Tijdreeks 1 - 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: Mon, 19 Jul 2010 16:41:23 +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/Jul/19/t12795580381izkmdjei1zgozk.htm/, Retrieved Mon, 19 Jul 2010 18:47:22 +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/Jul/19/t12795580381izkmdjei1zgozk.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:

Van Puyenbroeck Cassandra

Dataseries X:

» Textbox « » Textfile « » CSV «

349 348 347 345 365 364 349 339 340 340 341 343 341 343 341 335 355 357 337 325 336 338 337 328 326 327 319 310 320 322 303 292 303 315 311 307 308 312 309 310 309 304 287 275 290 298 294 286 294 292 287 281 280 271 264 259 271 279 279 273 286 286 280 277 269 255 252 245 257 267 261 258 271 262 258 253 236 228 235 226 231 235 227 222 233 221 218 220 204 196 208 190 191 194 179 162 179 176 168 170 153 142 155 136 136 144 135 114 135 132 123 123 103 97 113 108 111 121 111 97

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 4 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.702888259538534 beta 0.015960640491968 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 347 347 0 4 345 346 -1 5 365 344.285893193645 20.7141068063551 6 364 358.066759304812 5.93324069518786 7 349 361.524890499142 -12.5248904991415 8 339 351.868506913518 -12.8685069135184 9 340 341.826233437177 -1.82623343717711 10 340 339.524956660657 0.475043339343074 11 341 338.846549608244 2.15345039175622 12 343 339.372033751735 3.62796624826456 13 341 340.974638288475 0.0253617115248517 14 343 340.045298914128 2.95470108587165 15 341 341.208105246675 -0.208105246674506 16 335 340.145477502427 -5.1454775024273 17 355 335.554703986386 19.4452960136142 18 357 348.466644431431 8.53335556856916 19 337 353.804441897818 -16.8044418978180 20 325 341.14407758436 -16.1440775843603 21 336 328.766762503661 7.23323749633943 22 338 332.902234146205 5.09776585379456 23 337 335.593897367519 1.40610263248146 24 328 335.706508280612 -7.70650828061179 25 326 329.327516145211 -3.32751614521112 26 327 325.989136274737 1.01086372526260 27 319 325.711493102665 -6.71149310266492 28 310 319.930602780694 -9.93060278069396 29 320 311.775631127658 8.22436887234193 30 322 316.473841369027 5.52615863097333 31 303 319.337506779288 -16.3375067792877 32 292 306.650175377529 -14.6501753775289 33 303 294.984495729674 8.01550427032595 34 315 299.340178510673 15.6598214893275 35 311 309.244642557612 1.75535744238823 36 307 309.395514630429 -2.39551463042892 37 308 306.601913263385 1.39808673661457 38 312 306.490474260114 5.50952573988565 39 309 309.330726334501 -0.330726334501094 40 310 308.062223524189 1.93777647581129 41 309 308.409963742089 0.590036257911038 42 304 307.817012533302 -3.81701253330203 43 287 304.083577136154 -17.0835771361538 44 275 290.833576325356 -15.8335763253561 45 290 278.284556691603 11.7154433083973 46 298 285.230849769443 12.7691502305572 47 294 293.061032381532 0.938967618467814 48 286 292.586452379574 -6.58645237957404 49 294 286.748452588521 7.25154741147924 50 292 290.718372210223 1.28162778977662 51 287 290.506483420803 -3.50648342080348 52 281 286.889749827684 -5.88974982768434 53 280 281.531771823637 -1.53177182363663 54 271 279.219781140045 -8.21978114004548 55 264 272.114653228725 -8.1146532287251 56 259 264.992383874875 -5.99238387487532 57 271 259.294606894382 11.7053931056179 58 279 266.16770707397 12.8322929260299 59 279 273.976851585956 5.02314841404433 60 273 276.353392529076 -3.35339252907619 61 286 272.804540996652 13.1954590033482 62 286 281.035716789809 4.96428321019067 63 280 283.536987799363 -3.53698779936263 64 277 280.023135361929 -3.02313536192901 65 269 276.836548584312 -7.83654858431225 66 255 270.178755477202 -15.1787554772017 67 252 258.189927767039 -6.1899277670388 68 245 252.449799526919 -7.44979952691864 69 257 245.740546293488 11.2594537065116 70 267 252.308122211105 14.6918777888955 71 261 261.453130236783 -0.453130236782897 72 258 259.94780646782 -1.94780646781976 73 271 257.370040766201 13.6299592337992 74 262 265.894612021863 -3.89461202186340 75 258 262.057676001175 -4.05767600117491 76 253 258.060602995689 -5.06060299568924 77 236 253.301811768958 -17.3018117689582 78 228 239.744717427596 -11.7447174275957 79 235 229.961880793617 5.03811920638339 80 226 232.032023367599 -6.03202336759867 81 231 226.253422158363 4.74657784163674 82 235 228.104222899082 6.89577710091805 83 227 231.543031164801 -4.54303116480131 84 222 226.890669189623 -4.890669189623 85 233 221.939090326960 11.0609096730396 86 221 228.323776300967 -7.32377630096673 87 218 221.703920221235 -3.70392022123511 88 220 217.586865878759 2.41313412124055 89 204 217.796489074683 -13.7964890746828 90 196 206.45778187606 -10.4577818760602 91 208 197.348491653813 10.6515083461873 92 190 203.196168141023 -13.1961681410228 93 191 192.133550978011 -1.13355097801104 94 194 189.536889003473 4.46311099652746 95 179 190.924124643105 -11.9241246431048 96 162 180.659193394793 -18.6591933947934 97 179 165.450932359077 13.5490676409227 98 176 173.033480715168 2.96651928483172 99 168 173.210960111243 -5.21096011124308 100 170 167.582125847232 2.41787415276835 101 153 167.342634655738 -14.3426346557384 102 142 155.161475080496 -13.161475080496 103 155 143.662886078968 11.3371139210320 104 136 149.511253605161 -13.5112536051612 105 136 137.742418697375 -1.74241869737526 106 144 134.226212268989 9.77378773101117 107 135 138.914259828772 -3.91425982877249 108 114 133.937227155638 -19.9372271556380 109 135 117.474172149243 17.5258278507569 110 132 127.540072993532 4.45992700646849 111 123 128.472139433995 -5.4721394339953 112 123 122.361683528074 0.638316471926402 113 103 120.553356322076 -17.5533563220762 114 97 105.761392738122 -8.76139273812159 115 113 97.0509070410085 15.9490929589915 116 108 105.888057273932 2.11194272606754 117 111 105.022929991010 5.9770700089905 118 121 106.941609336597 14.0583906634034 119 111 114.698268805559 -3.69826880555915 120 97 109.932491603429 -12.9324916034289 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 98.5310038482057 80.0423829634544 117.019624732957 122 96.2196126076133 73.5008021037576 118.938423111469 123 93.9082213670209 67.5267966374233 120.289646096618 124 91.5968301264285 61.9080981776696 121.285562075187 125 89.285438885836 56.5355672076013 122.035310564071 126 86.9740476452437 51.3444885158435 122.603606774644 127 84.6626564046513 46.2928634222252 123.032449387077 128 82.3512651640589 41.3516709396948 123.350859388423 129 80.0398739234665 36.4999076252998 123.579840221633 130 77.7284826828741 31.7218215139909 123.735143851757 131 75.4170914422817 27.0052603583769 123.828922526186 132 73.1057002016893 22.3406309261031 123.870769477275

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jul/19/t12795580381izkmdjei1zgozk/142ey1279557678.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/19/t12795580381izkmdjei1zgozk/142ey1279557678.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/19/t12795580381izkmdjei1zgozk/242ey1279557678.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/19/t12795580381izkmdjei1zgozk/242ey1279557678.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/19/t12795580381izkmdjei1zgozk/3wcdj1279557678.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/19/t12795580381izkmdjei1zgozk/3wcdj1279557678.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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