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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 01 Jun 2008 12:57:06 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Jun/01/t1212346854gby4barmqtnwnl5.htm/, Retrieved Sun, 01 Jun 2008 19:00:58 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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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

Text written by user:

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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.185475284794787 beta 0.000362009975188999 gamma 0.521962133305418 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 37702 39722.9017575777 -2020.90175757771 14 30364 31535.1647279221 -1171.16472792215 15 32609 33590.6706490099 -981.670649009917 16 30212 30845.0542818760 -633.054281876044 17 29965 30291.5608338426 -326.560833842595 18 28352 28469.5184451802 -117.518445180220 19 25814 25831.228645627 -17.2286456269940 20 22414 22218.8079229484 195.192077051564 21 20506 20072.5399434038 433.46005659621 22 28806 27930.4449264667 875.555073533327 23 22228 21566.2431248707 661.756875129253 24 13971 13746.8693916781 224.130608321902 25 36845 37213.4050139222 -368.405013922224 26 35338 29947.1989476151 5390.8010523849 27 35022 33308.6175017054 1713.38249829464 28 34777 31165.8203156697 3611.17968433028 29 26887 31520.5411419802 -4633.5411419802 30 23970 28958.9890191579 -4988.98901915788 31 22780 25492.0388690566 -2712.03886905658 32 17351 21581.2380713672 -4230.23807136717 33 21382 18854.0296661705 2527.97033382945 34 24561 26884.7609272832 -2323.76092728319 35 17409 20297.5845264534 -2888.58452645336 36 11514 12446.0767867259 -932.076786725918 37 31514 32744.2952985226 -1230.29529852262 38 27071 28263.5475890453 -1192.54758904533 39 29462 28693.3350317851 768.66496821486 40 26105 27404.5074091278 -1299.50740912783 41 22397 23992.1600755131 -1595.16007551311 42 23843 22093.2602175141 1749.73978248594 43 21705 21025.8101504194 679.189849580605 44 18089 17487.4969484945 601.503051505471 45 20764 18432.1220109144 2331.87798908564 46 25316 23929.2056032309 1386.79439676912 47 17704 18076.7317399466 -372.731739946568 48 15548 11701.2390141250 3846.76098587502 49 28029 33682.2332964637 -5653.23329646367 50 29383 28310.7491611424 1072.25083885759 51 36438 30049.5703336383 6388.42966636171 52 32034 28761.9441145578 3272.05588544218 53 22679 25730.3147471641 -3051.3147471641 54 24319 24963.345203299 -644.345203298995 55 18004 22866.9428489641 -4862.94284896405 56 17537 18177.4902171704 -640.490217170398 57 20366 19623.4814012913 742.518598708695 58 22782 24395.3863212826 -1613.38632128263 59 19169 17424.4224011487 1744.57759885132 60 13807 13167.5829631341 639.417036865883 61 29743 29499.3786647034 243.621335296575 62 25591 28109.0855152347 -2518.08551523470 63 29096 31165.2654727367 -2069.26547273666 64 26482 27303.0021100248 -821.002110024816 65 22405 21530.9386521882 874.06134781181 66 27044 22431.6796050799 4612.3203949201 67 17970 19629.5503743847 -1659.55037438469 68 18730 17383.6798500638 1346.32014993621 69 19684 19765.1142051533 -81.1142051532843 70 19785 23314.0381640939 -3529.03816409385 71 18479 17568.5563000246 910.443699975433 72 10698 12888.4569955771 -2190.45699557713 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 27245.5103222079 24298.6735269801 30192.3471174356 74 24823.019525219 21764.5473174085 27881.4917330295 75 28275.3351838741 25018.2405341883 31532.4298335599 76 25480.8261514187 22176.9497044063 28784.7025984312 77 20816.6481598162 17541.8136275938 24091.4826920386 78 22940.02389854 19452.4402507178 26427.6075463621 79 17177.6691322870 13845.4495559034 20509.8887086707 80 16556.0822544390 13135.4716237349 19976.6928851431 81 17936.3113768611 14302.8783731139 21569.7443806084 82 19798.5316238424 15897.4397206963 23699.6235269885 83 16793.3755880923 13050.9727845666 20535.7783916181 84 11047.7166824145 9412.97807837183 12682.4552864573

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212346854gby4barmqtnwnl5/1cxow1212346620.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212346854gby4barmqtnwnl5/1cxow1212346620.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212346854gby4barmqtnwnl5/2slwf1212346620.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212346854gby4barmqtnwnl5/2slwf1212346620.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212346854gby4barmqtnwnl5/3dsae1212346620.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212346854gby4barmqtnwnl5/3dsae1212346620.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=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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