Exponential Smoothing - Omzetcijfers Carrefour Burcht - Jeroen Van Eeckhoven

*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 09:04:55 -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/t12439551843430551rrilgdgp.htm/, Retrieved Tue, 02 Jun 2009 17:06:28 +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/t12439551843430551rrilgdgp.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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2291180 1971664 2193270 2197733 2345324 2195121 2170583 2241521 2154945 2912568 2392562 3336621 4080642 3735329 4018383 4171360 3855698 4101316 4199346 3959646 3960841 4784025 4105467 5929558 4048642 3828808 4268127 4171816 4004783 4295447 3968177 3918480 4040260 4530715 4103330 6025506 4632308 4133863 4519182 4151573 4486595 4504699 4180443 4222193 4373727 4734738 4403232 5903985 4414074 4061816 4504697 3994176 4114925 4485120 4171230 4476075 4179369 4823185 4585751 6110454 4279575 3782118 4098678 4065616 4413733 4481214 4345018 4294488 4361269 4535031 4318397 6040168

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.538050873276852 beta 0.0438182063827687 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 4080642 3176369.41212607 904272.587873931 14 3735329 3335539.4904987 399789.509501302 15 4018383 3870350.74007012 148032.25992988 16 4171360 4136728.01967935 34631.9803206502 17 3855698 3878142.30307426 -22444.3030742551 18 4101316 4119535.8192681 -18219.8192680990 19 4199346 4058108.47280823 141237.527191766 20 3959646 4247154.58338358 -287508.583383575 21 3960841 4039735.59209069 -78894.5920906914 22 4784025 4778152.07195307 5872.92804693151 23 4105467 4297801.37769399 -192334.377693994 24 5929558 5173145.17927921 756412.820720788 25 4048642 6772887.1396508 -2724245.13965080 26 3828808 4703358.88601399 -874550.886013987 27 4268127 4362841.05907513 -94714.0590751283 28 4171816 4367130.14716556 -195314.147165559 29 4004783 3873940.90668424 130842.093315756 30 4295447 4118861.27412441 176585.725875588 31 3968177 4159602.69666782 -191425.696667817 32 3918480 3887449.46186033 31030.5381396674 33 4040260 3871149.0717204 169110.928279602 34 4530715 4711369.80119669 -180654.801196693 35 4103330 3963904.7315582 139425.268441805 36 6025506 5388655.47043412 636850.529565884 37 4632308 5245991.50930802 -613683.509308024 38 4133863 5146088.50435656 -1012225.50435656 39 4519182 5068064.86997888 -548882.869978877 40 4151573 4747133.43335462 -595560.433354619 41 4486595 4145440.0667464 341154.933253599 42 4504699 4485790.24443902 18908.7555609755 43 4180443 4229112.99294911 -48669.9929491067 44 4222193 4097320.83443356 124872.165566443 45 4373727 4158298.36137719 215428.638622811 46 4734738 4825958.63990418 -91220.6399041796 47 4403232 4240675.18306797 162556.816932035 48 5903985 5874403.17156251 29581.8284374904 49 4414074 4779743.55854506 -365669.558545060 50 4061816 4587454.74218423 -525638.742184228 51 4504697 4955028.43373544 -450331.433735436 52 3994176 4637631.68256575 -643455.682565747 53 4114925 4413825.54093354 -298900.540933545 54 4485120 4216784.21208906 268335.787910937 55 4171230 4024826.28750856 146403.712491442 56 4476075 4044493.33376011 431581.666239887 57 4179369 4285891.75095349 -106522.750953489 58 4823185 4604642.06612746 218542.933872543 59 4585751 4276535.19204577 309215.807954230 60 6110454 5904478.94031623 205975.059683773 61 4279575 4703033.98939944 -423458.989399437 62 3782118 4385283.58952102 -603165.589521022 63 4098678 4723633.92759812 -624955.92759812 64 4065616 4196651.60483322 -131035.604833215 65 4413733 4393386.38134009 20346.6186599061 66 4481214 4623343.19976922 -142129.199769218 67 4345018 4137723.12519333 207294.874806668 68 4294488 4306841.32790667 -12353.3279066654 69 4361269 4035287.77517791 325981.224822092 70 4535031 4721592.44561686 -186561.445616863 71 4318397 4192535.55285227 125861.447147725 72 6040168 5644941.00494496 395226.995055038 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 4229826.24901010 3231984.967804 5227667.53021619 74 4042156.20514179 2897712.19822964 5186600.21205395 75 4694447.9595121 3409637.26823938 5979258.65078482 76 4746097.67895097 3324917.3927469 6167277.96515503 77 5100564.41184689 3545603.42633062 6655525.39736315 78 5261335.70022221 3574238.72754458 6948432.67289985 79 5033772.95843437 3215521.63004836 6852024.28682037 80 5005170.85202519 3056264.57890238 6954077.12514799 81 4912129.79135969 2832707.65985313 6991551.92286626 82 5194158.29047474 2984084.30687496 7404232.2740745 83 4922089.83108914 2581014.35207643 7263165.31010186 84 6440526.64055173 3967931.75695053 8913121.52415293

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439551843430551rrilgdgp/17vtl1243955093.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439551843430551rrilgdgp/17vtl1243955093.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439551843430551rrilgdgp/283ep1243955093.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439551843430551rrilgdgp/283ep1243955093.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439551843430551rrilgdgp/36vou1243955093.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439551843430551rrilgdgp/36vou1243955093.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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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