Gemiddelde prijs van een kiwi

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 22 May 2008 08:03:16 -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/22/t1211465149intazvhe49fkqg0.htm/, Retrieved Thu, 22 May 2008 16:05:53 +0200

User-defined keywords:

Dataseries X:

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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 2 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.841006539333911 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 0.36 0.354168721864335 0.00583127813566497 14 0.36 0.358265959594702 0.00173404040529840 15 0.36 0.357714665960194 0.00228533403980585 16 0.36 0.356450497137153 0.00354950286284744 17 0.38 0.375248721294845 0.00475127870515524 18 0.37 0.366454836418137 0.00354516358186269 19 0.39 0.388561175974231 0.00143882402576945 20 0.39 0.389771236388853 0.000228763611146654 21 0.4 0.399962695468502 3.73045314979725e-05 22 0.42 0.41999377226461 6.22773538955235e-06 23 0.42 0.421370062093576 -0.00137006209357576 24 0.4 0.401080320516783 -0.00108032051678314 25 0.36 0.37287669013049 -0.0128766901304904 26 0.36 0.360579552610568 -0.000579552610567746 27 0.36 0.358167729915886 0.00183227008411407 28 0.36 0.356721258383452 0.0032787416165479 29 0.35 0.375451722368071 -0.025451722368071 30 0.38 0.341947527779654 0.0380524722203462 31 0.4 0.392939718067491 0.00706028193250913 32 0.39 0.398680671937991 -0.00868067193799055 33 0.39 0.401384074199658 -0.0113840741996585 34 0.39 0.411395362682129 -0.0213953626821292 35 0.36 0.394480424556518 -0.0344804245565176 36 0.35 0.348868532187066 0.00113146781293416 37 0.35 0.324255375431368 0.0257446245686317 38 0.33 0.346374979781771 -0.016374979781771 39 0.33 0.331178679034397 -0.001178679034397 40 0.32 0.327654643061797 -0.00765464306179681 41 0.36 0.331175132966034 0.0288248670339658 42 0.37 0.352857888890978 0.0171421111090218 43 0.38 0.380849704025799 -0.000849704025799314 44 0.38 0.377545196333015 0.00245480366698503 45 0.38 0.388885662661695 -0.0088856626616951 46 0.38 0.398858044040577 -0.0188580440405772 47 0.39 0.38158739313176 0.00841260686823964 48 0.4 0.376838409032491 0.0231615909675089 49 0.38 0.371510696837184 0.00848930316281599 50 0.41 0.371795243930462 0.0382047560695378 51 0.41 0.405138344847736 0.00486165515226394 52 0.43 0.404779120023733 0.0252208799762673 53 0.42 0.446551397531768 -0.0265513975317682 54 0.41 0.418890906862472 -0.00889090686247168 55 0.41 0.423327191628258 -0.0133271916282584 56 0.43 0.409877629034235 0.0201223709657654 57 0.44 0.43516284611313 0.00483715388687 58 0.46 0.457419222733862 0.0025807772661377 59 0.44 0.463097787048965 -0.0230977870489652 60 0.43 0.432682919853982 -0.002682919853982 61 0.43 0.401195212514832 0.0288047874851679 62 0.42 0.422494194554144 -0.00249419455414446 63 0.42 0.416196279419709 0.00380372058029144 64 0.42 0.41795232043303 0.00204767956696966 65 0.43 0.431491381418336 -0.00149138141833588 66 0.44 0.427626624570958 0.0123733754290418 67 0.45 0.449945737531405 5.42624685953008e-05 68 0.44 0.453229223192051 -0.0132292231920506 69 0.47 0.448194926265441 0.0218050737345586 70 0.48 0.485435798511558 -0.00543579851155845 71 0.48 0.480095501569868 -9.55015698678174e-05 72 0.45 0.471564862662166 -0.0215648626621663 73 0.44 0.427608752169333 0.0123912478306673 74 0.44 0.429977921153402 0.0100220788465976 75 0.45 0.435062591504202 0.0149374084957979 76 0.46 0.445788243938788 0.0142117560612118 77 0.45 0.470005218999662 -0.0200052189996620 78 0.46 0.452703462501075 0.00729653749892489 79 0.47 0.469220487753507 0.000779512246492975 80 0.48 0.470996383531979 0.00900361646802111 81 0.48 0.491104277428729 -0.0111042774287292 82 0.46 0.496693396821315 -0.0366933968213146 83 0.47 0.465911954756431 0.00408804524356932 84 0.47 0.457615348774467 0.0123846512255326 85 0.43 0.446742803797396 -0.0167428037973964 86 0.41 0.424343805119414 -0.0143438051194145 87 0.39 0.409817091292825 -0.0198170912928252 88 0.41 0.391393683328863 0.0186063166711372 89 0.44 0.412976062794227 0.0270239372057733 90 0.45 0.439429166345048 0.0105708336549523 91 0.45 0.457426281922807 -0.00742628192280742 92 0.46 0.453489671319325 0.0065103286806748 93 0.45 0.46786169251636 -0.0178616925163598 94 0.45 0.462720207810253 -0.0127202078102533 95 0.46 0.458465877973486 0.00153412202651398 96 0.46 0.449524660402054 0.0104753395979463 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 0.432974134123719 0.403102192962413 0.462846075285025 98 0.424915282141273 0.386019997961423 0.463810566321122 99 0.421321883795095 0.374724298914723 0.467919468675467 100 0.4259005073314 0.372340108865994 0.479460905796805 101 0.433222432878028 0.373954977615026 0.492489888141030 102 0.43428238219294 0.369210026705203 0.499354737680677 103 0.440294015383573 0.369968809332606 0.51061922143454 104 0.444709110360873 0.369358775041915 0.520059445679832 105 0.449472905966086 0.368428321304057 0.530517490628115 106 0.460110345670358 0.373820982507095 0.546399708833621 107 0.469015125853249 0.380677986977151 0.557352264729347 108 0.46 NA NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/22/t1211465149intazvhe49fkqg0/1skm11211464993.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/22/t1211465149intazvhe49fkqg0/1skm11211464993.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/22/t1211465149intazvhe49fkqg0/2atqk1211464993.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/22/t1211465149intazvhe49fkqg0/2atqk1211464993.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/22/t1211465149intazvhe49fkqg0/3knat1211464993.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/22/t1211465149intazvhe49fkqg0/3knat1211464993.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')

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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