additive hw

*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, 15 Dec 2010 18:29:19 +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/15/t1292437813rh1tp5gvfp8xb2t.htm/, Retrieved Wed, 15 Dec 2010 19:30:16 +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/15/t1292437813rh1tp5gvfp8xb2t.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 «

597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516 528 533 536 537 524 536 587 597 581 564 558 575 580 575 563 552 537 545 601 604 586 564 549

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.902430979310268 beta 0.171889535288598 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 557 582.066773504274 -25.0667735042737 14 561 560.513715405438 0.486284594562449 15 549 545.554293592953 3.4457064070466 16 532 529.34170497986 2.65829502014026 17 526 523.830882518767 2.16911748123323 18 511 508.298414548989 2.70158545101117 19 499 514.290527895811 -15.2905278958111 20 555 541.174157915786 13.8258420842142 21 565 555.519611956253 9.48038804374698 22 542 556.080843337813 -14.0808433378133 23 527 507.487157800751 19.512842199249 24 510 502.819589809251 7.18041019074894 25 514 499.774259953008 14.2257400469916 26 517 523.357456043095 -6.35745604309477 27 508 508.633474020973 -0.633474020973267 28 493 494.152819018376 -1.15281901837568 29 490 490.053765896008 -0.0537658960076328 30 469 477.121206562276 -8.12120656227648 31 478 474.46616468344 3.53383531656021 32 528 526.973485273004 1.02651472699631 33 534 533.154182718774 0.845817281225663 34 518 526.0948171399 -8.09481713989953 35 506 489.57970660244 16.4202933975604 36 502 483.83724861902 18.1627513809797 37 516 496.012878429499 19.9871215705006 38 528 528.303486745401 -0.30348674540096 39 533 526.056805109543 6.9431948904571 40 536 525.993707568230 10.0062924317696 41 537 541.434008533813 -4.43400853381263 42 524 532.443786526393 -8.44378652639284 43 536 539.267107680346 -3.2671076803457 44 587 592.969756290473 -5.96975629047301 45 597 599.311267383891 -2.31126738389071 46 581 594.532895626929 -13.5328956269292 47 564 560.661037434374 3.33896256562559 48 558 546.41326303539 11.5867369646098 49 575 554.942106479032 20.0578935209677 50 580 587.437435597709 -7.43743559770917 51 575 580.473890899085 -5.47389089908484 52 563 568.591956654152 -5.59195665415223 53 552 565.215275065266 -13.2152750652664 54 537 543.215486277513 -6.21548627751315 55 545 548.206578842009 -3.20657884200909 56 601 597.361345661228 3.63865433877197 57 604 609.882370920297 -5.88237092029669 58 586 597.38412898002 -11.3841289800203 59 564 564.028555948256 -0.0285559482556437 60 549 543.955192456023 5.04480754397673 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 542.800781344236 523.096887611713 562.504675076759 62 546.795067217103 518.116520134701 575.473614299506 63 540.171072944562 502.842858183237 577.499287705887 64 527.502726293093 481.462127800306 573.54332478588 65 523.581313943002 468.625277354667 578.537350531336 66 511.393008216494 447.257472209831 575.528544223158 67 520.453507751861 446.846283979418 594.060731524304 68 571.834056317333 488.450491910470 655.217620724195 69 578.2422506406 484.773342110523 671.711159170677 70 569.527866088077 465.664681296064 673.391050880089 71 548.331748990947 433.767900805657 662.895597176237 72 529.561701063319 403.994735075952 655.128667050687

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292437813rh1tp5gvfp8xb2t/1kb7d1292437755.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292437813rh1tp5gvfp8xb2t/1kb7d1292437755.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292437813rh1tp5gvfp8xb2t/2ukpf1292437755.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292437813rh1tp5gvfp8xb2t/2ukpf1292437755.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292437813rh1tp5gvfp8xb2t/3ukpf1292437755.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292437813rh1tp5gvfp8xb2t/3ukpf1292437755.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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