ws 8 - exponential smoothing double

*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 09:21:35 +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/t1290936010k66py6vmoggl08v.htm/, Retrieved Sun, 28 Nov 2010 10:20:13 +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/t1290936010k66py6vmoggl08v.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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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 33 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.124512197994220 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 469 464 5 4 471 479.622560989971 -8.62256098997108 5 443 480.54894696877 -37.5489469687706 6 437 447.87364504932 -10.8736450493205 7 444 440.519743604021 3.48025639597932 8 451 447.953077977468 3.0469220225325 9 457 455.33245693561 1.66754306438997 10 460 461.540086387807 -1.54008638780726 11 454 464.348326846560 -10.3483268465604 12 439 457.059833925333 -18.0598339253326 13 441 439.811164307879 1.18883569212119 14 446 441.959188852959 4.04081114704121 15 459 447.462319130556 11.5376808694435 16 456 461.898901135367 -5.89890113536671 17 433 458.164415989252 -25.1644159892516 18 424 432.031139243189 -8.03113924318899 19 430 422.031164443622 7.96883555637811 20 428 429.023381674201 -1.02338167420106 21 424 426.895958172559 -2.89595817255929 22 419 422.535376055195 -3.53537605519460 23 409 417.095178611826 -8.09517861182616 24 397 406.087230129712 -9.08723012971188 25 397 392.955759132582 4.04424086741784 26 413 393.459316452202 19.5406835477976 27 413 411.892369911048 1.10763008895179 28 390 412.030283367988 -22.0302833679881 29 385 386.287244363404 -1.28724436340440 30 397 381.126966738361 15.8730332616387 31 398 395.103352998603 2.89664700139673 32 406 396.464020883561 9.53597911643948 33 412 405.651366603375 6.34863339662462 34 409 412.441848901849 -3.44184890184863 35 404 409.013296729915 -5.01329672991545 36 412 403.389080134876 8.61091986512355 37 418 412.461244694035 5.53875530596491 38 434 419.150887291333 14.8491127086671 39 431 436.999782952953 -5.99978295295296 40 406 433.252736789993 -27.2527367899925 41 416 404.859438630913 11.1405613690874 42 424 416.246574413867 7.75342558613283 43 427 425.211970475581 1.78802952441879 44 401 428.434601961745 -27.4346019617452 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 45 399.018659370392 374.640595329226 423.396723411558 46 397.037318740783 360.352360359012 433.722277122555 47 395.055978111175 347.380875669479 442.731080552872 48 393.074637481567 334.815693378092 451.333581585042 49 391.093296851959 322.334438551781 459.852155152136 50 389.11195622235 309.787493598912 468.436418845789 51 387.130615592742 297.095617992327 477.165613193158 52 385.149274963134 284.213658060242 486.084891866026 53 383.167934333526 271.114861336513 495.221007330538 54 381.186593703917 257.783170266717 504.590017141117 55 379.205253074309 244.209079421114 514.201426727504 56 377.223912444701 230.387254826051 524.060570063351

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/28/t1290936010k66py6vmoggl08v/1z09x1290936061.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290936010k66py6vmoggl08v/1z09x1290936061.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290936010k66py6vmoggl08v/29a901290936061.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290936010k66py6vmoggl08v/29a901290936061.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290936010k66py6vmoggl08v/39a901290936061.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290936010k66py6vmoggl08v/39a901290936061.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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