892 237313.539001899 79 190121.875229136 163585.742718653 216658.00773962 80 165123.004770323 138597.231209813 191648.778330833 81 188421.627648825 156498.093646389 220345.16165126 82 236652.735908474 194534.003945037 278771.467871911 83 179832.658266007 143315.356784557 216349.959747457 84 206684.005369926 164914.322234310 248453.688505542

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243952266jl5dr8qx9plle5i/1lu5v1243952204.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243952266jl5dr8qx9plle5i/1lu5v1243952204.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243952266jl5dr8qx9plle5i/25jmk1243952204.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243952266jl5dr8qx9plle5i/25jmk1243952204.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243952266jl5dr8qx9plle5i/36u2d1243952204.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243952266jl5dr8qx9plle5i/36u2d1243952204.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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