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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 26 Jan 2010 12:22:55 -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/26/t1264533846xtugkgavdu4vxb8.htm/, Retrieved Tue, 26 Jan 2010 20:24:10 +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/26/t1264533846xtugkgavdu4vxb8.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:

KEYWORD: KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

124.9 122.7 148.1 176.9 234.6 254.6 279.7 275.8 283 295.4 297.6 276.8 250.1 239.1 258.9 276.1 264.1 265.5 287.7 285.1 304.5 301.5 274.2 258.6 253.9 269.6 266.9 269.6 257.9 258.2 254.7 237.2 267.2 228.8 196.3 194.8 186.6 176.7 162.1 154.9 150.1 150.5 143.6 143.8 141.5 147.9 151.4 144.6 140.4 139.5 138.1 136.7 130 128.5 130.4 125.7 121.7 129.9 129.6 128.2 119.7 112.2 105.6 101.2 94.9 95.1 93.1 91.4 89.8 85.9 89.7 91.6 88.6

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 0.357504192131878 beta 0.200940707428541 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 250.1 220.441693376069 29.6583066239315 14 239.1 224.458053833803 14.6419461661969 15 258.9 254.395338091194 4.50466190880641 16 276.1 278.565436115028 -2.46543611502847 17 264.1 272.737418316742 -8.63741831674241 18 265.5 278.494903533154 -12.9949035331539 19 287.7 329.644386077925 -41.9443860779247 20 285.1 302.44780896338 -17.3478089633801 21 304.5 294.498394206664 10.0016057933361 22 301.5 302.961663352859 -1.46166335285932 23 274.2 300.409264001131 -26.2092640011305 24 258.6 267.805861633489 -9.20586163348867 25 253.9 254.671095080908 -0.771095080908253 26 269.6 231.559780009973 38.0402199900274 27 266.9 258.428659593779 8.4713404062208 28 269.6 274.903334892304 -5.30333489230384 29 257.9 259.256148990486 -1.35614899048585 30 258.2 260.500983430093 -2.3009834300928 31 254.7 293.325817658484 -38.6258176584837 32 237.2 279.809388422839 -42.6093884228392 33 267.2 275.276565757883 -8.07656575788258 34 228.8 263.488854501053 -34.6888545010526 35 196.3 224.347562875663 -28.0475628756633 36 194.8 193.069715077274 1.73028492272587 37 186.6 181.107729846187 5.49227015381257 38 176.7 177.465404544223 -0.765404544222918 39 162.1 160.969247425387 1.13075257461261 40 154.9 154.948151715486 -0.0481517154864548 41 150.1 133.071974630052 17.0280253699478 42 150.5 130.959051315580 19.5409486844196 43 143.6 140.499851186095 3.10014881390546 44 143.8 134.584613744054 9.21538625594638 45 141.5 169.732914322033 -28.2329143220331 46 147.9 131.159320703048 16.7406792969519 47 151.4 115.884236631745 35.5157633682552 48 144.6 132.241826304560 12.3581736954404 49 140.4 133.039032288560 7.3609677114396 50 139.5 132.721103019803 6.7788969801968 51 138.1 127.359157990198 10.7408420098019 52 136.7 131.925449534373 4.77455046562679 53 130 131.000411103601 -1.00041110360144 54 128.5 131.017307672957 -2.5173076729574 55 130.4 127.484960068976 2.91503993102424 56 125.7 130.795178791412 -5.09517879141232 57 121.7 141.101605045243 -19.4016050452431 58 129.9 139.549591732372 -9.64959173237216 59 129.6 129.975991063662 -0.375991063661814 60 128.2 119.11831572055 9.08168427944997 61 119.7 115.792947402479 3.90705259752085 62 112.2 113.877599890108 -1.67759989010841 63 105.6 107.441813150535 -1.84181315053543 64 101.2 102.176391693773 -0.976391693773166 65 94.9 93.5718037387872 1.32819626121280 66 95.1 91.7006930269767 3.3993069730233 67 93.1 92.45295874133 0.647041258669972 68 91.4 88.3220381479946 3.07796185200536 69 89.8 91.461924309446 -1.66192430944595 70 85.9 102.895263679034 -16.9952636790344 71 89.7 96.5038267266136 -6.8038267266136 72 91.6 88.8129552612187 2.78704473878125 73 88.6 78.8486241347878 9.75137586521217 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 74.7904467569966 43.0784411307395 106.502452383254 75 68.3253325443649 33.8140733432684 102.836591745461 76 63.8831371318454 25.8880535529317 101.878220710759 77 56.7871830562333 14.6703352014703 98.9040309109964 78 55.3553843910084 8.53643543212566 102.174333349891 79 52.4633357476681 0.419496725554822 104.507174769781 80 48.9557412045722 -8.7837595524323 106.695241961577 81 47.0215638417077 -16.8396901621975 110.882817845613 82 48.3885074809065 -21.9831494899258 118.760164451739 83 55.032860911676 -22.2067691501459 132.272490973498 84 56.8372050763588 -27.6021831471619 141.276593299880 85 51.0515583301586 -40.8978792867074 143.000995947025

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/26/t1264533846xtugkgavdu4vxb8/1rjub1264533772.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/26/t1264533846xtugkgavdu4vxb8/1rjub1264533772.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/26/t1264533846xtugkgavdu4vxb8/2nvza1264533772.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/26/t1264533846xtugkgavdu4vxb8/2nvza1264533772.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/26/t1264533846xtugkgavdu4vxb8/31ddw1264533772.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/26/t1264533846xtugkgavdu4vxb8/31ddw1264533772.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=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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