Exponential Smoothing - Prijsevolutie slagroom - Van Hal Elien

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 02 Jun 2009 12:36:57 -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/Jun/02/t1243967862u5wrfe2ld9wfmvc.htm/, Retrieved Tue, 02 Jun 2009 20:37:42 +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/Jun/02/t1243967862u5wrfe2ld9wfmvc.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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4.2 4.19 4.19 4.19 4.19 4.18 4.2 4.19 4.17 4.21 4.22 4.23 4.21 4.23 4.23 4.22 4.25 4.28 4.3 4.32 4.33 4.32 4.34 4.33 4.31 4.31 4.3 4.3 4.29 4.33 4.32 4.32 4.35 4.37 4.39 4.4 4.41 4.44 4.47 4.47 4.47 4.48 4.47 4.48 4.46 4.44 4.43 4.41 4.41 4.38 4.35 4.37 4.4 4.39 4.36 4.34 4.33 4.33 4.34 4.34 4.35 4.37 4.39 4.4 4.38 4.37 4.36 4.33 4.33 4.33 4.32 4.33 4.34

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.187080608713926 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 4.19 4.18 0.00999999999999979 4 4.19 4.18187080608714 0.00812919391286027 5 4.19 4.18339162063271 0.00660837936728864 6 4.18 4.18462792026736 -0.0046279202673567 7 4.2 4.17376212612666 0.0262378738733409 8 4.19 4.19867072354224 -0.0086707235422434 9 4.17 4.18704859930397 -0.0170485993039708 10 4.21 4.16385913696846 0.0461408630315363 11 4.22 4.21249119771099 0.00750880228901085 12 4.23 4.22389594901393 0.00610405098607103 13 4.21 4.23503789858803 -0.0250378985880255 14 4.23 4.21035379327926 0.0196462067207408 15 4.23 4.23402921759150 -0.00402921759149510 16 4.22 4.23327542911184 -0.0132754291118387 17 4.25 4.22079185375266 0.0292081462473437 18 4.28 4.25625613153202 0.0237438684679852 19 4.3 4.29069814889823 0.00930185110177106 20 4.32 4.31243834486451 0.00756165513548623 21 4.33 4.33385298391015 -0.00385298391014643 22 4.32 4.34313216533487 -0.0231321653348706 23 4.34 4.32880458576315 0.0111954142368473 24 4.33 4.35089903067339 -0.0208990306733856 25 4.31 4.33698922729348 -0.0269892272934786 26 4.31 4.31194006622269 -0.00194006622269516 27 4.3 4.31157711745281 -0.0115771174528083 28 4.3 4.29941126327258 0.000588736727415551 29 4.29 4.29952140449792 -0.00952140449792171 30 4.33 4.28774013434864 0.0422598656513609 31 4.32 4.33564613573886 -0.0156461357388640 32 4.32 4.32271904714082 -0.0027190471408165 33 4.35 4.32221036614659 0.0277896338534083 34 4.37 4.35740926776382 0.0125907322361769 35 4.39 4.37976474961472 0.0102352503852776 36 4.4 4.40167956648714 -0.00167956648713830 37 4.41 4.41136535216635 -0.00136535216635014 38 4.44 4.42110992125196 0.0188900787480399 39 4.47 4.4546438886828 0.0153561113172023 40 4.47 4.4875167193355 -0.0175167193354984 41 4.47 4.48423968081954 -0.0142396808195420 42 4.48 4.48157571266393 -0.00157571266392953 43 4.47 4.49128092737960 -0.0212809273796051 44 4.48 4.47729967853143 0.00270032146856991 45 4.46 4.48780485631549 -0.0278048563154947 46 4.44 4.46260310687079 -0.0226031068707879 47 4.43 4.43837450387858 -0.00837450387857608 48 4.41 4.42680779659529 -0.0168077965952937 49 4.41 4.40366338377711 0.00633661622289328 50 4.38 4.40484884179727 -0.0248488417972723 51 4.35 4.370200105348 -0.0202001053480023 52 4.37 4.33642105734341 0.0335789426565878 53 4.4 4.36270302637558 0.0372969736244233 54 4.39 4.39968056690442 -0.00968056690442243 55 4.36 4.38786952055525 -0.0278695205552459 56 4.34 4.35265567368521 -0.0126556736852059 57 4.33 4.33028804254849 -0.000288042548492129 58 4.33 4.32023415537318 0.0097658446268154 59 4.34 4.32206115553058 0.0179388444694242 60 4.34 4.33541716547354 0.00458283452646047 61 4.35 4.33627452494638 0.0137254750536151 62 4.37 4.3488422951743 0.021157704825697 63 4.39 4.37280049147208 0.0171995085279155 64 4.4 4.39601818599707 0.00398181400293396 65 4.38 4.40676310618452 -0.0267631061845215 66 4.37 4.38175624798845 -0.011756247988445 67 4.36 4.36955688195858 -0.0095568819585754 68 4.33 4.35776897466436 -0.0277689746643581 69 4.33 4.32257393798079 0.0074260620192117 70 4.33 4.32396321018369 0.00603678981631006 71 4.32 4.3250925764972 -0.00509257649720318 72 4.33 4.31413985418618 0.0158601458138152 73 4.34 4.32710697991932 0.0128930200806749 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 4.33951901396418 4.30411565811095 4.37492236981741 75 4.33903802792836 4.28408681464403 4.39398924121269 76 4.33855704189253 4.26516460073345 4.41194948305162 77 4.33807605585671 4.24619800052617 4.42995411118725 78 4.33759506982089 4.22681261882094 4.44837752082084 79 4.33711408378507 4.20685392362074 4.46737424394939 80 4.33663309774925 4.18625295812702 4.48701323737147 81 4.33615211171342 4.16497992249482 4.50732430093203 82 4.3356711256776 4.14302471137059 4.52831753998461 83 4.33519013964178 4.12038769585863 4.54999258342493 84 4.33470915360596 4.09707497928852 4.5723433279234 85 4.33422816757014 4.07309580744918 4.59536052769109

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243967862u5wrfe2ld9wfmvc/1rxv31243967812.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243967862u5wrfe2ld9wfmvc/1rxv31243967812.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243967862u5wrfe2ld9wfmvc/2z5o91243967812.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243967862u5wrfe2ld9wfmvc/2z5o91243967812.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243967862u5wrfe2ld9wfmvc/3jetl1243967812.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243967862u5wrfe2ld9wfmvc/3jetl1243967812.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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')

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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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