Exponental smoothing Nicolas Van hoeij

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 23 Jan 2010 08:31:48 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/23/t1264260782an71zfrgjvifte3.htm/, Retrieved Sat, 23 Jan 2010 16:33:06 +0100

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/Jan/23/t1264260782an71zfrgjvifte3.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:

KDGP2W61

Dataseries X:

» Textbox « » Textfile « » CSV «

1 4 -3 -3 0 6 -1 0 -1 1 -4 -1 -1 0 3 0 8 8 8 8 11 13 5 12 13 9 11 7 12 11 10 13 14 10 13 12 13 17 15 6 9 6 11 12 13 11 16 16 19 14 15 12 14 16 13 13 15 12 13 12 15 10 8 11 8 13 9 8 8 6 8 6 12 16

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.6087902561648 beta 0.147224753220598 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 -3 7 -10 4 -3 3.01580748608233 -6.01580748608233 5 0 0.91796177286605 -0.91796177286605 6 6 1.84135886592859 4.15864113407141 7 -1 6.2280771695089 -7.2280771695089 8 0 3.03482702605008 -3.03482702605008 9 -1 2.12237821455813 -3.12237821455813 10 1 0.876773470497409 0.123226529502591 11 -4 1.61810594000773 -5.61810594000773 12 -1 -1.63937404580397 0.63937404580397 13 -1 -1.03005473480765 0.0300547348076465 14 0 -0.788989307556312 0.788989307556312 15 3 -0.0151755884679016 3.0151755884679 16 0 2.38416580527450 -2.38416580527450 17 8 1.28275038321801 6.71724961678199 18 8 6.32424832125845 1.67575167874155 19 8 8.44672737736045 -0.446727377360446 20 8 9.2370221392205 -1.23702213922049 21 11 9.43532009915021 1.56467990084979 22 13 11.4795076491168 1.52049235088324 23 5 13.6330744508798 -8.63307445087983 24 12 8.8314749296592 3.16852507034080 25 13 11.4985659225229 1.50143407747705 26 9 13.2853201905549 -4.28532019055495 27 11 11.1650659024837 -0.16506590248372 28 7 11.5383875869256 -4.53838758692564 29 12 8.8425025234384 3.15749747656159 30 11 11.1148006254223 -0.114800625422323 31 10 11.3846660629438 -1.38466606294383 32 13 10.7573435675153 2.24265643248474 33 14 12.5393067059539 1.46069329404611 34 10 13.9761387773112 -3.97613877731116 35 13 11.7467031357285 1.25329686427155 36 12 12.8132286966480 -0.813228696647988 37 13 12.5487847609939 0.451215239006084 38 17 13.0945639413359 3.90543605866408 39 15 16.0932794091885 -1.09327940918854 40 6 15.9508360719243 -9.9508360719243 41 9 9.5241151061641 -0.524115106164102 42 6 8.78931410159438 -2.78931410159438 43 11 6.4254786000341 4.57452139996591 44 12 8.95468415654735 3.04531584345265 45 13 10.8258728697797 2.17412713022031 46 11 12.3615552132928 -1.36155521329276 47 16 11.6227137714677 4.37728622853231 48 16 14.7699548475847 1.23004515241534 49 19 16.1114339338548 2.88856606614521 50 14 18.7215036662045 -4.72150366620451 51 15 16.2754534672027 -1.27545346720271 52 12 15.8130074388838 -3.81300743888383 53 14 13.4639672525731 0.536032747426901 54 16 13.8106244319181 2.18937556808189 55 13 15.3600521429195 -2.36005214291955 56 13 13.9283034900841 -0.928303490084055 57 15 13.2849865572900 1.71501344271003 58 12 14.4046101488072 -2.40461014880719 59 13 12.8007242471919 0.19927575280807 60 12 12.7999195961422 -0.799919596142221 61 15 12.1191185629818 2.8808814370182 62 10 13.9373638422587 -3.93736384225873 63 8 11.2518258663456 -3.25182586634558 64 11 8.69217884534568 2.30782115465432 65 8 9.72403844970138 -1.72403844970138 66 13 8.14681737872148 4.85318262127852 67 9 11.0087302903941 -2.00873029039412 68 8 9.51313700517903 -1.51313700517903 69 8 8.18363513360865 -0.183635133608647 70 6 7.64706201448947 -1.64706201448947 71 8 6.0719443562452 1.92805564375480 72 6 6.84613318307419 -0.846133183074189 73 12 5.8555848163413 6.1444151836587 74 16 9.6715319396928 6.3284680603072 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 75 14.1667428945383 7.23886810776676 21.0946176813098 76 14.8092441578186 6.3589706240481 23.2595176915891 77 15.4517454210989 5.3912653906388 25.5122254515591 78 16.0942466843793 4.33903570638372 27.8494576623748 79 16.7367479476596 3.20554578340201 30.2679501119171 80 17.3792492109399 1.99387537100605 32.7646230508737 81 18.0217504742202 0.706872397159149 35.3366285512813 82 18.6642517375005 -0.652849106820909 37.981352581822 83 19.3067530007808 -2.08289411986775 40.6964001214294 84 19.9492542640612 -3.58106636071609 43.4795748888384 85 20.5917555273415 -5.14534742616306 46.328858480846 86 21.2342567906218 -6.77387724722625 49.2423908284699

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/23/t1264260782an71zfrgjvifte3/17hzn1264260706.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/23/t1264260782an71zfrgjvifte3/17hzn1264260706.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/23/t1264260782an71zfrgjvifte3/249al1264260706.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/23/t1264260782an71zfrgjvifte3/249al1264260706.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/23/t1264260782an71zfrgjvifte3/3f5ig1264260706.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/23/t1264260782an71zfrgjvifte3/3f5ig1264260706.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=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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