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: Wed, 16 Dec 2009 15:59:52 -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/17/t1261004425e81kpi5bnpirwul.htm/, Retrieved Thu, 17 Dec 2009 00:00:30 +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/17/t1261004425e81kpi5bnpirwul.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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441 449 452 462 455 461 461 463 462 456 455 456 472 472 471 465 459 465 468 467 463 460 462 461 476 476 471 453 443 442 444 438 427 424 416 406 431 434 418 412 404 409 412 406 398 397 385 390 413 413 401 397 397 409 419 424 428 430 424 433 456

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.496552453079008 beta 0.754829928324468 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 472 467.552073817476 4.44792618252364 14 472 471.54850894744 0.451491052560584 15 471 472.976831065811 -1.97683106581104 16 465 467.425440215685 -2.42544021568494 17 459 460.484037397678 -1.48403739767849 18 465 465.434792758289 -0.434792758288552 19 468 469.131791819429 -1.13179181942866 20 467 467.890571160227 -0.8905711602265 21 463 463.931827028758 -0.931827028757766 22 460 455.47224916567 4.52775083433016 23 462 457.053333971861 4.94666602813948 24 461 462.670208747762 -1.67020874776165 25 476 481.778156539560 -5.77815653955957 26 476 476.159533096608 -0.159533096607561 27 471 473.334825803449 -2.33482580344872 28 453 464.559690518383 -11.5596905183833 29 443 447.488480081972 -4.4884800819724 30 442 443.925487876679 -1.92548787667863 31 444 438.374154508666 5.62584549133408 32 438 435.163620832066 2.83637916793441 33 427 429.183211059192 -2.18321105919199 34 424 418.692768607932 5.30723139206805 35 416 416.78219736737 -0.782197367370088 36 406 410.193636427058 -4.19363642705838 37 431 416.648199042165 14.3518009578351 38 434 423.864431068114 10.1355689318856 39 418 429.279831313427 -11.2798313134268 40 412 412.978207551179 -0.978207551178912 41 404 409.319373675879 -5.31937367587898 42 409 410.188424164302 -1.18842416430232 43 412 412.74575799633 -0.745757996330099 44 406 407.150269621264 -1.15026962126410 45 398 397.604780713275 0.395219286724853 46 397 393.692604890684 3.30739510931636 47 385 388.767006210686 -3.76700621068613 48 390 378.910515708274 11.0894842917255 49 413 406.607408154395 6.39259184560484 50 413 410.379196248942 2.62080375105825 51 401 401.670332331658 -0.670332331658472 52 397 399.63788759354 -2.63788759353974 53 397 396.063772627295 0.936227372704877 54 409 407.369181851178 1.63081814882185 55 419 418.110931949052 0.88906805094797 56 424 420.256668310323 3.74333168967712 57 428 422.664516361855 5.33548363814509 58 430 433.555060520055 -3.55506052005478 59 424 429.068051710437 -5.06805171043675 60 433 433.995324171498 -0.995324171498396 61 456 458.713676668363 -2.71367666836289 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 62 455.436667540855 445.905989794802 464.967345286908 63 441.067604793601 428.621646659256 453.513562927946 64 436.903693812768 420.015228667572 453.792158957965 65 436.274732156254 413.753549163715 458.795915148792 66 448.059427170016 418.310984053078 477.807870286953 67 457.338038587239 419.472750193873 495.203326980606 68 459.214373606561 413.034558421519 505.394188791604 69 457.642469162477 402.965005973521 512.319932351434 70 456.593014579788 392.945431670767 520.24059748881 71 449.342923605335 377.320355620725 521.365491589946 72 457.859049842284 374.543513588018 541.174586096549 73 482.401481211949 384.152608633567 580.650353790332

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261004425e81kpi5bnpirwul/1gavb1261004390.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/17/t1261004425e81kpi5bnpirwul/1gavb1261004390.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/17/t1261004425e81kpi5bnpirwul/2zvua1261004390.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/17/t1261004425e81kpi5bnpirwul/2zvua1261004390.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/17/t1261004425e81kpi5bnpirwul/3amsb1261004390.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/17/t1261004425e81kpi5bnpirwul/3amsb1261004390.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = 2 ; par3 = 1 ; par4 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;

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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