Tijdreeks 2 - Stap 27

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 05 Aug 2010 17:03:11 +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/05/t12810278244a62ahwuv728cua.htm/, Retrieved Thu, 05 Aug 2010 19:04:40 +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/05/t12810278244a62ahwuv728cua.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:

Mathias Goossenaerts

Dataseries X:

» Textbox « » Textfile « » CSV «

430 429 428 426 424 423 424 426 427 427 428 430 432 435 426 411 405 403 402 399 392 387 380 379 386 385 365 356 338 338 343 338 320 316 317 315 317 321 303 303 290 285 300 291 278 273 277 269 275 278 255 254 245 240 261 247 229 213 218 206 217 219 196 193 188 171 190 180 149 135 151 134 145 151 137 124 125 109 131 133 103 85 104 82

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 0.307424590775851 beta 0.196794089031134 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 432 438.758814102564 -6.7588141025642 14 435 439.444724495245 -4.4447244952446 15 426 429.114806696529 -3.11480669652906 16 411 413.546961243023 -2.54696124302302 17 405 407.541262632317 -2.54126263231717 18 403 405.841904530174 -2.84190453017379 19 402 402.211521694026 -0.211521694025691 20 399 400.58531963483 -1.5853196348296 21 392 397.607534177317 -5.60753417731712 22 387 392.928968930485 -5.92896893048527 23 380 389.501221348796 -9.50122134879553 24 379 385.608791220062 -6.60879122006196 25 386 377.649749274919 8.35025072508051 26 385 382.370006021355 2.62999397864479 27 365 373.350881557889 -8.35088155788901 28 356 354.464617184795 1.53538281520508 29 338 347.862860828351 -9.86286082835107 30 338 341.406476921289 -3.40647692128869 31 343 337.092143569424 5.90785643057598 32 338 334.433822958113 3.56617704188653 33 320 328.603802339481 -8.60380233948132 34 316 320.949975484108 -4.94997548410754 35 317 313.57685155197 3.42314844803042 36 315 314.670543541699 0.329456458300683 37 317 318.634140610284 -1.63414061028442 38 321 315.148578134086 5.85142186591372 39 303 298.534947075446 4.46505292455373 40 303 290.231186940131 12.7688130598685 41 290 279.663922395435 10.3360776045649 42 285 285.585946458503 -0.585946458502747 43 300 290.457456862391 9.54254313760856 44 291 289.382500018535 1.61749998146513 45 278 276.494647276101 1.50535272389885 46 273 277.060638715541 -4.0606387155413 47 277 278.395207605667 -1.39520760566705 48 269 278.208765185761 -9.20876518576063 49 275 279.646844913491 -4.64684491349061 50 278 282.003858504252 -4.00385850425232 51 255 262.388507852757 -7.3885078527565 52 254 256.462720068085 -2.46272006808482 53 245 238.877625542906 6.12237445709434 54 240 235.034572697918 4.96542730208247 55 261 248.057953539296 12.9420464607039 56 247 242.175564125598 4.8244358744015 57 229 230.026115936374 -1.02611593637397 58 213 225.636034702473 -12.6360347024727 59 218 225.338554057704 -7.33855405770413 60 206 216.712160422525 -10.7121604225253 61 217 219.555236335325 -2.55523633532545 62 219 221.83482240719 -2.83482240719007 63 196 199.139707201191 -3.13970720119136 64 193 197.093604263142 -4.09360426314203 65 188 184.016313318857 3.98368668114301 66 171 177.648465039572 -6.64846503957168 67 190 190.857190139797 -0.857190139796927 68 180 172.507003930328 7.4929960696723 69 149 154.683919932116 -5.68391993211577 70 135 138.097308371729 -3.09730837172867 71 151 142.254395661699 8.74560433830081 72 134 135.062496105495 -1.06249610549492 73 145 145.931504579047 -0.931504579046731 74 151 148.024969406048 2.97503059395223 75 137 126.764620578345 10.2353794216547 76 124 128.838716875522 -4.83871687552221 77 125 121.75042860112 3.24957139887967 78 109 108.372850439621 0.62714956037911 79 131 128.848864899479 2.15113510052055 80 133 118.408339110442 14.5916608895578 81 103 95.272709433396 7.72729056660397 82 85 87.0429849328856 -2.04298493288563 83 104 102.232620766311 1.76737923368931 84 82 88.1867294804112 -6.1867294804112 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 99.3452668127692 87.3595368519948 111.330996773544 86 106.261147361343 93.4899146782371 119.032380044449 87 90.765030748451 77.0001385637869 104.529922933115 88 80.2838282979614 65.3234484894669 95.2442081064558 89 81.6088263231211 65.2632419280442 97.954410718198 90 66.543424376475 48.6375768412269 84.4492719117233 91 88.9715696628839 69.345354344465 108.597784981303 92 87.4450491408084 65.9523385621415 108.937759719475 93 55.1460189695004 31.6531298255621 78.6389081134387 94 37.3831157484463 11.7671510359541 62.9990804609386 95 55.5724121275189 27.7196985258109 83.4251257292269 96 35.1000718417996 4.90478273398765 65.2953609496116

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/05/t12810278244a62ahwuv728cua/1sojq1281027787.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/05/t12810278244a62ahwuv728cua/1sojq1281027787.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/05/t12810278244a62ahwuv728cua/2lf0b1281027787.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/05/t12810278244a62ahwuv728cua/2lf0b1281027787.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/05/t12810278244a62ahwuv728cua/3lf0b1281027787.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/05/t12810278244a62ahwuv728cua/3lf0b1281027787.ps (open in new window)

Parameters (Session):

par1 = additive ; par2 = 12 ;

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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