W8-exponentieel smoothing (single)

*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: Mon, 29 Nov 2010 11:56:04 +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/29/t1291031679yujdnnqnjw5ftdq.htm/, Retrieved Mon, 29 Nov 2010 12:54:42 +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/29/t1291031679yujdnnqnjw5ftdq.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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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

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.999933893038648 beta FALSE gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 590 593 -3 3 580 590.000198320884 -10.0001983208841 4 574 580.000661082724 -6.00066108272392 5 573 574.00039668547 -1.00039668547026 6 573 573.000066133185 -6.61331851006253e-05 7 620 573.000000004372 46.9999999956281 8 626 619.996892972817 6.0031070271832 9 620 625.999603152836 -5.99960315283579 10 588 620.000396615534 -32.0003966155338 11 566 588.002115448982 -22.0021154489824 12 557 566.001454492996 -9.00145449299566 13 561 557.000595058804 3.99940494119573 14 549 560.999735611492 -11.9997356114922 15 532 549.000793266058 -17.0007932660583 16 526 532.001123870783 -6.00112387078343 17 511 526.000396716064 -15.0003967160637 18 499 511.000991630646 -12.0009916306460 19 555 499.00079334909 55.9992066509101 20 565 554.99629806261 10.0037019373898 21 542 564.999338685663 -22.9993386856626 22 527 542.001520416394 -15.0015204163936 23 510 527.00099170493 -17.0009917049304 24 514 510.001123883902 3.99887611609842 25 517 513.999735646451 3.00026435354891 26 508 516.99980166164 -8.9998016616404 27 493 508.000594949541 -15.0005949495406 28 490 493.000991643751 -3.00099164375058 29 469 490.000198386439 -21.0001983864386 30 478 469.001388259303 8.9986117406969 31 528 477.999405129121 50.0005948708786 32 534 527.996694612607 6.00330538739263 33 518 533.999603139723 -15.9996031397228 34 506 518.001057685146 -12.0010576851464 35 502 506.000793353457 -4.00079335345657 36 516 502.000264480292 13.9997355197085 37 528 515.999074520025 12.0009254799750 38 533 527.999206655283 5.00079334471684 39 536 532.999669412748 3.00033058725239 40 537 535.999801657262 1.00019834273814 41 524 536.999933879927 -12.9999338799267 42 536 524.000859386127 11.9991406138735 43 587 535.999206773275 51.0007932267248 44 597 586.996628492533 10.0033715074668 45 581 596.999338707506 -15.9993387075064 46 564 581.001057667666 -17.0010576676656 47 558 564.001123888262 -6.00112388826221 48 575 558.000396716065 16.999603283935 49 580 574.998876207883 5.00112379211726 50 575 579.999669390903 -4.99966939090268 51 563 575.000330512951 -12.0003305129512 52 552 563.000793305385 -11.0007933053854 53 537 552.000727229018 -15.0007272290178 54 545 537.000991652495 7.99900834750486 55 601 544.999471209864 56.0005287901356 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 56 600.996297975208 562.01815314626 639.974442804155 57 600.996297975208 545.874698912787 656.117897037628 58 600.996297975208 533.487146061632 668.505449888783 59 600.996297975208 523.043873375443 678.948722574972 60 600.996297975208 513.843125859249 688.149470091166 61 600.996297975208 505.524991716386 696.46760423403 62 600.996297975208 497.875663630487 704.116932319929 63 600.996297975208 490.755832915641 711.236763034774 64 600.996297975208 484.068734734364 717.92386121605 65 600.996297975208 477.743914816368 724.248681134047 66 600.996297975208 471.728185653471 730.264410296944 67 600.996297975208 465.980225701878 736.012370248537

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/29/t1291031679yujdnnqnjw5ftdq/1fsan1291031761.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291031679yujdnnqnjw5ftdq/1fsan1291031761.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291031679yujdnnqnjw5ftdq/2fsan1291031761.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291031679yujdnnqnjw5ftdq/2fsan1291031761.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291031679yujdnnqnjw5ftdq/381rq1291031761.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/29/t1291031679yujdnnqnjw5ftdq/381rq1291031761.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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