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, 29 Jul 2010 12:58:25 +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/29/t1280408287beok07dnsz0w69u.htm/, Retrieved Thu, 29 Jul 2010 14:58:07 +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/29/t1280408287beok07dnsz0w69u.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:

Habimana Christelle

Dataseries X:

» Textbox « » Textfile « » CSV «

376 375 374 372 370 369 370 372 373 373 374 376 371 374 369 363 357 366 362 366 361 362 358 363 360 360 348 345 332 333 323 327 332 337 336 337 343 337 326 321 309 302 293 287 292 292 289 302 310 295 276 264 257 243 227 226 226 229 224 240 244 226 208 199 193 180 167 164 166 173 169 191 193 166 143 147 139 129 115 108 106 116 108 135

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.17405321302253 beta 0.155374088159449 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 371 374.488782051282 -3.48878205128227 14 374 376.675603202716 -2.67560320271582 15 369 371.098270113510 -2.09827011351041 16 363 364.773012764285 -1.77301276428483 17 357 358.623085947253 -1.62308594725272 18 366 367.538694011388 -1.53869401138763 19 362 362.469045974832 -0.469045974831545 20 366 363.572889037032 2.42711096296767 21 361 364.246454753421 -3.24645475342118 22 362 363.178056418678 -1.17805641867830 23 358 363.771144190277 -5.77114419027686 24 363 364.158719151829 -1.15871915182885 25 360 355.227884193784 4.77211580621605 26 360 359.136574941226 0.86342505877434 27 348 354.360166038926 -6.36016603892637 28 345 347.15459982716 -2.15459982716004 29 332 340.644611286876 -8.64461128687589 30 333 347.80044107954 -14.8004410795398 31 323 340.340011049965 -17.3400110499645 32 327 339.477227717233 -12.4772277172326 33 332 331.045266404497 0.954733595502944 34 337 330.704783985323 6.29521601467667 35 336 327.295373765936 8.70462623406428 36 337 332.893995199172 4.10600480082832 37 343 328.802306737405 14.1976932625948 38 337 330.402328537964 6.59767146203558 39 326 320.091904650806 5.90809534919407 40 321 318.261240514118 2.73875948588221 41 309 307.140883508303 1.85911649169736 42 302 311.222919851203 -9.22291985120336 43 293 302.968947385222 -9.96894738522155 44 287 307.938081689494 -20.9380816894941 45 292 309.431316986699 -17.4313169866991 46 292 310.108167252241 -18.1081672522406 47 289 303.587894503197 -14.5878945031967 48 302 299.850833366293 2.14916663370724 49 310 302.217501217653 7.78249878234749 50 295 294.713988433853 0.28601156614684 51 276 280.855022415635 -4.85502241563495 52 264 272.361805144265 -8.36180514426519 53 257 256.111129203723 0.88887079627699 54 243 248.373188462661 -5.37318846266055 55 227 237.779274345754 -10.7792743457542 56 226 231.131712717639 -5.13171271763855 57 226 236.284220987578 -10.2842209875784 58 229 235.851008086266 -6.85100808626552 59 224 232.707073538354 -8.70707353835397 60 240 242.485982721617 -2.48598272161672 61 244 247.241843180283 -3.2418431802825 62 226 229.872796143532 -3.8727961435317 63 208 209.176275068043 -1.17627506804314 64 199 196.658944637181 2.34105536281902 65 193 188.433148300843 4.56685169915735 66 180 174.784155461458 5.21584453854172 67 167 160.475431552542 6.5245684474582 68 164 160.879473035130 3.1205269648697 69 166 162.811009062392 3.18899093760788 70 173 167.521260638162 5.47873936183774 71 169 165.28654222958 3.71345777042015 72 191 182.997662933404 8.00233706659606 73 193 189.870476200535 3.12952379946466 74 166 174.177283218823 -8.17728321882322 75 143 155.930358198954 -12.9303581989537 76 147 144.926072651367 2.07392734863311 77 139 139.138700169714 -0.138700169714326 78 129 125.725999540620 3.27400045938026 79 115 112.626988832728 2.37301116727181 80 108 109.851370345917 -1.85137034591713 81 106 111.194111504069 -5.1941115040689 82 116 116.329792502009 -0.329792502009028 83 108 111.462294570306 -3.46229457030607 84 135 131.109024918507 3.89097508149294 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 132.772559242198 118.798813406849 146.746305077547 86 106.642210105287 92.3887165158134 120.895703694760 87 85.5602901482995 70.9546327335236 100.165947563075 88 89.2165064048414 74.1818586857312 104.251154123951 89 81.201751627796 65.658460393508 96.745042862084 90 70.5967562596923 54.4638503864421 86.7296621329425 91 56.0600410021235 39.2565743083007 72.8635076959463 92 49.1944187264228 31.6405861600407 66.7482512928049 93 47.9606785629975 29.5786792495783 66.3426778764167 94 58.0207542715621 38.7354052151096 77.3061033280146 95 50.6349707270281 30.3740966464391 70.895844807617 96 77.062959049322 55.7575958295069 98.3683222691372

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jul/29/t1280408287beok07dnsz0w69u/1wb6s1280408300.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/29/t1280408287beok07dnsz0w69u/1wb6s1280408300.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/29/t1280408287beok07dnsz0w69u/2plnv1280408300.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/29/t1280408287beok07dnsz0w69u/2plnv1280408300.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/29/t1280408287beok07dnsz0w69u/3plnv1280408300.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/29/t1280408287beok07dnsz0w69u/3plnv1280408300.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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