exponential smoothing -- eigen reeks -- triple additief

*Unverified author*

R Software Module: rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Sun, 07 Jun 2009 14:58:04 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/07/t1244408319eqif0m8hy1v2lvq.htm/, Retrieved Sun, 07 Jun 2009 22:58:43 +0200

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/Jun/07/t1244408319eqif0m8hy1v2lvq.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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517 540 454 292 445 483 545 355 370 372 422 445 471 413 307 308 389 377 521 420 413 384 466 434 263 334 334 416 309 334 350 337 277 439 433 455 372 409 471 382 417 405 410 357 360 329 359 393 448 593 535 449 742 631 513 526 677 631 547 533 433 427 470 418 485 464 439 452 423 537 384 380

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 2 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.475951406937993 beta 0 gamma 0.691257448858544 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 471 508.236912393163 -37.2369123931626 14 413 428.665321013479 -15.6653210134794 15 307 308.569092234181 -1.56909223418131 16 308 304.390316708243 3.60968329175660 17 389 382.634720013425 6.36527998657505 18 377 370.148986775792 6.85101322420769 19 521 513.561105622674 7.43889437732582 20 420 332.169693998162 87.8303060018383 21 413 398.2490211754 14.7509788245996 22 384 410.587806431217 -26.5878064312172 23 466 447.459672016754 18.5403279832462 24 434 483.893670002675 -49.8936700026745 25 263 475.933912666138 -212.933912666138 26 334 320.553449578188 13.4465504218119 27 334 219.419450991615 114.580549008385 28 416 272.398284978060 143.601715021940 29 309 418.270314519158 -109.270314519158 30 334 350.923615460928 -16.9236154609276 31 350 483.2331277493 -133.233127749300 32 337 264.010658595215 72.9893414047847 33 277 296.553239297600 -19.5532392976005 34 439 277.589805636326 161.410194363674 35 433 420.287363421173 12.7126365788266 36 455 429.157277072158 25.8427229278421 37 372 398.182628058698 -26.1826280586980 38 409 413.693588864495 -4.69358886449515 39 471 340.56180862998 130.438191370020 40 382 411.601099562374 -29.6010995623738 41 417 383.43348257424 33.5665174257604 42 405 417.522996644755 -12.5229966447546 43 410 509.793578803763 -99.7935788037627 44 357 381.191313688174 -24.1913136881745 45 360 333.956844255885 26.0431557441154 46 329 402.249534045382 -73.2495340453822 47 359 379.394402854661 -20.3944028546613 48 393 377.263381027762 15.7366189722375 49 448 322.63240449695 125.367595503050 50 593 418.058365460134 174.941634539866 51 535 479.376046884018 55.6239531159819 52 449 456.832763659304 -7.83276365930368 53 742 461.908443534473 280.091556465527 54 631 596.635855384334 34.3641446156662 55 513 679.608452395675 -166.608452395675 56 526 546.592663243359 -20.5926632433593 57 677 519.268538365756 157.731461634244 58 631 614.269438156591 16.7305618434092 59 547 653.387363269613 -106.387363269613 60 533 623.4164236966 -90.4164236966004 61 433 557.975851771901 -124.975851771901 62 427 552.208816041707 -125.208816041707 63 470 427.446340601637 42.5536593983634 64 418 375.694878810619 42.3051211893809 65 485 508.935058430096 -23.9350584300960 66 464 409.945207505465 54.0547924945351 67 439 429.486771682138 9.51322831786217 68 452 433.190927971132 18.8090720288681 69 423 489.218473323462 -66.2184733234618 70 537 426.55215895 110.447841050000 71 384 465.675179586851 -81.6751795868508 72 380 453.251551290307 -73.2515512903074 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 383.461385542462 210.240425497985 556.682345586939 74 437.092390408741 245.252250209825 628.932530607657 75 432.695602171671 223.890004104116 641.501200239226 76 360.600632733704 136.108057851685 585.093207615722 77 449.70996016418 210.557175171054 688.862745157306 78 390.364051941037 137.399246162096 643.328857719979 79 368.042868890005 101.982102606085 634.103635173926 80 370.586633340256 92.0449492992551 649.128317381256 81 386.860534075656 96.3736873145569 677.347380836754 82 419.708808148194 117.748965563099 721.66865073329 83 336.666980156134 23.6543846798093 649.679575632458 84 366.168248850756 42.4800913293010 689.856406372212

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244408319eqif0m8hy1v2lvq/1lb4p1244408282.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244408319eqif0m8hy1v2lvq/1lb4p1244408282.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244408319eqif0m8hy1v2lvq/29qb91244408282.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244408319eqif0m8hy1v2lvq/29qb91244408282.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244408319eqif0m8hy1v2lvq/3uvmh1244408282.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t1244408319eqif0m8hy1v2lvq/3uvmh1244408282.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=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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