opgave 10 - oef 2/blog - Van Mechelen Wout

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 05 Jun 2009 04:32:45 -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/05/t12441979984u7p0xgp0kch1ub.htm/, Retrieved Fri, 05 Jun 2009 12:33:22 +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/2009/Jun/05/t12441979984u7p0xgp0kch1ub.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:

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266433 267722 266003 262971 265521 264676 270223 269508 268457 265814 266680 263018 269285 269829 270911 266844 271244 269907 271296 270157 271322 267179 264101 265518 269419 268714 272482 268351 268175 270674 272764 272599 270333 270846 270491 269160 274027 273784 276663 274525 271344 271115 270798 273911 273985 271917 273338 270601 273547 275363 281229 277793 279913 282500 280041 282166 290304 283519 287816 285226 287595 289741 289148 288301 290155 289648 288225 289351 294735 305333 309030 310215 321935

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 0.909335006287375 beta 0.0820112173986116 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 269285 267036.963587938 2248.03641206183 14 269829 269956.087441595 -127.087441595097 15 270911 271170.191826702 -259.19182670163 16 266844 267062.253623455 -218.253623455414 17 271244 271674.78701356 -430.787013560126 18 269907 270275.071238274 -368.071238273929 19 271296 272914.495646938 -1618.49564693752 20 270157 270694.894581584 -537.894581584318 21 271322 268996.716820131 2325.28317986906 22 267179 268383.934385677 -1204.93438567704 23 264101 267978.393974333 -3877.39397433336 24 265518 260308.99111018 5209.00888982008 25 269419 271628.582124246 -2209.58212424570 26 268714 270038.900248436 -1324.90024843649 27 272482 269817.627795619 2664.37220438116 28 268351 268240.110135488 110.889864511730 29 268175 273069.616157436 -4894.61615743616 30 270674 267210.580163912 3463.41983608826 31 272764 273090.010729606 -326.010729606496 32 272599 272101.221012437 497.77898756275 33 270333 271632.364748922 -1299.36474892183 34 270846 267185.517699482 3660.48230051773 35 270491 271094.687152619 -603.687152618659 36 269160 267511.707926336 1648.29207366367 37 274027 275102.447981403 -1075.44798140280 38 273784 274824.034737523 -1040.03473752266 39 276663 275462.551664384 1200.44833561569 40 274525 272360.730914948 2164.2690850519 41 271344 278947.796646886 -7603.79664688563 42 271115 271430.998603056 -315.99860305601 43 270798 273309.685809758 -2511.68580975791 44 273911 270026.684724045 3884.31527595507 45 273985 272336.431310992 1648.56868900813 46 271917 271064.142755852 852.857244147512 47 273338 271909.167855247 1428.83214475308 48 270601 270373.748501195 227.251498804777 49 273547 276373.387849601 -2826.38784960087 50 275363 274294.375559287 1068.62444071274 51 281229 277007.145761278 4221.85423872236 52 277793 276839.591703434 953.408296566282 53 279913 281538.258895376 -1625.25889537612 54 282500 280645.135185097 1854.86481490283 55 280041 285071.065866953 -5030.06586695346 56 282166 280569.156570317 1596.84342968272 57 290304 280881.215734922 9422.78426507779 58 283519 287335.198788099 -3816.19878809917 59 287816 284532.050513842 3283.94948615762 60 285226 285085.409702811 140.590297188726 61 287595 291692.649041344 -4097.64904134435 62 289741 289440.89696119 300.103038810194 63 289148 292368.828148631 -3220.82814863132 64 288301 284980.202394883 3320.79760511749 65 290155 291869.663409974 -1714.66340997408 66 289648 291381.338234087 -1733.33823408716 67 288225 291839.019646254 -3614.01964625437 68 289351 289230.559528781 120.440471219423 69 294735 288746.471936757 5988.5280632429 70 305333 290445.089464971 14887.9105350295 71 309030 306356.042143161 2673.95785683906 72 310215 306766.552391678 3448.44760832243 73 321935 317666.33408638 4268.66591362015 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 325422.61644011 318581.935284816 332263.297595403 75 329803.748539347 320181.520720576 339425.976358117 76 327380.366946838 315458.450049121 339302.283844554 77 332982.676776855 318675.494227277 347289.859326433 78 336076.143786297 319534.599115959 352617.688456635 79 340252.288218566 321450.873076376 359053.703360755 80 343784.157516855 322754.771464654 364813.543569056 81 346015.722146355 322825.365145904 369206.079146805 82 344266.049813088 319171.722529072 369360.377097103 83 346237.360765989 318977.958341959 373496.763190018 84 344379.765529816 315241.895051493 373517.63600814 85 353143.58931973 321962.433955165 384324.744684294

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t12441979984u7p0xgp0kch1ub/1t0hw1244197963.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t12441979984u7p0xgp0kch1ub/1t0hw1244197963.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t12441979984u7p0xgp0kch1ub/2ero71244197963.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t12441979984u7p0xgp0kch1ub/2ero71244197963.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t12441979984u7p0xgp0kch1ub/3pi2y1244197963.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t12441979984u7p0xgp0kch1ub/3pi2y1244197963.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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