Tripple exponential smoothing

*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: Fri, 17 Dec 2010 14:30:56 +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/17/t1292596449uj61ofnr2p5d1ps.htm/, Retrieved Fri, 17 Dec 2010 15:34:09 +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/17/t1292596449uj61ofnr2p5d1ps.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:

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300 302 400 392 373 379 303 324 353 392 327 376 329 359 413 338 422 390 370 367 406 418 346 350 330 318 382 337 372 422 428 426 396 458 315 337 386 352 383 439 397 453 363 365 474 373 403 384 364 361 419 352 363 410 361 383 342 369 361 317 386 318 407 393 404 498 438

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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.295879428539368 beta FALSE gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 302 300 2 3 400 300.591758857079 99.4082411429213 4 392 330.00461243855 61.99538756145 5 373 348.347772282308 24.6522277176916 6 379 355.641859331641 23.3581406683587 7 303 362.553052644337 -59.5530526443375 8 324 344.932529460156 -20.9325294601560 9 353 338.739024605602 14.2609753943984 10 392 342.95855385571 49.0414461442898 11 327 357.468908915627 -30.4689089156269 12 376 348.453785557453 27.5462144425468 13 329 356.604143745137 -27.6041437451368 14 359 348.436645468507 10.5633545314928 15 413 351.562124770744 61.437875229256 16 338 369.740328184249 -31.7403281842492 17 422 360.349018019442 61.6509819805584 18 390 378.59027533674 11.4097246632600 19 370 381.966178149897 -11.9661781498969 20 367 378.425632197105 -11.4256321971051 21 406 375.045022671925 30.9549773280754 22 418 384.203963674205 33.7960363257953 23 346 394.203515589177 -48.2035155891767 24 350 379.941086943063 -29.9410869430626 25 330 371.082135248502 -41.0821352485017 26 318 358.926776547998 -40.926776547998 27 382 346.817385291018 35.1826147089820 28 337 357.227197225632 -20.2271972256323 29 372 351.242385669559 20.7576143304408 30 422 357.384136735491 64.6158632645094 31 428 376.502641432772 51.4973585672284 32 426 391.73965045693 34.26034954307 33 396 401.876583101293 -5.87658310129257 34 458 400.137823051518 57.862176948482 35 315 417.258050901079 -102.258050901079 36 337 387.001997236918 -50.0019972369179 37 386 372.207434868632 13.7925651313684 38 352 376.288371157793 -24.2883711577929 39 383 369.101941779473 13.8980582205269 40 439 373.214091303569 65.7859086964306 41 397 392.678788374612 4.32121162538766 42 453 393.95734600093 59.0426539990703 43 363 411.426852725622 -48.4268527256222 44 365 397.098343215205 -32.098343215205 45 474 387.60110376763 86.3988962323704 46 373 413.164759811295 -40.1647598112955 47 403 401.280833630908 1.71916636909157 48 384 401.789499593759 -17.7894995937593 49 364 396.525952619957 -32.5259526199565 50 361 386.902192346065 -25.9021923460652 51 419 379.238266476795 39.7617335232053 52 352 391.002945469375 -39.0029454693753 53 363 379.462776252544 -16.4627762525444 54 410 374.59177942277 35.4082205772299 55 361 385.068343492757 -24.0683434927568 56 383 377.947015774231 5.05298422576931 57 342 379.44208985937 -37.4420898593697 58 369 368.36374570846 0.63625429154024 59 361 368.552000264646 -7.55200026464638 60 317 366.317518742014 -49.3175187420136 61 386 351.725479479647 34.2745205203529 62 318 361.86660502467 -43.8666050246699 63 407 348.887378998008 58.1126210019916 64 393 366.081708091003 26.9182919089974 65 404 374.046276918293 29.9537230817074 66 498 382.908967386335 115.091032613665 67 438 416.962036346072 21.0379636539283 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 68 423.186737009628 339.072912714504 507.300561304752 69 423.186737009628 335.468291995314 510.905182023942 70 423.186737009628 332.006060581411 514.367413437845 71 423.186737009628 328.670569545615 517.702904473641 72 423.186737009628 325.44884225911 520.924631760146 73 423.186737009628 322.329976064010 524.043497955246 74 423.186737009628 319.304705904054 527.068768115202 75 423.186737009628 316.365079351653 530.008394667603 76 423.186737009628 313.504210128745 532.869263890511 77 423.186737009628 310.716088122224 535.657385897032 78 423.186737009628 307.995430830160 538.378043189096 79 423.186737009628 305.337565703632 541.035908315624

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292596449uj61ofnr2p5d1ps/1ngh71292596251.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292596449uj61ofnr2p5d1ps/1ngh71292596251.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292596449uj61ofnr2p5d1ps/2ngh71292596251.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292596449uj61ofnr2p5d1ps/2ngh71292596251.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292596449uj61ofnr2p5d1ps/3fqga1292596251.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t1292596449uj61ofnr2p5d1ps/3fqga1292596251.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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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