Paper 'Smoothing model - triple additive'

*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: Sat, 25 Dec 2010 09:42:23 +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/Dec/25/t12932719159q3ifubpvsxwd9r.htm/, Retrieved Sat, 25 Dec 2010 11:11:59 +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/Dec/25/t12932719159q3ifubpvsxwd9r.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:

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Dataseries X:

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9,3 14,2 17,3 23 16,3 18,4 14,2 9,1 5,9 7,2 6,8 8 14,3 14,6 17,5 17,2 17,2 14,1 10,4 6,8 4,1 6,5 6,1 6,3 9,3 16,4 16,1 18 17,6 14 10,5 6,9 2,8 0,7 3,6 6,7 12,5 14,4 16,5 18,7 19,4 15,8 11,3 9,7 2,9 0,1 2,5 6,7 10,3 11,2 17,4 20,5 17 14,2 10,6 6,1

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 19 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.157445652416388 beta 0.00916996697365402 gamma 0.694119859153262 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 14.3 15.2827457264957 -0.982745726495732 14 14.6 15.5184975911223 -0.918497591122335 15 17.5 18.2797056114228 -0.779705611422848 16 17.2 17.7949734421629 -0.594973442162864 17 17.2 17.5926342108219 -0.392634210821914 18 14.1 14.3632522043784 -0.263252204378409 19 10.4 12.8996940896714 -2.49969408967138 20 6.8 7.00957560299231 -0.209575602992307 21 4.1 3.57972373629064 0.520276263709361 22 6.5 5.02386836624918 1.47613163375082 23 6.1 4.8914727985768 1.20852720142320 24 6.3 6.25618891351627 0.0438110864837329 25 9.3 12.1586793020158 -2.8586793020158 26 16.4 12.1290418842469 4.27095811575306 27 16.1 15.7883635878636 0.311636412136444 28 18 15.5849579390829 2.41504206091707 29 17.6 15.9806750037264 1.61932499627360 30 14 13.1524466336763 0.847553366323726 31 10.5 10.5661496303475 -0.0661496303475051 32 6.9 6.41235029789332 0.48764970210668 33 2.8 3.53395180909005 -0.733951809090051 34 0.7 5.35266561425973 -4.65266561425973 35 3.6 4.10299038614618 -0.502990386146184 36 6.7 4.51877612928182 2.18122387071818 37 12.5 9.06511046800151 3.43488953199849 38 14.4 14.2098986508605 0.190101349139466 39 16.5 14.9191488751772 1.58085112482282 40 18.7 16.1555369979277 2.54446300207229 41 19.4 16.116274436426 3.28372556357401 42 15.8 13.1111494201982 2.68885057980178 43 11.3 10.2954595438098 1.00454045619018 44 9.7 6.6507292525452 3.04927074745481 45 2.9 3.48152454435278 -0.58152454435278 46 0.1 3.05297293779391 -2.95297293779391 47 2.5 4.52076233020462 -2.02076233020462 48 6.7 6.28819459232851 0.411805407671486 49 10.3 11.3073671284030 -1.00736712840301 50 11.2 13.8669057227964 -2.66690572279635 51 17.4 14.9473909884565 2.45260901154354 52 20.5 16.8935459635882 3.60645403641182 53 17 17.4643278672635 -0.464327867263485 54 14.2 13.5262667910885 0.673733208911457 55 10.6 9.41043634514365 1.18956365485635 56 6.1 6.9931037051144 -0.8931037051144 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 57 1.07652528957599 -2.7437553665554 4.89680594570738 58 -0.649783694223311 -4.51798688862558 3.21841950017896 59 1.82997711226625 -2.08642097960063 5.74637520413314 60 5.34298521953185 1.37812213009878 9.30784830896492 61 9.47151429793148 5.45791831564233 13.4851102802206 62 11.2247322159054 7.16213759777913 15.2873268340317 63 15.7286532192823 11.6167963238585 19.8405101147061 64 17.9694002786119 13.8080195168156 22.1307810404082 65 15.5923615641978 11.3811973517984 19.8035257765972 66 12.3943841049656 8.13317881657199 16.6555893933591 67 8.4745803456872 4.1630782702243 12.7860824211501 68 4.65065257374453 0.288599871356671 9.01270527613238

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/25/t12932719159q3ifubpvsxwd9r/1otbs1293270123.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/25/t12932719159q3ifubpvsxwd9r/1otbs1293270123.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/25/t12932719159q3ifubpvsxwd9r/2h2sv1293270123.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/25/t12932719159q3ifubpvsxwd9r/2h2sv1293270123.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/25/t12932719159q3ifubpvsxwd9r/3h2sv1293270123.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/25/t12932719159q3ifubpvsxwd9r/3h2sv1293270123.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')

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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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