WS9

*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 06 Dec 2009 12:48:01 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/06/t1260128930yfzj4dsd79pyl0v.htm/, Retrieved Sun, 06 Dec 2009 20:48:54 +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/2009/Dec/06/t1260128930yfzj4dsd79pyl0v.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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286602 283042 276687 277915 277128 277103 275037 270150 267140 264993 287259 291186 292300 288186 281477 282656 280190 280408 276836 275216 274352 271311 289802 290726 292300 278506 269826 265861 269034 264176 255198 253353 246057 235372 258556 260993 254663 250643 243422 247105 248541 245039 237080 237085 225554 226839 247934 248333 246969 245098 246263 255765 264319 268347 273046 273963 267430 271993 292710 295881 293299

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 0.799417188372112 beta 0.422190477532405 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 292300 290291.770120968 2008.22987903241 14 288186 288526.781022269 -340.781022268697 15 281477 281924.588728638 -447.588728637842 16 282656 282923.979980075 -267.979980075033 17 280190 280523.26700116 -333.26700115978 18 280408 280923.379699651 -515.379699651443 19 276836 279339.314168009 -2503.31416800898 20 275216 271491.851983584 3724.14801641589 21 274352 271778.663359737 2573.33664026338 22 271311 272872.405552972 -1561.40555297176 23 289802 295292.393645528 -5490.39364552771 24 290726 293926.459101318 -3200.45910131827 25 292300 290901.776356128 1398.22364387190 26 278506 285882.607107438 -7376.60710743768 27 269826 269283.338910379 542.661089621193 28 265861 266850.516668761 -989.516668760625 29 269034 259595.816721313 9438.18327868666 30 264176 266632.636152248 -2456.63615224784 31 255198 261426.245701112 -6228.24570111238 32 253353 249155.978306184 4197.0216938165 33 246057 247095.315829582 -1038.31582958231 34 235372 240854.375870797 -5482.3758707974 35 258556 250838.046946566 7717.953053434 36 260993 258734.938452711 2258.06154728914 37 254663 261328.739824001 -6665.73982400139 38 250643 246790.738227599 3852.26177240099 39 243422 242951.597210893 470.402789106796 40 247105 241734.949760818 5370.05023918199 41 248541 245398.102703747 3142.89729625257 42 245039 246782.333627287 -1743.33362728695 43 237080 243361.216796867 -6281.21679686697 44 237085 235012.816447624 2072.18355237567 45 225554 231524.989152044 -5970.98915204394 46 226839 220116.770772564 6722.22922743642 47 247934 245367.758590598 2566.2414094024 48 248333 250006.91676132 -1673.91676132006 49 246969 248374.219351017 -1405.21935101683 50 245098 242719.652505235 2378.34749476527 51 246263 239081.687069545 7181.31293045534 52 255765 248411.741493572 7353.25850642825 53 264319 258029.436893688 6289.56310631183 54 268347 266603.574888203 1743.42511179729 55 273046 271635.505546721 1410.49445327930 56 273963 280621.827498534 -6658.82749853382 57 267430 273977.766705942 -6547.76670594158 58 271993 270562.705499243 1430.29450075666 59 292710 299400.744027915 -6690.74402791483 60 295881 297713.759841143 -1832.75984114257 61 293299 297618.678154695 -4319.67815469479 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 62 290423.164376725 281803.519274877 299042.809478573 63 284761.477897907 271844.816634783 297678.139161031 64 285875.110741399 267749.636242918 304000.585239881 65 284081.978579323 260294.307565511 307869.649593135 66 279242.248772801 249601.137227562 308883.360318040 67 275021.427668052 239145.64533088 310897.210005225 68 273155.086456089 230408.492547598 315901.680364579 69 266160.410812533 217099.655115901 315221.166509166 70 266083.509562310 209210.366969692 322956.652154927 71 287344.969085467 217113.220222853 357576.717948081 72 289853.487633864 209692.427613869 370014.547653860 73 289266.142055396 200007.518008578 378524.766102213

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260128930yfzj4dsd79pyl0v/1uovk1260128879.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260128930yfzj4dsd79pyl0v/1uovk1260128879.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260128930yfzj4dsd79pyl0v/2qzx61260128879.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260128930yfzj4dsd79pyl0v/2qzx61260128879.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260128930yfzj4dsd79pyl0v/3yebz1260128879.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260128930yfzj4dsd79pyl0v/3yebz1260128879.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=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')

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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