Exponential smoothing - Joachim Van Der Aa - Eigen reeks

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 27 May 2008 13:48:37 -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/May/27/t1211917793otsox47usmh8a0k.htm/, Retrieved Tue, 27 May 2008 21:49:53 +0200

User-defined keywords:

Dataseries X:

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66.2 66.2 66.08 66.31 66.39 66.37 66.23 66.27 66.27 66.27 66.28 66.28 66.28 66.26 66.13 65.86 65.9 65.94 65.94 65.91 65.95 65.91 66.08 66.47 66.47 66.56 66.78 67.08 67.28 67.27 67.27 67.26 67.37 67.5 67.63 67.64 67.64 67.71 67.87 67.93 68.33 68.39 68.39 68.58 68.44 68.49 68.52 68.54 68.54 68.54 68.62 68.75 68.71 68.72 68.72 68.72 68.92 68.9 69.12 69.09 69.09 69.1 69.16 68.83 68.52 68.53 68.53 68.51 68.38 68.44 68.41 68.42 68.42 68.45 68.63 68.84 68.72 68.37 68.37 68.47 68.69 68.46 68.17 68.17

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 3 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.831008185222246 beta 0.0653557661833785 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 66.28 66.1985055555556 0.0814944444444166 14 66.26 66.3090027158319 -0.0490027158318611 15 66.13 66.1996442726144 -0.0696442726144255 16 65.86 65.9293500643624 -0.0693500643623537 17 65.9 65.9605338619797 -0.0605338619796498 18 65.94 65.9728396640016 -0.0328396640016138 19 65.94 65.9501260104337 -0.0101260104337371 20 65.91 65.9111543000223 -0.00115430002233552 21 65.95 65.9304087963392 0.0195912036608235 22 65.91 65.8496336640127 0.0603663359872826 23 66.08 65.9856049004739 0.0943950995260678 24 66.47 66.3703976935608 0.0996023064392375 25 66.47 66.579115797402 -0.109115797401998 26 66.56 66.502219728533 0.0577802714669673 27 66.78 66.476968471304 0.303031528695982 28 67.08 66.5355189880808 0.544481011919189 29 67.28 67.1307275534083 0.149272446591723 30 67.27 67.3858952883628 -0.115895288362850 31 67.27 67.3573203843956 -0.0873203843956532 32 67.26 67.3108433774492 -0.0508433774492119 33 67.37 67.3447407062187 0.0252592937812892 34 67.5 67.328303349625 0.171696650374969 35 67.63 67.6213249343205 0.00867506567951182 36 67.64 67.9898914602985 -0.349891460298451 37 67.64 67.8195201855698 -0.179520185569828 38 67.71 67.7382130901932 -0.0282130901932334 39 67.87 67.7041672267076 0.165832773292436 40 67.93 67.70327714137 0.226722858630012 41 68.33 67.9641509488087 0.365849051191333 42 68.39 68.3627588494793 0.0272411505206662 43 68.39 68.4740087424403 -0.084008742440318 44 68.58 68.452676231572 0.127323768428028 45 68.44 68.6733972916619 -0.233397291661888 46 68.49 68.4786176127797 0.0113823872202801 47 68.52 68.6140172656088 -0.0940172656088407 48 68.54 68.8342233209066 -0.294223320906596 49 68.54 68.7394999838469 -0.199499983846906 50 68.54 68.6666699541216 -0.126669954121581 51 68.62 68.5777612662337 0.0422387337663253 52 68.75 68.4719043835078 0.278095616492209 53 68.71 68.7892216109981 -0.0792216109980899 54 68.72 68.7268189234054 -0.00681892340541879 55 68.72 68.7551831907983 -0.0351831907983353 56 68.72 68.777009246645 -0.057009246644995 57 68.92 68.7404484820047 0.179551517995307 58 68.9 68.9094854681044 -0.0094854681044012 59 69.12 68.9878857878893 0.132114212110736 60 69.09 69.3526109382738 -0.262610938273767 61 69.09 69.292317295045 -0.202317295044978 62 69.1 69.2214528005383 -0.121452800538307 63 69.16 69.1577062104204 0.00229378957959625 64 68.83 69.0486255925776 -0.218625592577609 65 68.52 68.8559151873218 -0.335915187321788 66 68.53 68.541627612602 -0.0116276126019415 67 68.53 68.5101354396431 0.0198645603568934 68 68.51 68.5259408593804 -0.0159408593803505 69 68.38 68.5176382229576 -0.137638222957591 70 68.44 68.3280684159883 0.111931584011657 71 68.41 68.474816971077 -0.0648169710770219 72 68.42 68.5420102967654 -0.12201029676541 73 68.42 68.5492071759047 -0.129207175904739 74 68.45 68.4971950293378 -0.0471950293378285 75 68.63 68.4645342455037 0.165465754496338 76 68.84 68.4110441899692 0.428955810030772 77 68.72 68.7291560485346 -0.0091560485346207 78 68.37 68.7514544109398 -0.38145441093981 79 68.37 68.4081138047678 -0.038113804767832 80 68.47 68.3566977762908 0.113302223709240 81 68.69 68.429260556021 0.260739443978949 82 68.46 68.6285866800685 -0.168586680068472 83 68.17 68.5127834999137 -0.342783499913665 84 68.17 68.3246527691646 -0.154652769164557 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 68.2870680299479 67.9407554111104 68.6333806487854 86 68.3468656364445 67.8843352980614 68.8093959748276 87 68.3825036084745 67.8169743679947 68.9480328489543 88 68.2201925478088 67.5581449785059 68.8822401171116 89 68.0686589328802 67.313614013166 68.8237038525945 90 67.9970055802247 67.1509036995673 68.843107460882 91 68.0107506114174 67.0745875917825 68.9469136310522 92 68.0007376891554 66.974902038702 69.0265733396087 93 67.9820496529561 66.8665189855182 69.097580320394 94 67.8559740739685 66.6504375152499 69.0615106326871 95 67.823813619074 66.5277520907143 69.1198751474336 96 67.9439319622515 66.5566729839169 69.3311909405861

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211917793otsox47usmh8a0k/11gm71211917710.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211917793otsox47usmh8a0k/11gm71211917710.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211917793otsox47usmh8a0k/26y6r1211917711.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211917793otsox47usmh8a0k/26y6r1211917711.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211917793otsox47usmh8a0k/3q7j01211917711.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211917793otsox47usmh8a0k/3q7j01211917711.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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=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')

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Software written by Ed van Stee & Patrick Wessa

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