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 14:34:16 +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/t1280414120g9tg96bd55q01d4.htm/, Retrieved Thu, 29 Jul 2010 16:35:21 +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/t1280414120g9tg96bd55q01d4.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:

Patrick Fieremans

Dataseries X:

» Textbox « » Textfile « » CSV «

259 258 257 255 253 252 253 255 256 256 257 259 267 263 266 257 249 249 251 252 252 252 256 257 259 260 261 253 243 233 241 239 233 228 228 227 225 230 222 207 190 184 192 187 173 167 163 156 153 157 152 128 115 114 136 132 126 124 123 119 105 107 108 92 74 73 100 97 99 102 99 103 92 99 97 87 69 66 95 91 93 99 91 91

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 1 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.703339343785154 beta 0.111780621846133 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 267 266.698985042735 0.30101495726484 14 263 263.06737923417 -0.0673792341703461 15 266 266.254703294283 -0.25470329428282 16 257 257.331916940614 -0.331916940614121 17 249 249.203727978248 -0.203727978248168 18 249 249.066348988811 -0.0663489888105175 19 251 252.72871104278 -1.72871104277996 20 252 252.710957701073 -0.710957701073482 21 252 252.311468372467 -0.311468372467147 22 252 251.293468053218 0.706531946781695 23 256 252.588681413358 3.41131858664176 24 257 257.262807842518 -0.262807842518498 25 259 265.33808068527 -6.33808068526997 26 260 256.443489695685 3.55651030431545 27 261 261.924815363002 -0.924815363002153 28 253 252.255871755537 0.744128244462729 29 243 244.755199868646 -1.75519986864552 30 233 243.278051869614 -10.2780518696139 31 241 238.172810262115 2.82718973788542 32 239 240.927358314087 -1.92735831408686 33 233 238.961236034472 -5.96123603447214 34 228 232.997746078847 -4.99774607884723 35 228 229.361064976328 -1.36106497632835 36 227 227.491159037687 -0.491159037686742 37 225 231.488117681057 -6.48811768105722 38 230 223.296128368875 6.70387163112531 39 222 227.781921449197 -5.78192144919723 40 207 212.930267047946 -5.93026704794619 41 190 197.207412128505 -7.20741212850544 42 184 186.152096617264 -2.15209661726439 43 192 188.073811607013 3.92618839298657 44 187 187.701087248775 -0.70108724877477 45 173 183.007411860488 -10.0074118604882 46 167 171.772462666732 -4.77246266673185 47 163 166.679350019811 -3.67935001981115 48 156 160.560964536619 -4.56096453661883 49 153 156.720434909742 -3.72043490974195 50 157 151.4102321477 5.58976785230041 51 152 148.342420283441 3.65757971655884 52 128 137.762092616605 -9.76209261660503 53 115 116.34019078805 -1.3401907880498 54 114 108.74742080641 5.25257919359026 55 136 116.098661806031 19.9013381939695 56 132 125.263457993688 6.73654200631194 57 126 123.299183564407 2.70081643559263 58 124 123.813596043138 0.186403956862137 59 123 124.180558819298 -1.18055881929804 60 119 121.402611306797 -2.40261130679667 61 105 121.343657746784 -16.343657746784 62 107 110.938751721999 -3.93875172199904 63 108 100.868558657663 7.13144134233664 64 92 89.2961654422711 2.70383455772891 65 74 80.6662748405034 -6.66627484050345 66 73 72.3903279513047 0.609672048695259 67 100 81.5637682203232 18.4362317796768 68 97 86.4194621839055 10.5805378160945 69 99 86.8906359175686 12.1093640824314 70 102 94.9452758171043 7.05472418289565 71 99 101.946212647575 -2.94621264757464 72 103 99.6337995345362 3.36620046546376 73 92 102.019983676966 -10.0199836769657 74 99 102.763444802236 -3.76344480223604 75 97 99.1350561276357 -2.13505612763575 76 87 82.03755798873 4.96244201127006 77 69 74.6999471899395 -5.69994718993945 78 66 71.8215712556196 -5.82157125561956 79 95 83.8139090291303 11.1860909708697 80 91 82.7236194674907 8.27638053250928 81 93 83.3303802369769 9.66961976302308 82 99 89.2803760936421 9.71962390635794 83 91 96.5091078205981 -5.5091078205981 84 91 95.3856107981544 -4.38561079815436 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 88.8578982572924 76.1752451530761 101.540551361509 86 99.8020565938264 83.7022791195334 115.901834068119 87 100.896786044547 81.4461449149307 120.347427174162 88 89.1674233036494 66.3592679771602 111.975578630139 89 76.5471926387797 50.3394684988334 102.754916778726 90 79.4606331550801 49.7922248949589 109.129041415201 91 102.869605920986 69.6685618949362 136.070649947036 92 94.4456452978064 57.633719587132 131.257571008481 93 90.3910780776652 49.886404992253 130.895751163077 94 89.541118282155 45.2598607475646 133.822375816745 95 84.6379706609443 36.4953699985855 132.780571323303 96 87.3777478361247 35.2888078049693 139.46668786728

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jul/29/t1280414120g9tg96bd55q01d4/12xdd1280414053.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/29/t1280414120g9tg96bd55q01d4/12xdd1280414053.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/29/t1280414120g9tg96bd55q01d4/2douy1280414053.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/29/t1280414120g9tg96bd55q01d4/2douy1280414053.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/29/t1280414120g9tg96bd55q01d4/3douy1280414053.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/29/t1280414120g9tg96bd55q01d4/3douy1280414053.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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