Triple exponential smoothing gemiddelde prijs pilsbieren

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 03 Jun 2010 12:04:55 +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/Jun/03/t1275566780mj1r5qmzqchoddb.htm/, Retrieved Thu, 03 Jun 2010 14:06:24 +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/2010/Jun/03/t1275566780mj1r5qmzqchoddb.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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

0,47 0,47 0,47 0,47 0,47 0,47 0,47 0,47 0,47 0,47 0,47 0,46 0,46 0,46 0,45 0,45 0,46 0,46 0,46 0,46 0,46 0,44 0,44 0,43 0,44 0,44 0,44 0,44 0,44 0,44 0,44 0,44 0,44 0,44 0,44 0,43 0,43 0,42 0,42 0,42 0,42 0,42 0,42 0,42 0,42 0,42 0,42 0,42 0,42 0,42 0,42 0,41 0,41 0,41 0,41 0,41 0,41 0,41 0,41 0,41 0,41 0,41 0,41 0,41 0,41 0,41 0,41 0,41 0,41 0,41 0,41 0,41

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.731166173353888 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 0.46 0.466830516713388 -0.00683051671338769 14 0.46 0.461427505600215 -0.00142750560021521 15 0.45 0.44997224146999 2.77585300099692e-05 16 0.45 0.450404624744055 -0.000404624744055115 17 0.46 0.461375566736432 -0.00137556673643241 18 0.46 0.461642562585364 -0.00164256258536388 19 0.46 0.454146875094009 0.00585312490599121 20 0.46 0.457990824794375 0.00200917520562460 21 0.46 0.459435118913758 0.000564881086241864 22 0.44 0.460236399386104 -0.0202363993861041 23 0.44 0.445377537437643 -0.00537753743764258 24 0.43 0.431592291510087 -0.00159229151008661 25 0.44 0.428253841794443 0.0117461582055569 26 0.44 0.437770075517025 0.00222992448297515 27 0.44 0.429774388275788 0.0102256117242123 28 0.44 0.437503772591721 0.00249622740827943 29 0.44 0.450043144789146 -0.0100431447891458 30 0.44 0.443807166053091 -0.00380716605309078 31 0.44 0.436854614469646 0.00314538553035443 32 0.44 0.437693489096854 0.00230651090314604 33 0.44 0.438928998479739 0.00107100152026091 34 0.44 0.434510131914643 0.00548986808535729 35 0.44 0.442425766086351 -0.00242576608635148 36 0.43 0.431803936589844 -0.00180393658984418 37 0.43 0.431837409477797 -0.00183740947779731 38 0.42 0.428869689010611 -0.00886968901061114 39 0.42 0.41511297228229 0.00488702771771032 40 0.42 0.416887495830328 0.00311250416967246 41 0.42 0.426056944620637 -0.00605694462063683 42 0.42 0.424236971520616 -0.00423697152061631 43 0.42 0.418879722317182 0.00112027768281830 44 0.42 0.418030009671073 0.00196999032892742 45 0.42 0.418664733742606 0.00133526625739361 46 0.42 0.415742095006135 0.00425790499386514 47 0.42 0.420480813730523 -0.000480813730522611 48 0.42 0.411783037948139 0.00821696205186068 49 0.42 0.419059505460376 0.000940494539623749 50 0.42 0.416250957851564 0.0037490421484358 51 0.42 0.41541333909062 0.00458666090938031 52 0.41 0.416489742659472 -0.00648974265947211 53 0.41 0.416045043366751 -0.00604504336675132 54 0.41 0.414628009118193 -0.00462800911819339 55 0.41 0.410415342127111 -0.000415342127110863 56 0.41 0.408673811663632 0.00132618833636827 57 0.41 0.408659419465873 0.00134058053412711 58 0.41 0.406563980753393 0.00343601924660725 59 0.41 0.409385895791372 0.000614104208627952 60 0.41 0.403911280413689 0.00608871958631058 61 0.41 0.407659664572826 0.00234033542717355 62 0.41 0.406661235682144 0.00333876431785562 63 0.41 0.405794207555857 0.00420579244414276 64 0.41 0.403701737623476 0.00629826237652359 65 0.41 0.412685999968824 -0.00268599996882368 66 0.41 0.414103841193898 -0.00410384119389845 67 0.41 0.411411052462003 -0.00141105246200296 68 0.41 0.409409096656436 0.000590903343563487 69 0.41 0.408859988064725 0.00114001193527502 70 0.41 0.407176496343624 0.00282350365637624 71 0.41 0.40879025722972 0.00120974277028024 72 0.41 0.405207625737702 0.00479237426229845 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 0.406999313201695 0.396988126170802 0.417010500232588 74 0.404561577859124 0.392172481627639 0.416950674090608 75 0.401502436918196 0.387145925173321 0.415858948663071 76 0.396948680299299 0.380915664839511 0.412981695759087 77 0.398807381922821 0.381089268520666 0.416525495324976 78 0.401684129296761 0.382369095723446 0.420999162870076 79 0.402668508684583 0.381924787600868 0.423412229768297 80 0.402221517396403 0.38018904167957 0.424253993113235 81 0.401379280469937 0.378143067624379 0.424615493315496 82 0.399328052534751 0.375006206072174 0.423649898997329 83 0.398433112494345 0.373014126988399 0.42385209800029 84 0.394981904427651 -7.6611802057714 8.4511440146267

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/03/t1275566780mj1r5qmzqchoddb/16jm21275566693.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/03/t1275566780mj1r5qmzqchoddb/16jm21275566693.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/03/t1275566780mj1r5qmzqchoddb/2zb3n1275566693.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/03/t1275566780mj1r5qmzqchoddb/2zb3n1275566693.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/03/t1275566780mj1r5qmzqchoddb/3zb3n1275566693.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/03/t1275566780mj1r5qmzqchoddb/3zb3n1275566693.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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