Triple Smoothing - Gem. prijs gebakken tong of forel - Niels Braspennincx

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 18 Aug 2009 16:41:31 -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/Aug/19/t1250635372nc2pag2njq9j05v.htm/, Retrieved Wed, 19 Aug 2009 00:42:56 +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/Aug/19/t1250635372nc2pag2njq9j05v.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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15.22 15.27 15.31 15.33 15.42 15.49 15.65 15.67 15.69 15.83 15.92 15.99 15.94 15.96 16.03 16.09 16.04 16.23 16.2 16.2 16.26 16.28 16.27 16.29 16.3 16.37 16.39 16.42 16.43 16.37 16.37 16.39 16.48 16.51 16.5 16.54 16.52 16.56 16.61 16.75 16.75 16.79 16.82 16.84 17.14 17.25 17.28 17.3 17.34 17.44 17.48 17.55 17.59 17.66 17.67 17.64 17.68 17.72 17.78 17.83 17.88 18.11 18.16 18.27 18.29 18.35 18.35 18.38 18.41 18.41 18.42 18.43 18.48 18.54 18.65 18.66 18.69 18.72 18.72 18.73 18.84 18.83 18.91 18.91 18.94 18.97 19 19.08 19.18 19.24 19.23 19.25 19.3 19.33 19.35 19.35 19.31 19.47 19.7 19.76 19.9 19.97 20.1 20.26 20.44 20.43 20.57 20.6 20.69 20.93 20.98 21.11 21.14 21.16 21.32 21.32 21.48 21.58 21.74 21.75 21.81 21.89 22.21 22.37 22.47 22.51 22.55 22.61 22.58 22.85 22.93 22.98

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 40 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.78099895625679 beta 0.0460781151747984 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 15.94 15.5914423076923 0.348557692307683 14 15.96 15.9015528561049 0.0584471438950818 15 16.03 16.036357370696 -0.0063573706960156 16 16.09 16.1136541779200 -0.023654177920033 17 16.04 16.0757576214709 -0.035757621470907 18 16.23 16.2733714801529 -0.043371480152949 19 16.2 16.2613947821027 -0.0613947821026599 20 16.2 16.233549159149 -0.0335491591490076 21 16.26 16.2262436064149 0.0337563935850831 22 16.28 16.3898017434307 -0.109801743430666 23 16.27 16.3914563610085 -0.121456361008452 24 16.29 16.3604712225677 -0.0704712225676651 25 16.3 16.3260205440628 -0.0260205440628347 26 16.37 16.2642303874771 0.105769612522860 27 16.39 16.4076834556650 -0.0176834556650469 28 16.42 16.4578210034749 -0.0378210034749067 29 16.43 16.3911741032615 0.0388258967385156 30 16.37 16.6330188018747 -0.263018801874679 31 16.37 16.4252948465807 -0.0552948465806722 32 16.39 16.3882751992325 0.00172480076753345 33 16.48 16.4044916730933 0.075508326906732 34 16.51 16.5519542841776 -0.0419542841776277 35 16.5 16.5892225865623 -0.0892225865623253 36 16.54 16.5809150497607 -0.0409150497607378 37 16.52 16.5666833520677 -0.0466833520677064 38 16.56 16.504275049913 0.055724950087015 39 16.61 16.5664632869964 0.0435367130035935 40 16.75 16.6470630552125 0.102936944787491 41 16.75 16.6992586440200 0.050741355979973 42 16.79 16.8768587281696 -0.0868587281696271 43 16.82 16.8511005634444 -0.0311005634443582 44 16.84 16.8452278608033 -0.00522786080325588 45 17.14 16.8716866498639 0.268313350136115 46 17.25 17.1504574824488 0.0995425175511997 47 17.28 17.2994270054886 -0.019427005488609 48 17.3 17.3702650501609 -0.0702650501609341 49 17.34 17.3448474558009 -0.00484745580092394 50 17.44 17.3520457039816 0.0879542960183919 51 17.48 17.4524008600910 0.0275991399089754 52 17.55 17.5486536384464 0.00134636155355494 53 17.59 17.5215117884466 0.0684882115534435 54 17.66 17.6949118306985 -0.0349118306985403 55 17.67 17.7358788903356 -0.0658788903356111 56 17.64 17.7212025887058 -0.0812025887057928 57 17.68 17.7581889949228 -0.078188994922769 58 17.72 17.726869292852 -0.00686929285200577 59 17.78 17.7603358394301 0.0196641605698673 60 17.83 17.8456362174876 -0.0156362174876001 61 17.88 17.8742418898192 0.00575811018079264 62 18.11 17.9074601004972 0.202539899502785 63 18.16 18.0856255846851 0.0743744153149173 64 18.27 18.2158806519469 0.0541193480531277 65 18.29 18.2497779573940 0.0402220426060325 66 18.35 18.3825595933806 -0.0325595933805616 67 18.35 18.4227687387518 -0.072768738751801 68 18.38 18.4032944312908 -0.0232944312908465 69 18.41 18.4921898312556 -0.0821898312556293 70 18.41 18.4792433945053 -0.0692433945052784 71 18.42 18.4734408576235 -0.0534408576234568 72 18.43 18.4949188166158 -0.0649188166157728 73 18.48 18.4889500231198 -0.00895002311979098 74 18.54 18.5524771258536 -0.0124771258536320 75 18.65 18.5256088653524 0.124391134647638 76 18.66 18.6832537095085 -0.0232537095084737 77 18.69 18.6436574444144 0.0463425555856141 78 18.72 18.7554784301133 -0.0354784301132547 79 18.72 18.774695571888 -0.0546955718879865 80 18.73 18.7709151618363 -0.0409151618363097 81 18.84 18.8232603670298 0.0167396329701965 82 18.83 18.8840829238590 -0.0540829238589566 83 18.91 18.8877969521628 0.0222030478372339 84 18.91 18.9627767129206 -0.0527767129205934 85 18.94 18.9759227468811 -0.0359227468811305 86 18.97 19.0140157079538 -0.0440157079537542 87 19 18.9877591285915 0.0122408714085473 88 19.08 19.0167134011551 0.0632865988449147 89 19.18 19.0542940457728 0.125705954227175 90 19.24 19.2073822936661 0.0326177063338591 91 19.23 19.2752278577121 -0.0452278577120993 92 19.25 19.2818543458718 -0.0318543458717926 93 19.3 19.3542232694736 -0.0542232694735603 94 19.33 19.3418806909311 -0.0118806909311360 95 19.35 19.3945470878261 -0.0445470878260821 96 19.35 19.3978580432810 -0.0478580432810354 97 19.31 19.4155972240627 -0.105597224062727 98 19.47 19.3920553864561 0.077944613543913 99 19.7 19.4723121838791 0.227687816120863 100 19.76 19.687404886923 0.0725951130769964 101 19.9 19.7529558844908 0.147044115509186 102 19.97 19.9101211952505 0.0598788047495376 103 20.1 19.9909888376085 0.109011162391489 104 20.26 20.1353346946396 0.124665305360434 105 20.44 20.3450091933819 0.0949908066181209 106 20.43 20.4838081908987 -0.0538081908986747 107 20.57 20.5203989052842 0.0496010947158467 108 20.6 20.6237261234222 -0.0237261234221826 109 20.69 20.6757475350861 0.0142524649139268 110 20.93 20.8183972269465 0.111602773053491 111 20.98 20.9913393777712 -0.0113393777712325 112 21.11 21.0107892142907 0.0992107857093316 113 21.14 21.1393918370511 0.000608162948857682 114 21.16 21.1837921463301 -0.0237921463300665 115 21.32 21.2277524563352 0.092247543664751 116 21.32 21.3795105021167 -0.0595105021167086 117 21.48 21.449293497694 0.0307065023059891 118 21.58 21.5134343446360 0.0665656553640375 119 21.74 21.6791504973297 0.0608495026703118 120 21.75 21.7880756175723 -0.0380756175723462 121 21.81 21.8495626896373 -0.0395626896373393 122 21.89 21.9819212271168 -0.0919212271168348 123 22.21 21.9720812829236 0.237918717076436 124 22.37 22.2224764696382 0.147523530361788 125 22.47 22.3810202841406 0.0889797158593701 126 22.51 22.5060782802277 0.00392171977229339 127 22.55 22.6150765311661 -0.065076531166099 128 22.61 22.6230484803313 -0.0130484803313493 129 22.58 22.7628669235168 -0.182866923516777 130 22.85 22.6743655204089 0.175634479591139 131 22.93 22.9342427036316 -0.00424270363162904 132 22.98 22.9785539395449 0.00144606045514450 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 133 23.0798917610436 22.9090176439802 23.2507658781069 134 23.2424159148826 23.0217654862246 23.4630663435406 135 23.3906433820852 23.1262006436783 23.6550861204921 136 23.4409074244417 23.1359424414115 23.7458724074720 137 23.4715852014548 23.1280982658845 23.8150721370250 138 23.5054910751703 23.1247753146618 23.8862068356787 139 23.5931433800802 23.1760547643692 24.0102319957912 140 23.6625037381069 23.2096084186554 24.1153990575584 141 23.7749616981524 23.2866238154518 24.263299580853 142 23.91401126119 23.3904487610442 24.4375737613358 143 23.9972241656123 23.4385460755449 24.5559022556796 144 24.0461468332257 23.4523791477858 24.6399145186656

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250635372nc2pag2njq9j05v/1mb081250635251.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250635372nc2pag2njq9j05v/1mb081250635251.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250635372nc2pag2njq9j05v/2qqeg1250635251.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250635372nc2pag2njq9j05v/2qqeg1250635251.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250635372nc2pag2njq9j05v/33no21250635251.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250635372nc2pag2njq9j05v/33no21250635251.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=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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