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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 31 May 2010 13:20:15 +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/May/31/t1275312074xjfbfqpnbgfq97v.htm/, Retrieved Mon, 31 May 2010 15:21:15 +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/2010/May/31/t1275312074xjfbfqpnbgfq97v.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:

KDGP2W61

Dataseries X:

» Textbox « » Textfile « » CSV «

41086 39690 43129 37863 35953 29133 24693 22205 21725 27192 21790 13253 37702 30364 32609 30212 29965 28352 25814 22414 20506 28806 22228 13971 36845 35338 35022 34777 26887 23970 22780 17351 21382 24561 17409 11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.594274923316697 beta 0.0241142539120687 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 43129 38294 4835 4 37863 39840.6072043033 -1977.60720430332 5 35953 37310.3126917716 -1357.31269177163 6 29133 35129.1926884729 -5996.19268847293 7 24693 30105.3742131567 -5412.3742131567 8 22205 25350.9424083429 -3145.94240834294 9 21725 21898.3112741975 -173.311274197535 10 27192 20209.7566427552 6982.24335724478 11 21790 22873.6277044578 -1083.62770445777 12 13253 20728.624936573 -7475.62493657304 13 37702 14677.8890875328 23024.1109124672 14 30364 27082.3283597766 3281.67164022343 15 32609 27801.3590310311 4807.64096896892 16 30212 29496.130889681 715.86911031901 17 29965 28769.5241005066 1195.47589949338 18 28352 28345.0673622583 6.93263774165825 19 25814 27214.3885164141 -1400.38851641414 20 22414 25227.3057370168 -2813.30573701676 21 20506 22360.2456169722 -1854.24561697216 22 28806 20036.5586160947 8769.44138390525 23 22228 24151.9328411376 -1923.9328411376 24 13971 21884.9320059533 -7913.93200595332 25 36845 15944.814302354 20900.185697646 26 35338 27427.7142232825 7910.28577671746 27 35022 31304.4006866119 3717.5993133881 28 34777 32742.7537670117 2034.24623298828 29 26887 33209.8840829492 -6322.88408294923 30 23970 28619.9713536822 -4649.97135368221 31 22780 24957.5923105977 -2177.59231059771 32 17351 22733.2801549965 -5382.28015499649 33 21382 18527.3716300562 2854.62836994377 34 24561 19257.3595287044 5303.64047129559 35 17409 21518.7377067364 -4109.73770673639 36 11514 18127.0867084789 -6613.08670847889 37 31514 13152.989358944 18361.010641056 38 27071 23283.4941934975 3787.50580650251 39 29462 24807.6073983452 4654.39260165482 40 26105 26913.5894433026 -808.58944330256 41 22397 25761.4707643106 -3364.47076431058 42 23843 23042.2413731128 800.758626887156 43 21705 22809.778627581 -1104.77862758102 44 18089 21429.0708501338 -3340.0708501338 45 20764 18672.1200852636 2091.87991473636 46 25316 19173.2191222225 6142.78087777753 47 17704 22169.6961175769 -4465.69611757692 48 15548 18797.8256178986 -3249.82561789859 49 28029 16101.9448518798 11927.0551481202 50 29383 22596.2243600698 6786.77563993018 51 36438 26133.0225215417 10304.9774784583 52 32034 31908.2752534173 125.724746582709 53 22679 31636.0550466638 -8957.05504666383 54 24319 25837.8075297254 -1518.80752972539 55 18004 24438.1587196976 -6434.15871969757 56 17537 20025.2352698406 -2488.23526984057 57 20366 17921.6175289979 2444.38247100207 58 22782 18784.3600320324 3997.63996796756 59 19169 20627.4526801144 -1458.45268011441 60 13807 19207.2259372748 -5400.22593727484 61 29743 15367.1142759812 14375.8857240188 62 25591 23485.4634342401 2105.53656575987 63 29096 24342.0251715696 4753.9748284304 64 26482 26840.6141734947 -358.614173494661 65 22405 26295.7806192307 -3890.78061923066 66 27044 23596.1123036497 3447.88769635033 67 17970 25307.0404807582 -7337.0404807582 68 18730 20503.6128602842 -1773.61286028416 69 19684 18980.9740096459 703.025990354101 70 19785 18940.2142334738 844.78576652619 71 18479 18995.804936797 -516.804936797049 72 10698 18234.8303580307 -7536.83035803075 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 13194.0241901083 447.148586398211 25940.8997938184 74 12632.1673052555 -2289.84902000663 27554.1836305177 75 12070.3104204028 -4832.88156097437 28973.5024017799 76 11508.45353555 -7245.30761967926 30262.2146907793 77 10946.5966506972 -9564.13912603422 31457.3324274287 78 10384.7397658445 -11813.1161899237 32582.5957216126 79 9822.88288099172 -14008.4803663138 33654.2461282973 80 9261.02599613895 -16161.88126574 34683.9332580179 81 8699.16911128618 -18281.982889017 35680.3211115893 82 8137.31222643342 -20375.4157918455 36650.0402447123 83 7575.45534158065 -22447.3732552716 37598.2839384329 84 7013.59845672789 -24502.0013783625 38529.1982918183

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/31/t1275312074xjfbfqpnbgfq97v/1d0kg1275312011.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275312074xjfbfqpnbgfq97v/1d0kg1275312011.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275312074xjfbfqpnbgfq97v/2o9jj1275312011.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275312074xjfbfqpnbgfq97v/2o9jj1275312011.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275312074xjfbfqpnbgfq97v/3o9jj1275312011.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275312074xjfbfqpnbgfq97v/3o9jj1275312011.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

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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