*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 17 May 2011 15:23:40 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/17/t1305645569mmc921u411mjgkp.htm/, Retrieved Tue, 17 May 2011 17:19:33 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

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 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 0,43 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 0,44 0,44 0,46 0,46 0,46 0,46 0,46 0,45 0,45 0,46 0,46 0,46 0,47 0,47 0,47 0,47 0,47 0,47 0,47 0,47 0,47 0,47 0,47

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.913882252944706 beta 0.0156442872297025 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 0.41 0.409910561495626 8.94385043740398e-05 14 0.41 0.41012333698141 -0.000123336981409539 15 0.41 0.410139897373554 -0.000139897373553799 16 0.41 0.409722938299467 0.000277061700532488 17 0.41 0.409276230044584 0.000723769955416176 18 0.41 0.409249580559903 0.000750419440096961 19 0.41 0.412170784068899 -0.00217078406889887 20 0.41 0.410308310797649 -0.000308310797648648 21 0.41 0.410143510864863 -0.000143510864863083 22 0.42 0.410127266885869 0.0098727331141305 23 0.42 0.419405841345727 0.00059415865427298 24 0.42 0.420213385982037 -0.000213385982037462 25 0.42 0.42028777462779 -0.000287774627789616 26 0.42 0.420263393099985 -0.000263393099985076 27 0.42 0.420274837118587 -0.000274837118586724 28 0.42 0.419883452885855 0.000116547114144716 29 0.42 0.419428887912329 0.000571112087671355 30 0.42 0.419362198615303 0.000637801384696601 31 0.42 0.422088671475199 -0.00208867147519926 32 0.42 0.420583058047971 -0.000583058047971208 33 0.42 0.420295245913563 -0.000295245913562947 34 0.42 0.421116845638211 -0.00111684563821135 35 0.42 0.41950722060541 0.000492779394590026 36 0.43 0.420105409046739 0.00989459095326095 37 0.43 0.42950826132353 0.000491738676469455 38 0.44 0.430306447060416 0.00969355293958424 39 0.44 0.439667101644497 0.000332898355502542 40 0.44 0.440107206085745 -0.000107206085745326 41 0.44 0.439706075963128 0.000293924036872228 42 0.44 0.43960290281348 0.000397097186520146 43 0.44 0.442200424281174 -0.00220042428117367 44 0.44 0.440983673304023 -0.000983673304022936 45 0.44 0.440597952773114 -0.000597952773114085 46 0.44 0.441347497928141 -0.00134749792814121 47 0.44 0.439868014508225 0.000131985491775288 48 0.44 0.441191778795396 -0.00119177879539639 49 0.43 0.439704532677982 -0.00970453267798227 50 0.44 0.431886015934066 0.00811398406593383 51 0.44 0.438900026623818 0.00109997337618228 52 0.46 0.439916131014449 0.0200838689855511 53 0.46 0.458170731405145 0.00182926859485477 54 0.46 0.459662818603304 0.000337181396695918 55 0.46 0.46227131537547 -0.00227131537546976 56 0.46 0.461335037728099 -0.00133503772809945 57 0.45 0.460881477536563 -0.0108814775365635 58 0.45 0.452257087949292 -0.00225708794929202 59 0.46 0.450117386618263 0.0098826133817374 60 0.46 0.460462176689568 -0.000462176689567939 61 0.46 0.459025685845696 0.00097431415430388 62 0.47 0.463008216742976 0.00699178325702354 63 0.47 0.46864117293212 0.00135882706787982 64 0.47 0.471885428322728 -0.00188542832272848 65 0.47 0.468469817295679 0.00153018270432076 66 0.47 0.469565730172129 0.000434269827870926 67 0.47 0.472095823205018 -0.0020958232050185 68 0.47 0.471443579426219 -0.00144357942621898 69 0.47 0.470061621557005 -6.16215570045653e-05 70 0.47 0.472320438823448 -0.00232043882344773 71 0.47 0.471356374901362 -0.00135637490136215 72 0.47 0.470557974629451 -0.000557974629451452 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 0.469146409424026 0.460461490249579 0.477831328598473 74 0.472815556706152 0.460930854673596 0.484700258738707 75 0.471470171555323 0.457077526720887 0.485862816389758 76 0.473084620566732 0.456441250379226 0.489727990754237 77 0.471588119270883 0.452995961851256 0.490180276690509 78 0.471082019132024 0.450657583157576 0.491506455106472 79 0.472887490167706 0.450651006341395 0.495123973994017 80 0.474128047315862 0.450186775870378 0.498069318761345 81 0.474117356122735 0.448596850804476 0.499637861440995 82 0.476188838613987 0.449038443503376 0.503339233724598 83 0.477408009088578 0.448716577681789 0.506099440495366 84 0.477907428000934 -12.7621810705055 13.7179959265073

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/17/t1305645569mmc921u411mjgkp/1doqd1305645816.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/17/t1305645569mmc921u411mjgkp/1doqd1305645816.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/17/t1305645569mmc921u411mjgkp/2qcz81305645816.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/17/t1305645569mmc921u411mjgkp/2qcz81305645816.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/17/t1305645569mmc921u411mjgkp/3qecr1305645816.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/17/t1305645569mmc921u411mjgkp/3qecr1305645816.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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