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: Mon, 02 Aug 2010 14:17:42 +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/02/t12807588609cyavhudg1gbie0.htm/, Retrieved Mon, 02 Aug 2010 16:21:01 +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/02/t12807588609cyavhudg1gbie0.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 «

408 407 406 404 402 401 402 404 405 405 406 408 405 400 402 404 410 402 400 392 390 397 394 397 400 395 391 392 395 386 385 372 367 364 364 368 370 357 350 353 353 348 337 322 315 316 317 326 329 310 301 299 300 295 274 258 250 247 248 256 253 237 225 214 221 221 207 194 191 185 180 185 189 179 162 148 152 151 134 122 119 115 113 109

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.385319959597228 beta 0.126395076856841 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 405 404.604433760684 0.395566239316054 14 400 399.990716313063 0.00928368693701032 15 402 402.770275293822 -0.770275293822124 16 404 405.045273605086 -1.04527360508581 17 410 411.038402092426 -1.03840209242622 18 402 403.10860548517 -1.10860548516996 19 400 397.306099533256 2.6939004667438 20 392 400.349974832255 -8.3499748322547 21 390 397.773426181316 -7.77342618131627 22 397 393.748780921141 3.25121907885949 23 394 394.630494173634 -0.630494173633792 24 397 394.944132494406 2.05586750559428 25 400 392.052818909084 7.94718109091576 26 395 389.87967380815 5.12032619185021 27 391 394.166585508922 -3.16658550892197 28 392 395.249640657892 -3.24964065789209 29 395 400.190686981649 -5.19068698164949 30 386 390.208633337376 -4.2086333373764 31 385 384.98882387509 0.0111761249100937 32 372 379.519761302911 -7.51976130291058 33 367 376.967156034955 -9.96715603495471 34 364 378.116664632598 -14.1166646325984 35 364 368.31712618489 -4.31712618489041 36 368 367.078888357448 0.921111642552262 37 370 365.533741905851 4.46625809414854 38 357 358.274324945194 -1.27432494519417 39 350 352.684623450914 -2.68462345091416 40 353 351.606981379291 1.39301862070857 41 353 355.074569403655 -2.07456940365512 42 348 344.979384539434 3.02061546056621 43 337 343.573582111179 -6.57358211117884 44 322 329.052069877344 -7.05206987734368 45 315 323.311994559176 -8.31199455917624 46 316 320.765944176461 -4.76594417646083 47 317 319.265703917486 -2.26570391748641 48 326 320.810368033207 5.18963196679306 49 329 322.069593990196 6.93040600980396 50 310 311.331546432876 -1.33154643287583 51 301 303.950633025261 -2.95063302526131 52 299 304.361701015488 -5.36170101548828 53 300 301.850895219406 -1.85089521940648 54 295 293.740490047029 1.2595099529708 55 274 284.439651568884 -10.439651568884 56 258 266.626976107296 -8.62697610729606 57 250 257.921532865865 -7.92153286586466 58 247 256.140563474066 -9.1405634740658 59 248 252.713429684825 -4.7134296848252 60 256 256.000258710118 -0.000258710118487215 61 253 254.179650712091 -1.17965071209116 62 237 232.693114207109 4.30688579289065 63 225 224.219122111241 0.780877888758567 64 214 222.49725549439 -8.49725549438966 65 221 218.694845863751 2.30515413624943 66 221 212.058729264729 8.94127073527062 67 207 196.8616825976 10.1383174023995 68 194 187.429621346776 6.57037865322368 69 191 185.091090587889 5.90890941211131 70 185 188.640977102408 -3.64097710240847 71 180 191.073082575933 -11.0730825759331 72 185 195.515639332241 -10.5156393322413 73 189 189.11530756775 -0.115307567749511 74 179 171.66019541497 7.33980458502995 75 162 162.584038865561 -0.584038865560757 76 148 154.96324233736 -6.96324233735993 77 152 158.796737688916 -6.79673768891575 78 151 152.694077120603 -1.69407712060283 79 134 133.578359025701 0.421640974299237 80 122 117.179440476513 4.82055952348716 81 119 112.645169699733 6.35483030026651 82 115 109.403563445133 5.59643655486659 83 113 110.18335708669 2.81664291330964 84 109 120.353711739743 -11.353711739743 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 120.015674235211 109.084749489666 130.946598980755 86 107.185460738125 95.2693712604991 119.101550215751 87 90.0509951095194 77.0188799564509 103.083110262588 88 78.4030080845916 64.1348460048849 92.6711701642983 89 85.0299911248548 69.4161100469001 100.643872202809 90 85.0218356304147 67.9619016480715 102.081769612758 91 68.2809575938653 49.682799964765 86.8791152229656 92 54.8245534507639 34.6030187901786 75.0460881113492 93 49.5421906324489 27.6181134444128 71.466267820485 94 43.2425556470354 19.5418725489075 66.9432387451634 95 39.741469927042 14.1944751348966 65.2884647191874 96 39.56332700865 12.1040540049651 67.0226000123348

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/02/t12807588609cyavhudg1gbie0/1aef01280758657.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/02/t12807588609cyavhudg1gbie0/1aef01280758657.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/02/t12807588609cyavhudg1gbie0/235w31280758657.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/02/t12807588609cyavhudg1gbie0/235w31280758657.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/02/t12807588609cyavhudg1gbie0/335w31280758657.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/02/t12807588609cyavhudg1gbie0/335w31280758657.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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