exponential smoothing wijnprijzen

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 02 Jun 2010 11:54:57 +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/02/t1275479910076ssvw7qlm8sym.htm/, Retrieved Wed, 02 Jun 2010 13:58:31 +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/02/t1275479910076ssvw7qlm8sym.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 «

2.17 2.18 2.18 2.18 2.17 2.17 2.18 2.17 2.18 2.17 2.17 2.17 2.17 2.17 2.17 2.17 2.17 2.17 2.18 2.18 2.18 2.18 2.18 2.18 2.18 2.18 2.18 2.18 2.18 2.18 2.18 2.19 2.19 2.19 2.20 2.20 2.21 2.21 2.21 2.20 2.21 2.20 2.21 2.21 2.22 2.22 2.23 2.24 2.24 2.25 2.25 2.32 2.36 2.37 2.37 2.37 2.38 2.38 2.41 2.42 2.43 2.44 2.44 2.44 2.43 2.43 2.43 2.42 2.42 2.42 2.42 2.42

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 1 beta 0.217390091297997 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 2.18 2.19 -0.0100000000000002 4 2.18 2.18782609908702 -0.00782609908702003 5 2.17 2.18612478269199 -0.0161247826919859 6 2.17 2.17261941471041 -0.0026194147104146 7 2.18 2.17204997990737 0.0079500200926299 8 2.17 2.18377823550113 -0.0137782355011282 9 2.18 2.17078298362761 0.00921701637238792 10 2.17 2.1827866716583 -0.0127866716583012 11 2.17 2.17000697593911 -6.97593910548022e-06 12 2.17 2.17000545943907 -5.45943906615776e-06 13 2.17 2.17000427261111 -4.27261110935717e-06 14 2.17 2.17000334378779 -3.34378779021094e-06 15 2.17 2.17000261688146 -2.61688145730687e-06 16 2.17 2.17000204799736 -2.04799735836758e-06 17 2.17 2.17000160278303 -1.60278302541172e-06 18 2.17 2.17000125435388 -1.2543538772114e-06 19 2.18 2.17000098166977 0.00999901833022676 20 2.18 2.18217466917747 -0.00217466917747178 21 2.18 2.18170191764644 -0.00170191764643812 22 2.18 2.1813319376139 -0.00133193761389716 23 2.18 2.18104238757441 -0.001042387574409 24 2.18 2.18081578284444 -0.000815782844440172 25 2.18 2.18063843973741 -0.00063843973740818 26 2.18 2.1804996492646 -0.000499649264604773 27 2.18 2.18039103046536 -0.000391030465355158 28 2.18 2.18030602431679 -0.000306024316791387 29 2.18 2.18023949766262 -0.000239497662624544 30 2.18 2.18018743324388 -0.000187433243881152 31 2.18 2.18014668711388 -0.000146687113881327 32 2.19 2.1801147987888 0.00988520121119718 33 2.19 2.1922637435826 -0.00226374358260362 34 2.19 2.19177162815851 -0.00177162815850629 35 2.2 2.19138649375138 0.00861350624861767 36 2.2 2.20325898466117 -0.00325898466116525 37 2.21 2.20255051368814 0.00744948631186393 38 2.21 2.2141699581976 -0.00416995819759514 39 2.21 2.21326345060431 -0.00326345060431121 40 2.2 2.21255400877949 -0.0125540087794933 41 2.21 2.19982489166476 0.0101751083352362 42 2.2 2.21203685939473 -0.0120368593947275 43 2.21 2.19942016543197 0.0105798345680332 44 2.21 2.21172011663463 -0.00172011663462923 45 2.22 2.21134618032238 0.00865381967761625 46 2.22 2.22322743497218 -0.00322743497217726 47 2.23 2.22252582258892 0.00747417741108247 48 2.24 2.23415063469869 0.00584936530131008 49 2.24 2.24542222875558 -0.00542222875557696 50 2.25 2.24424348995136 0.00575651004863609 51 2.25 2.25549489819639 -0.00549489819639426 52 2.32 2.25430036177581 0.0656996382241926 53 2.36 2.33858281212761 0.0214171878723906 54 2.37 2.38323869655453 -0.0132386965545348 55 2.37 2.39036073510188 -0.0203607351018782 56 2.37 2.38593451303919 -0.0159345130391864 57 2.38 2.38247050779481 -0.00247050779480906 58 2.38 2.39193344387974 -0.0119334438797427 59 2.41 2.38933923142523 0.0206607685747744 60 2.42 2.42383067779198 -0.00383067779198321 61 2.43 2.43299792639705 -0.00299792639705032 62 2.44 2.44234620690389 -0.00234620690389109 63 2.44 2.45183616477085 -0.01183616477085 64 2.44 2.4492630998307 -0.00926309983069684 65 2.43 2.4472493937128 -0.0172493937127989 66 2.43 2.43349954643874 -0.00349954643873884 67 2.43 2.43273877971892 -0.00273877971891956 68 2.42 2.43214339614578 -0.0121433961457789 69 2.42 2.41950354214898 0.000496457851019816 70 2.42 2.41961146716654 0.000388532833460964 71 2.42 2.41969593035468 0.000304069645322702 72 2.42 2.41976203208263 0.000237967917365189 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 2.41981376394992 2.39744387098496 2.44218365691487 74 2.41962752789983 2.38438490890985 2.45487014688982 75 2.41944129184975 2.37177382234167 2.46710876135784 76 2.41925505579967 2.35893801108898 2.47957210051036 77 2.41906881974958 2.34567117471563 2.49246646478354 78 2.4188825836995 2.33189585888315 2.50586930851585 79 2.41869634764942 2.31758318688811 2.51980950841073 80 2.41851011159934 2.30272559340107 2.53429462979761 81 2.41832387554925 2.28732563959418 2.54932211150433 82 2.41813763949917 2.27139085694765 2.56488442205069 83 2.41795140344909 2.25493118030076 2.58097162659741 84 2.417765167399 2.23795760325074 2.59757273154726

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/02/t1275479910076ssvw7qlm8sym/1v6er1275479693.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275479910076ssvw7qlm8sym/1v6er1275479693.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275479910076ssvw7qlm8sym/2oxvt1275479693.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275479910076ssvw7qlm8sym/2oxvt1275479693.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275479910076ssvw7qlm8sym/3oxvt1275479693.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275479910076ssvw7qlm8sym/3oxvt1275479693.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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