exponential smoothing 10b - Kelly Michielsen - MAR 201b

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 03 Jun 2009 02:19:01 -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/03/t1244017172r1wocut1zhjyxwq.htm/, Retrieved Wed, 03 Jun 2009 10:19:35 +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/03/t1244017172r1wocut1zhjyxwq.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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104.9 110.9 104.8 94.1 95.8 99.3 101.1 104.0 99.0 105.4 107.1 110.7 117.1 118.7 126.5 127.5 134.6 131.8 135.9 142.7 141.7 153.4 145.0 137.7 148.3 152.2 169.4 168.6 161.1 174.1 179.0 190.6 190.0 181.6 174.8 180.5 196.8 193.8 197.0 216.3 221.4 217.9 229.7 227.4 204.2 196.6 198.8 207.5 190.7 201.6 210.5 223.5 223.8 231.2 244.0 234.7 250.2 265.7 287.6 283.3 295.4 312.3 333.8 347.7 383.2 407.1 413.6 362.7 321.9 239.4 191.0 159.7 166.7

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.957353257069885 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 117.1 102.176630818784 14.9233691812163 14 118.7 117.89579914111 0.804200858889956 15 126.5 125.944512373948 0.555487626051615 16 127.5 126.579275046608 0.920724953391655 17 134.6 133.844318573042 0.755681426957523 18 131.8 131.948238356519 -0.148238356518533 19 135.9 132.864555390299 3.03544460970102 20 142.7 141.423918784884 1.27608121511639 21 141.7 136.911380455069 4.78861954493138 22 153.4 150.256350933496 3.14364906650397 23 145 154.300635295941 -9.3006352959407 24 137.7 149.168704141094 -11.4687041410942 25 148.3 146.356713665365 1.94328633463502 26 152.2 148.507653062294 3.69234693770568 27 169.4 160.519859943898 8.8801400561016 28 168.6 168.205148518705 0.394851481295092 29 161.1 176.055387922463 -14.9553879224631 30 174.1 157.968453386798 16.1315466132021 31 179 174.089560519295 4.91043948070464 32 190.6 185.221677432176 5.37832256782394 33 190 182.007472051937 7.99252794806296 34 181.6 200.333118707867 -18.7331187078675 35 174.8 182.444294692526 -7.64429469252596 36 180.5 178.942793406800 1.55720659320033 37 196.8 190.980463055551 5.81953694444854 38 193.8 196.099520064709 -2.29952006470918 39 197 204.141850797993 -7.14185079799313 40 216.3 195.455026844545 20.8449731554553 41 221.4 223.226498741323 -1.82649874132269 42 217.9 216.960528308513 0.93947169148717 43 229.7 217.392807828502 12.3071921714979 44 227.4 236.619824888423 -9.21982488842281 45 204.2 217.385637574193 -13.1856375741935 46 196.6 214.734558725146 -18.1345587251464 47 198.8 197.681111574902 1.11888842509794 48 207.5 203.154724883023 4.34527511697695 49 190.7 219.195992521388 -28.4959925213879 50 201.6 191.206462772830 10.3935372271696 51 210.5 211.451524222904 -0.951524222904283 52 223.5 209.551429079484 13.948570920516 53 223.8 229.871774609051 -6.07177460905118 54 231.2 219.572119327681 11.6278806723193 55 244 230.528062143687 13.4719378563130 56 234.7 250.154272103299 -15.4542721032990 57 250.2 224.281654995413 25.9183450045866 58 265.7 260.304191031535 5.39580896846536 59 287.6 266.022524621445 21.5774753785553 60 283.3 291.985011157394 -8.68501115739411 61 295.4 296.698905157106 -1.29890515710639 62 312.3 295.317737440162 16.9822625598378 63 333.8 325.121147513917 8.67885248608269 64 347.7 331.108987711213 16.5910122887865 65 383.2 354.837338626846 28.3626613731541 66 407.1 373.549925520866 33.5500744791339 67 413.6 403.30566988664 10.2943301133598 68 362.7 420.409578669385 -57.7095786693847 69 321.9 348.989932621302 -27.0899326213023 70 239.4 335.578167141133 -96.1781671411326 71 191 244.812215446257 -53.812215446257 72 159.7 196.901756882860 -37.2017568828596 73 166.7 170.130429651811 -3.43042965181058 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 168.438280600603 127.694761980994 209.181799220213 75 176.915212761224 119.620827371940 234.209598150508 76 177.221119879369 108.579007853279 245.86323190546 77 182.887199178161 103.05313031362 262.721268042702 78 180.416761824090 93.6103414532014 267.223182194979 79 180.505292999767 86.5206998067393 274.489886192794 80 183.844248798887 81.853255678764 285.83524191901 81 177.597201280098 72.9635156010914 282.230886959105 82 183.258367614344 70.0029317216867 296.513803507002 83 185.82098109827 66.1442313889135 305.497730807626 84 189.753352818501 63.1727874231555 316.333918213847 85 201.424835708858 68.7698022934731 334.079869124243

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244017172r1wocut1zhjyxwq/1nt4f1244017139.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244017172r1wocut1zhjyxwq/1nt4f1244017139.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244017172r1wocut1zhjyxwq/2ufuo1244017139.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244017172r1wocut1zhjyxwq/2ufuo1244017139.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244017172r1wocut1zhjyxwq/3ehb01244017139.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244017172r1wocut1zhjyxwq/3ehb01244017139.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')

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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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