*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 14:07:58 -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/16/t12609977148vjm05nul7be8u6.htm/, Retrieved Wed, 16 Dec 2009 22:08:38 +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/16/t12609977148vjm05nul7be8u6.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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519 517 510 509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.948539541873247 beta 0.106971000311946 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 562 542.603753604565 19.396246395435 14 561 562.67893320641 -1.67893320641008 15 555 557.13712453219 -2.13712453218955 16 544 545.296186541336 -1.29618654133628 17 537 537.632301941896 -0.632301941895889 18 543 543.773941164938 -0.773941164938151 19 594 610.624553799897 -16.6245537998971 20 611 605.220496232711 5.77950376728927 21 613 607.932497543003 5.06750245699652 22 611 599.192822295501 11.8071777044992 23 594 592.659863243353 1.34013675664733 24 595 604.42270246888 -9.42270246887938 25 591 605.459975445812 -14.4599754458123 26 589 589.750678483172 -0.750678483171896 27 584 582.406025010541 1.59397498945930 28 573 571.610394058013 1.38960594198727 29 567 564.468985374050 2.53101462594952 30 569 572.567019939157 -3.56701993915726 31 621 637.298145630074 -16.2981456300740 32 629 632.134000993372 -3.13400099337161 33 628 623.664150525535 4.33584947446491 34 612 611.649859988715 0.350140011284793 35 595 590.144061783044 4.85593821695602 36 597 601.488049543403 -4.48804954340289 37 593 604.226360276133 -11.2263602761333 38 590 589.890697547126 0.109302452873521 39 580 581.20759472446 -1.20759472445945 40 574 565.366113719614 8.63388628038649 41 573 563.4339095829 9.56609041709953 42 573 576.913257121299 -3.91325712129913 43 620 639.963572355668 -19.9635723556677 44 626 630.448972435625 -4.44897243562536 45 620 619.473527042243 0.526472957757051 46 588 601.87013967871 -13.8701396787096 47 566 564.668413912835 1.33158608716542 48 557 568.276074636277 -11.2760746362766 49 561 559.450170798384 1.54982920161638 50 549 554.888995403075 -5.88899540307534 51 532 537.4170501947 -5.4170501947001 52 526 515.275982323141 10.7240176768589 53 511 512.601559463865 -1.60155946386476 54 499 509.754974120898 -10.7549741208981 55 555 551.070331799376 3.92966820062384 56 565 560.105194146801 4.89480585319893 57 542 555.981011405056 -13.9810114050563 58 527 521.951665254031 5.04833474596876 59 510 503.515694626668 6.48430537333206 60 514 509.332320109869 4.66767989013061 61 517 515.807527831614 1.19247216838585 62 508 510.715216383635 -2.71521638363527 63 493 497.137331636746 -4.13733163674567 64 490 478.281851245991 11.7181487540090 65 469 477.10886631827 -8.10886631826992 66 478 467.303404905063 10.6965950949365 67 528 529.452570270792 -1.45257027079163 68 534 534.633319338097 -0.633319338096726 69 518 525.705125960585 -7.70512596058461 70 506 500.932743898882 5.06725610111772 71 502 484.967570827735 17.0324291722645 72 516 503.342649755887 12.6573502441134 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 520.776912236449 504.512843323194 537.040981149703 74 517.728502638577 494.229076358109 541.227928919045 75 510.119883747051 480.414482196172 539.825285297931 76 499.574685313847 464.231949365219 534.917421262476 77 488.743325503956 448.047011282732 529.43963972518 78 491.203303334836 444.222961474632 538.183645195041 79 546.786284149215 488.220833488893 605.351734809537 80 556.628819766496 490.564551381029 622.693088151964 81 550.617506821196 478.756947017309 622.478066625084 82 536.58131880358 460.030384302385 613.132253304776 83 518.340686197876 437.888717695555 598.792654700197 84 521.696250914254 429.175056936751 614.217444891757

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/16/t12609977148vjm05nul7be8u6/1cchf1260997676.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/16/t12609977148vjm05nul7be8u6/1cchf1260997676.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/16/t12609977148vjm05nul7be8u6/2wso21260997676.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/16/t12609977148vjm05nul7be8u6/2wso21260997676.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/16/t12609977148vjm05nul7be8u6/3y1zg1260997676.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/16/t12609977148vjm05nul7be8u6/3y1zg1260997676.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

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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