triple exponential smoothing2 - Katrien Devillé

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 26 May 2008 10:20:06 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/26/t1211818882gw511xraai4axdh.htm/, Retrieved Mon, 26 May 2008 18:21:22 +0200

User-defined keywords:

Dataseries X:

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20.18 20.19 20.3 20.47 20.47 20.46 20.46 20.46 20.52 20.64 20.65 20.66 20.66 20.66 20.67 20.71 20.73 20.73 20.74 20.74 20.75 20.75 20.77 20.78 20.78 20.8 20.84 20.85 20.86 20.86 20.86 20.86 20.9 20.92 20.95 20.95 20.95 20.96 21.1 21.18 21.19 21.19 21.19 21.19 21.19 21.21 21.22 21.22 21.22 21.23 21.41 21.42 21.43 21.44 21.44 21.44 21.48 21.53 21.54 21.54 21.54 21.54 21.54 21.54 21.54 21.54 21.54 21.54 21.57 21.6 21.61 21.6 21.6 21.71 21.75 21.84 21.85 21.92 21.92 21.93 22 22 21.99 22.01 22.01 22.06 22.03 22.05 22.05 22.06 22.06 22.13 22.06 22.25 22.28 22.18

Text written by user:

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 0.793474145780884 beta 0.00479652073271958 gamma 0.737741601640285 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 20.66 20.5518301338475 0.108169866152533 14 20.66 20.6297788118178 0.0302211881822245 15 20.67 20.6580564341793 0.0119435658206584 16 20.71 20.7089500420184 0.00104995798160701 17 20.73 20.7357954823498 -0.00579548234976812 18 20.73 20.7367669411756 -0.00676694117561283 19 20.74 20.7469423940709 -0.00694239407087593 20 20.74 20.7461152430691 -0.00611524306907185 21 20.75 20.7538380170145 -0.00383801701451247 22 20.75 20.7533511954977 -0.00335119549767526 23 20.77 20.7749058575943 -0.00490585759431639 24 20.78 20.7856242723208 -0.00562427232076601 25 20.78 20.8404518388369 -0.0604518388369435 26 20.8 20.7722559588080 0.0277440411920438 27 20.84 20.7954507764770 0.0445492235230347 28 20.85 20.8706296669005 -0.0206296669004580 29 20.86 20.8790969409233 -0.0190969409233368 30 20.86 20.8690517876523 -0.00905178765234993 31 20.86 20.8771298462342 -0.0171298462342016 32 20.86 20.8679856040254 -0.00798560402539295 33 20.9 20.8742532359958 0.0257467640042393 34 20.92 20.8970357284829 0.0229642715171323 35 20.95 20.9392116957662 0.0107883042338450 36 20.95 20.9622350050685 -0.0122350050685149 37 20.95 21.0036805635178 -0.0536805635177693 38 20.96 20.9540727221945 0.00592727780550817 39 21.1 20.9623034350806 0.137696564919395 40 21.18 21.1018626805531 0.0781373194469275 41 21.19 21.1896932548365 0.000306745163527467 42 21.19 21.1971289285829 -0.0071289285829117 43 21.19 21.2061789227885 -0.0161789227885443 44 21.19 21.1997346735471 -0.00973467354705448 45 21.19 21.2104861590069 -0.0204861590069179 46 21.21 21.1964872883607 0.0135127116393505 47 21.22 21.2298839320915 -0.00988393209154026 48 21.22 21.2333421756721 -0.0133421756720722 49 21.22 21.268361062396 -0.0483610623959976 50 21.23 21.2323034501463 -0.00230345014628952 51 21.41 21.2544680510318 0.155531948968161 52 21.42 21.3996007380958 0.0203992619042452 53 21.43 21.4299730882271 2.69117729345680e-05 54 21.44 21.4361767058097 0.00382329419034022 55 21.44 21.4527830080177 -0.0127830080177311 56 21.44 21.4502035593178 -0.0102035593177519 57 21.48 21.4592424317815 0.0207575682184924 58 21.53 21.4834816235447 0.046518376455321 59 21.54 21.540120982806 -0.000120982805999148 60 21.54 21.5513302409796 -0.0113302409796461 61 21.54 21.5835841447035 -0.0435841447034768 62 21.54 21.5588725350669 -0.0188725350668868 63 21.54 21.592851032018 -0.0528510320180118 64 21.54 21.551719275084 -0.0117192750840189 65 21.54 21.5531290332296 -0.0131290332296388 66 21.54 21.5490287564667 -0.00902875646671575 67 21.54 21.5524391071715 -0.0124391071714847 68 21.54 21.5500450030218 -0.0100450030217978 69 21.57 21.5635111979405 0.0064888020595184 70 21.6 21.5798277552076 0.0201722447924197 71 21.61 21.6078492728866 0.00215072711336362 72 21.6 21.6185445899320 -0.0185445899319525 73 21.6 21.6395937379819 -0.0395937379818747 74 21.71 21.6212049497824 0.088795050217648 75 21.75 21.7354259407691 0.0145740592308918 76 21.84 21.7540435085763 0.0859564914237474 77 21.85 21.8331087971321 0.0168912028678925 78 21.92 21.8538794890115 0.0661205109884762 79 21.92 21.9171392201492 0.00286077985083111 80 21.93 21.9280067057243 0.00199329427568173 81 22 21.9546352177456 0.0453647822543672 82 22 22.004923190723 -0.00492319072300873 83 21.99 22.0111590373927 -0.0211590373927102 84 22.01 22.0009314113510 0.00906858864895455 85 22.01 22.0420028126096 -0.0320028126095586 86 22.06 22.0505206924941 0.00947930750593784 87 22.03 22.0915045060217 -0.0615045060216524 88 22.05 22.0610659523722 -0.0110659523721566 89 22.05 22.0525434402411 -0.00254344024108377 90 22.06 22.0653620495792 -0.00536204957916908 91 22.06 22.0618961530736 -0.00189615307357016 92 22.13 22.0685211274855 0.0614788725145097 93 22.06 22.1490177600930 -0.0890177600929754 94 22.25 22.0844088366212 0.165591163378789 95 22.28 22.2234583210571 0.0565416789429101 96 22.18 22.2797955253477 -0.0997955253476555 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 22.2282788169689 22.1451180908545 22.3114395430833 98 22.2688255995061 22.1600132646572 22.377637934355 99 22.2915557411237 22.1619160717279 22.4211954105196 100 22.317997697501 22.1702557021980 22.4657396928041 101 22.3196976321005 22.1558175567695 22.4835777074314 102 22.3344136300577 22.1556527271347 22.5131745329807 103 22.3358967678858 22.1433728696526 22.5284206661189 104 22.3540397600357 22.1484458255009 22.5596336945705 105 22.3628269047604 22.1449109038769 22.5807429056439 106 22.4083440994418 22.1783416241836 22.6383465747000 107 22.3990093465133 22.1579131381254 22.6401055549011 108 22.3860667756667 17.4222404242491 27.3498931270843

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211818882gw511xraai4axdh/1darl1211818800.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211818882gw511xraai4axdh/1darl1211818800.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211818882gw511xraai4axdh/2qc3o1211818800.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211818882gw511xraai4axdh/2qc3o1211818800.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211818882gw511xraai4axdh/39zsu1211818800.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211818882gw511xraai4axdh/39zsu1211818800.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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