10.2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 24 Dec 2010 14:48:17 +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/Dec/24/t1293201976z95ip0evnpqoeub.htm/, Retrieved Fri, 24 Dec 2010 15:46:20 +0100

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/Dec/24/t1293201976z95ip0evnpqoeub.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:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

89,3 88,1 93,6 79,7 83,8 62,3 62,3 77,6 80,3 97 94 75,1 74 77,6 75,1 85 75,4 63,2 64,7 77 82,6 97,6 99 75,3 71,6 76,8 83,9 79,7 77,5 73,1 65,6 85,2 98,3 98 100,6 84,1 76,7 82,4 95,5 79,9 82,4 83,6 73,1 91,1 118,6 102,9 111,8 93,9 91,6 92 91,1 97,5 94,7 96,7 78,7 103,5 113,8 106,1 120,3 114,2 106,3 98,8 113,1 97,7 116,3 107,2 94,5 123,5 126,6 126,5 141,4 124,3 124,9 108,9 126,7 107,7 121,8 118,3 122,8 149,5 147 139,3 162,1 142,2 141,4 124,7 114 126,6 121,9 125,1 122,1 135,9 148,4 137,5 145,3 139,9 128,2 115,4 124,7 111,5 121,1 122,5 127,4 143,7 157,8 148,8 162,9 153,9

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.238478317886849 beta 0.0332524755449531 gamma 0.786856072763765 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 74 76.1609807081855 -2.16098070818548 14 77.6 79.0715192698551 -1.47151926985515 15 75.1 75.9320633301454 -0.83206333014536 16 85 85.3702471707489 -0.370247170748897 17 75.4 75.2330732961018 0.16692670389817 18 63.2 62.7602291643611 0.439770835638889 19 64.7 59.9747603108474 4.72523968915258 20 77 76.9857929700979 0.0142070299020816 21 82.6 80.737854397984 1.862145602016 22 97.6 98.590085292572 -0.99008529257209 23 99 95.3036784097252 3.69632159027485 24 75.3 77.0443186004388 -1.7443186004388 25 71.6 73.9638293823682 -2.36382938236817 26 76.8 77.2147861428936 -0.414786142893647 27 83.9 74.7678706727276 9.13212932727244 28 79.7 87.221791561436 -7.52179156143598 29 77.5 75.7272089028127 1.77279109718732 30 73.1 63.7419643602922 9.35803563970784 31 65.6 65.7266265579438 -0.126626557943766 32 85.2 79.2392222151445 5.96077778485555 33 98.3 85.923694277481 12.376305722519 34 98 106.148503406018 -8.1485034060185 35 100.6 104.187778000516 -3.58777800051568 36 84.1 79.9568905416234 4.14310945837656 37 76.7 77.8784201026497 -1.17842010264968 38 82.4 83.1904662296599 -0.79046622965987 39 95.5 86.705936204537 8.79406379546302 40 79.9 89.2371047653084 -9.33710476530837 41 82.4 82.75425249186 -0.354252491859938 42 83.6 74.2039821018118 9.3960178981882 43 73.1 70.2437180091495 2.85628199085046 44 91.1 89.6339225146001 1.46607748539991 45 118.6 99.6214602990688 18.9785397009312 46 102.9 109.646879399444 -6.74687939944442 47 111.8 111.20817886582 0.59182113417981 48 93.9 90.9098801962 2.99011980379998 49 91.6 84.9414952417987 6.65850475820132 50 92 93.3551953110195 -1.3551953110195 51 91.1 103.838593280986 -12.7385932809861 52 97.5 89.578106760884 7.92189323911596 53 94.7 92.9771154747697 1.7228845252303 54 96.7 90.4818649150129 6.21813508498714 55 78.7 80.792937942156 -2.09293794215606 56 103.5 100.231119765343 3.26888023465663 57 113.8 123.074772075817 -9.27477207581728 58 106.1 110.425674864106 -4.32567486410616 59 120.3 117.373090491436 2.92690950856441 60 114.2 98.0002142902896 16.1997857097104 61 106.3 97.0108623302688 9.28913766973125 62 98.8 101.5715103602 -2.77151036020022 63 113.1 105.144676842999 7.95532315700119 64 97.7 108.537492182488 -10.8374921824884 65 116.3 103.648649972666 12.6513500273344 66 107.2 106.560862008207 0.639137991792992 67 94.5 88.821026272786 5.67897372721407 68 123.5 116.807493792395 6.69250620760509 69 126.6 135.306892493306 -8.70689249330616 70 126.5 124.849835511515 1.65016448848509 71 141.4 140.04766311641 1.35233688358954 72 124.3 126.053479973353 -1.75347997335339 73 124.9 115.508293700746 9.39170629925364 74 108.9 112.372600800479 -3.47260080047873 75 126.7 123.562341312867 3.13765868713308 76 107.7 113.357500396483 -5.65750039648297 77 121.8 125.153856399775 -3.35385639977471 78 118.3 116.411184433191 1.88881556680887 79 122.8 100.589716017468 22.2102839825317 80 149.5 136.795936209635 12.7040637903651 81 147 148.689573475122 -1.68957347512176 82 139.3 145.99850723732 -6.69850723732011 83 162.1 161.325666058821 0.774333941179265 84 142.2 143.165877883393 -0.965877883392778 85 141.4 139.02279915057 2.37720084943001 86 124.7 124.864928135823 -0.164928135823189 87 114 143.170115879426 -29.1701158794258 88 126.6 118.590286921694 8.00971307830588 89 121.9 136.628867189686 -14.7288671896856 90 125.1 127.843674456522 -2.7436744565224 91 122.1 121.985461586875 0.114538413125246 92 135.9 147.364252207196 -11.4642522071958 93 148.4 144.42242866009 3.97757133991038 94 137.5 139.721582528843 -2.22158252884333 95 145.3 160.004715605443 -14.7047156054434 96 139.9 137.327183895329 2.57281610467101 97 128.2 135.68006196386 -7.48006196386035 98 115.4 118.06081079513 -2.66081079512979 99 124.7 117.075888338417 7.62411166158346 100 111.5 123.266342255578 -11.7663422555776 101 121.1 122.295704578738 -1.1957045787378 102 122.5 123.608740001927 -1.10874000192676 103 127.4 119.66695035705 7.73304964294964 104 143.7 139.486618516595 4.21338148340496 105 157.8 149.575133025594 8.22486697440613 106 148.8 141.838162915263 6.96183708473666 107 162.9 157.143153892183 5.75684610781713 108 153.9 149.151505063144 4.74849493685602 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 109 141.406617179124 129.050372233495 153.762862124753 110 127.400448551296 114.621471934327 140.179425168265 111 133.89525133318 120.496490331273 147.294012335088 112 125.967364911902 112.207592956421 139.727136867383 113 135.248587930581 120.678153390128 149.819022471035 114 137.307558410042 122.113058613373 152.502058206711 115 139.273724885247 123.437805739424 155.109644031071 116 156.957822687201 139.630152314849 174.285493059552 117 169.65855869907 150.976538992097 188.340578406043 118 158.359978394713 139.825673108269 176.894283681157 119 172.225506261968 152.108321390685 192.342691133252 120 161.598571755364 134.580639386293 188.616504124436

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293201976z95ip0evnpqoeub/13y9m1293202093.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293201976z95ip0evnpqoeub/13y9m1293202093.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293201976z95ip0evnpqoeub/23y9m1293202093.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293201976z95ip0evnpqoeub/23y9m1293202093.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293201976z95ip0evnpqoeub/3w7971293202093.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/24/t1293201976z95ip0evnpqoeub/3w7971293202093.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=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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