*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 16 May 2011 10:01:00 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/16/t1305540297fpf607qurdlb64v.htm/, Retrieved Mon, 16 May 2011 12:05:02 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W101

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 4 seconds R Server 'George Udny Yule' @ 216.218.223.82 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.594274923316691 beta 0.0241142539120853 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 43129 38294 4835 4 37863 39840.6072043033 -1977.60720430333 5 35953 37310.3126917717 -1357.31269177168 6 29133 35129.192688473 -5996.19268847296 7 24693 30105.3742131567 -5412.37421315672 8 22205 25350.9424083429 -3145.94240834287 9 21725 21898.3112741974 -173.311274197404 10 27192 20209.756642755 6982.24335724496 11 21790 22873.6277044576 -1083.6277044576 12 13253 20728.6249365729 -7475.62493657291 13 37702 14677.8890875326 23024.1109124674 14 30364 27082.3283597765 3281.67164022354 15 32609 27801.3590310311 4807.64096896886 16 30212 29496.1308896812 715.869110318847 17 29965 28769.5241005069 1195.47589949314 18 28352 28345.0673622586 6.93263774138904 19 25814 27214.3885164144 -1400.38851641443 20 22414 25227.305737017 -2813.30573701704 21 20506 22360.2456169724 -1854.24561697241 22 28806 20036.558616095 8769.44138390503 23 22228 24151.9328411378 -1923.93284113783 24 13971 21884.9320059536 -7913.93200595359 25 36845 15944.8143023542 20900.1856976458 26 35338 27427.7142232828 7910.2857767172 27 35022 31304.4006866123 3717.59931338768 28 34777 32742.7537670123 2034.24623298775 29 26887 33209.8840829498 -6322.88408294984 30 23970 28619.9713536828 -4649.97135368283 31 22780 24957.5923105983 -2177.59231059827 32 17351 22733.280154997 -5382.28015499698 33 21382 18527.3716300566 2854.62836994335 34 24561 19257.3595287048 5303.64047129522 35 17409 21518.7377067368 -4109.73770673676 36 11514 18127.0867084793 -6613.08670847928 37 31514 13152.9893589443 18361.0106410557 38 27071 23283.4941934978 3787.50580650217 39 29462 24807.6073983456 4654.39260165436 40 26105 26913.5894433031 -808.589443303106 41 22397 25761.4707643112 -3364.47076431117 42 23843 23042.2413731134 800.758626886563 43 21705 22809.7786275816 -1104.77862758158 44 18089 21429.0708501344 -3340.07085013435 45 20764 18672.1200852641 2091.87991473585 46 25316 19173.219122223 6142.78087777705 47 17704 22169.6961175774 -4465.69611757741 48 15548 18797.8256178991 -3249.8256178991 49 28029 16101.9448518803 11927.0551481197 50 29383 22596.2243600703 6786.7756399297 51 36438 26133.0225215423 10304.9774784577 52 32034 31908.275253418 125.72474658204 53 22679 31636.0550466646 -8957.05504666461 54 24319 25837.8075297262 -1518.80752972615 55 18004 24438.1587196983 -6434.15871969827 56 17537 20025.2352698412 -2488.23526984119 57 20366 17921.6175289985 2444.38247100153 58 22782 18784.3600320329 3997.63996796707 59 19169 20627.4526801149 -1458.4526801149 60 13807 19207.2259372753 -5400.22593727535 61 29743 15367.1142759817 14375.8857240183 62 25591 23485.4634342406 2105.5365657594 63 29096 24342.0251715702 4753.97482842984 64 26482 26840.6141734953 -358.61417349528 65 22405 26295.7806192313 -3890.78061923132 66 27044 23596.1123036503 3447.88769634968 67 17970 25307.0404807588 -7337.04048075883 68 18730 20503.6128602848 -1773.61286028477 69 19684 18980.9740096464 703.025990353566 70 19785 18940.2142334743 844.785766525703 71 18479 18995.8049367975 -516.804936797522 72 10698 18234.8303580312 -7536.8303580312 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 13194.0241901087 447.148586398538 25940.8997938189 74 12632.1673052562 -2289.84902000616 27554.1836305185 75 12070.3104204036 -4832.8815609738 28973.502401781 76 11508.453535551 -7245.30761967863 30262.2146907806 77 10946.5966506984 -9564.13912603357 31457.3324274304 78 10384.7397658458 -11813.116189923 32582.5957216147 79 9822.88288099327 -14008.4803663132 33654.2461282998 80 9261.02599614069 -16161.8812657394 34683.9332580208 81 8699.16911128811 -18281.9828890165 35680.3211115927 82 8137.31222643554 -20375.4157918451 36650.0402447161 83 7575.45534158296 -22447.3732552713 37598.2839384372 84 7013.59845673038 -24502.0013783623 38529.1982918231

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/16/t1305540297fpf607qurdlb64v/176cs1305540055.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/16/t1305540297fpf607qurdlb64v/176cs1305540055.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/16/t1305540297fpf607qurdlb64v/2eyw91305540055.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/16/t1305540297fpf607qurdlb64v/2eyw91305540055.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/16/t1305540297fpf607qurdlb64v/3cscw1305540055.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/16/t1305540297fpf607qurdlb64v/3cscw1305540055.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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