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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: Sun, 06 Jun 2010 16:07:22 +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/Jun/06/t1275840530xtfndnnelchek0j.htm/, Retrieved Sun, 06 Jun 2010 18:08:50 +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/Jun/06/t1275840530xtfndnnelchek0j.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 «

5.074 4.643 5.451 5.397 5.635 5.708 5.578 5.574 5.352 5.302 4.923 4.982 5.101 4.763 5.505 5.385 5.794 5.695 5.798 5.705 5.422 5.311 4.968 5.053 5.236 4.782 5.531 5.566 5.961 5.868 5.872 5.908 5.594 5.526 5.111 5.177 5.835 5.348 6.038 6.039 6.408 6.214 6.138 6.529 6.058 6.026 5.678 5.733 6.488 5.936 6.84 6.694 7.193 6.991 7.209 7.104 6.83 6.848 6.396 6.414 7.151 6.882 7.698 7.626 7.936 8.054 8.128 8.062 7.708 7.574 7.039 7.146 7.07 6.607 7.699 7.663 7.988 7.723 8.087 8.028 7.362

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.559630632692926 beta 0.0234545572772744 gamma 0.256002529557058 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 5.101 5.07301556347594 0.0279844365240587 14 4.763 4.7449179365452 0.0180820634547976 15 5.505 5.49487822431458 0.0101217756854188 16 5.385 5.38496272894387 3.72710561293843e-05 17 5.794 5.79975376250684 -0.00575376250684023 18 5.695 5.70034313780302 -0.00534313780302309 19 5.798 5.66111500842549 0.136884991574514 20 5.705 5.73661660126565 -0.0316166012656511 21 5.422 5.49249451976837 -0.0704945197683662 22 5.311 5.40815241789843 -0.09715241789843 23 4.968 4.97144204584224 -0.00344204584224439 24 5.053 5.0294332835595 0.023566716440504 25 5.236 5.16448019332548 0.0715198066745204 26 4.782 4.85242116638604 -0.0704211663860352 27 5.531 5.55986841956288 -0.0288684195628779 28 5.566 5.42487731395309 0.141122686046906 29 5.961 5.92766553986306 0.0333344601369365 30 5.868 5.8486985667757 0.0193014332242951 31 5.872 5.83982362081296 0.0321763791870442 32 5.908 5.83733994039559 0.0706600596044149 33 5.594 5.64068079502438 -0.0466807950243826 34 5.526 5.56654521918851 -0.0405452191885098 35 5.111 5.1601603579849 -0.0491603579848992 36 5.177 5.19919322455277 -0.0221932245527690 37 5.835 5.31850287374055 0.516497126259449 38 5.348 5.2174563480268 0.130543651973195 39 6.038 6.12779419212348 -0.0897941921234828 40 6.039 5.97687436385332 0.0621256361466758 41 6.408 6.4682974133028 -0.0602974133028047 42 6.214 6.3342657063743 -0.120265706374304 43 6.138 6.2527012340951 -0.114701234095095 44 6.529 6.17479685606507 0.35420314393493 45 6.058 6.10934525352416 -0.0513452535241612 46 6.026 6.03568235453588 -0.00968235453587596 47 5.678 5.6177837491262 0.0602162508737987 48 5.733 5.73597020508194 -0.00297020508193935 49 6.488 5.95219468945357 0.535805310546427 50 5.936 5.78055611866845 0.155443881331553 51 6.84 6.77441599678465 0.0655840032153456 52 6.694 6.72742122244282 -0.033421222442823 53 7.193 7.21184406668911 -0.0188440666891099 54 6.991 7.09108209706072 -0.100082097060715 55 7.209 7.02979482794505 0.179205172054952 56 7.104 7.18774743122067 -0.083747431220667 57 6.83 6.8040776983585 0.0259223016415033 58 6.848 6.78202583694572 0.0659741630542792 59 6.396 6.370108388231 0.0258916117689951 60 6.414 6.48027661401617 -0.0662766140161706 61 7.151 6.76099735421847 0.390002645781527 62 6.882 6.4153440515842 0.466655948415798 63 7.698 7.70325146888048 -0.00525146888047789 64 7.626 7.60158611419885 0.0244138858011462 65 7.936 8.1982358398763 -0.262235839876304 66 8.054 7.92476783349304 0.129232166506958 67 8.128 8.03610715161735 0.0918928483826491 68 8.062 8.12739902701665 -0.0653990270166513 69 7.708 7.73081600475976 -0.0228160047597576 70 7.574 7.6891884823673 -0.115188482367305 71 7.039 7.12332248022609 -0.0843224802260876 72 7.146 7.17434038702171 -0.0283403870217143 73 7.07 7.57214065910529 -0.50214065910529 74 6.607 6.70755739519404 -0.100557395194036 75 7.699 7.60113660142225 0.097863398577747 76 7.663 7.5499338821622 0.113066117837794 77 7.988 8.1521536287938 -0.164153628793799 78 7.723 7.96754458481684 -0.244544584816841 79 8.087 7.85122221626515 0.235777783734851 80 8.028 7.99312241174013 0.0348775882598753 81 7.362 7.65033431707146 -0.288334317071460 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 82 7.43795866059125 7.2179360611372 7.6579812600453 83 6.94058579783755 6.65987695290096 7.22129464277413 84 7.03329310479988 6.69169928176905 7.37488692783072 85 7.37521787293669 6.96926868872621 7.78116705714716 86 6.82208278308186 6.39582706579329 7.24833850037044 87 7.81732520119703 7.29206027657601 8.34259012581805 88 7.70633658614493 7.14801863770682 8.26465453458304 89 8.21298434690198 7.58195204961806 8.8440166441859 90 8.10425593207339 7.44438343241672 8.76412843173005 91 8.17990193173653 7.47815680219502 8.88164706127805 92 8.16277586767828 7.42721510163502 8.89833663372153 93 7.75176068555115 -1.23059058928206 16.7341119603844

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/06/t1275840530xtfndnnelchek0j/13oes1275840438.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275840530xtfndnnelchek0j/13oes1275840438.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275840530xtfndnnelchek0j/2efdd1275840438.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275840530xtfndnnelchek0j/2efdd1275840438.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275840530xtfndnnelchek0j/3efdd1275840438.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275840530xtfndnnelchek0j/3efdd1275840438.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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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