ws 8 - exponential smoothing triple

*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, 28 Nov 2010 09:23:28 +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/Nov/28/t129093611169r0y8ocnim052n.htm/, Retrieved Sun, 28 Nov 2010 10:21:54 +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/2010/Nov/28/t129093611169r0y8ocnim052n.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

444 454 469 471 443 437 444 451 457 460 454 439 441 446 459 456 433 424 430 428 424 419 409 397 397 413 413 390 385 397 398 406 412 409 404 412 418 434 431 406 416 424 427 401

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 5 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.265744892612999 beta 0.769328451910273 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 441 446.912126068376 -5.91212606837621 14 446 448.999290695025 -2.99929069502508 15 459 460.039002805251 -1.03900280525141 16 456 456.137232370713 -0.137232370712638 17 433 432.94704633677 0.0529536632298573 18 424 423.859894053997 0.140105946002848 19 430 420.657879353683 9.34212064631686 20 428 428.811203915348 -0.811203915347903 21 424 433.392154327235 -9.39215432723483 22 419 431.064247665203 -12.0642476652028 23 409 416.5597694432 -7.55976944319997 24 397 392.623442097769 4.3765579022309 25 397 385.579556534289 11.4204434657109 26 413 392.638841045676 20.3611589543239 27 413 414.329068164031 -1.32906816403136 28 390 413.956284875514 -23.9562848755143 29 385 382.650204610606 2.34979538939410 30 397 372.781248598831 24.2187514011687 31 398 386.201228788178 11.7987712118219 32 406 391.521107008482 14.4788929915182 33 412 400.959543144718 11.0404568552824 34 409 413.371674972492 -4.37167497249203 35 404 417.063778247386 -13.0637782473863 36 412 412.148713774304 -0.148713774303701 37 418 419.868715458689 -1.86871545868939 38 434 438.038782486686 -4.03878248668593 39 431 440.407783726959 -9.40778372695905 40 406 422.711413717952 -16.7114137179522 41 416 415.564613324065 0.435386675935092 42 424 423.771532698647 0.228467301352566 43 427 419.319314412088 7.68068558791185 44 401 422.29333394394 -21.2933339439398 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 45 409.167945850895 387.737362492628 430.598529209163 46 394.539680436358 370.858365721759 418.220995150956 47 381.115064629995 353.369193982166 408.860935277825 48 379.929161941626 346.391886233272 413.46643764998 49 377.230744719644 336.439272778955 418.022216660332 50 385.491061458579 336.238526030081 434.743596887077 51 377.003872172532 318.277847313356 435.729897031707 52 350.380960603284 281.307533175343 419.454388031224 53 357.61794116767 277.422041437929 437.813840897411 54 362.820896823557 270.799862212444 454.841931434671 55 360.996754509321 256.502751075469 465.490757943172 56 336.302031318540 218.730125208514 453.873937428567

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/28/t129093611169r0y8ocnim052n/144zk1290936202.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t129093611169r0y8ocnim052n/144zk1290936202.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t129093611169r0y8ocnim052n/2xdy51290936202.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t129093611169r0y8ocnim052n/2xdy51290936202.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t129093611169r0y8ocnim052n/3xdy51290936202.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t129093611169r0y8ocnim052n/3xdy51290936202.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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