Ruts Wouter: exponentional smoothin plot opgave 10 eigen reeks

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 15:42:51 -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/t1212356983igag30s9h7a8l2f.htm/, Retrieved Sun, 01 Jun 2008 21:49:43 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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6,5300 6,5400 6,5400 6,5100 6,5100 6,4900 6,4600 6,4600 6,5200 6,4800 6,4900 6,4800 6,5300 6,4900 6,4800 6,5700 6,5300 6,5700 6,5500 6,5700 6,6200 6,5600 6,6500 6,5900 6,6800 6,7500 6,7700 6,8200 6,8800 6,8100 6,8700 6,9100 6,9800 7,0400 6,9900 7,0800 7,1300 7,1000 7,0200 7,0300 7,1200 7,1100 7,0900 7,0200 7,0300 7,0600 7,0500 7,1100 7,0600 7,0500 7,1100 7,0900 7,1300 7,0300 7,0600 7,1100 7,0800 7,1300 7,0000 7,0200 6,9600 6,9800 7,0200 7,0200 7,0600 7,0200 6,9400 6,9700 6,9700 6,9400 6,9300 7,0000 6,9700 6,9700 6,9800 6,9200 7,0000 6,9400 6,9700 6,9300 6,9200 6,8400 6,8600 6,8600 6,8400

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.740672708482406 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 6.54 6.53 0.00999999999999979 3 6.54 6.53740672708482 0.00259327291517586 4 6.51 6.53932749355874 -0.0293274935587418 5 6.51 6.51760541947159 -0.007605419471588 6 6.49 6.51197229283242 -0.0219722928324213 7 6.46 6.49569801518866 -0.0356980151886637 8 6.46 6.46925746959143 -0.00925746959143048 9 6.52 6.46240071451545 0.0575992854845477 10 6.48 6.50506293330194 -0.0250629333019425 11 6.49 6.48649950261068 0.00350049738932068 12 6.48 6.48909222549306 -0.00909222549306321 13 6.53 6.48235786221098 0.0476421377890164 14 6.49 6.51764509344507 -0.0276450934450665 15 6.48 6.49716912720686 -0.0171691272068593 16 6.57 6.48445242325628 0.085547576743724 17 6.53 6.54781517862716 -0.0178151786271563 18 6.57 6.53461996202128 0.035380037978717 19 6.55 6.56082499057719 -0.0108249905771904 20 6.57 6.55280721548709 0.0171927845129138 21 6.62 6.56554144175862 0.0544585582413797 22 6.56 6.60587740959131 -0.0458774095913101 23 6.65 6.57189726437116 0.0781027356288426 24 6.59 6.62974582910926 -0.0397458291092576 25 6.68 6.60030717821202 0.0796928217879751 26 6.75 6.65933347637233 0.0906665236276698 27 6.77 6.72648769599632 0.0435123040036789 28 6.82 6.75871607205504 0.0612839279449648 29 6.88 6.80410740495247 0.0758925950475264 30 6.81 6.86031897888008 -0.0503189788800835 31 6.87 6.8230490845049 0.0469509154950973 32 6.91 6.85782434625038 0.0521756537496154 33 6.98 6.89646942902995 0.0835305709700478 34 7.04 6.95833824327142 0.0816617567285807 35 6.99 7.01882287780701 -0.0288228778070083 36 7.08 6.99747455883543 0.0825254411645657 37 7.13 7.0585989008615 0.0714010991385008 38 7.1 7.11148374634903 -0.0114837463490334 39 7.02 7.10297804883717 -0.0829780488371696 40 7.03 7.04151847266036 -0.0115184726603568 41 7.12 7.03298705431743 0.0870129456825701 42 7.11 7.09743516846917 0.0125648315308284 43 7.09 7.10674159627074 -0.0167415962707356 44 7.02 7.09434155281657 -0.0743415528165716 45 7.03 7.03927879353913 -0.00927879353913319 46 7.06 7.03240624439705 0.0275937556029451 47 7.05 7.05284418609669 -0.00284418609668968 48 7.11 7.05073757507703 0.0592624249229736 49 7.06 7.09463163585596 -0.0346316358559609 50 7.05 7.06898092832735 -0.0189809283273501 51 7.11 7.05492227273362 0.0550777272663794 52 7.09 7.09571684216507 -0.0057168421650653 53 7.13 7.0914825331947 0.0385174668052999 54 7.03 7.12001136965726 -0.0900113696572626 55 7.06 7.05334240469901 0.00665759530099219 56 7.11 7.05827350384257 0.0517264961574275 57 7.08 7.0965859078518 -0.0165859078517991 58 7.13 7.08430117856057 0.0456988214394327 59 7 7.11814904841057 -0.118149048410566 60 7.02 7.03063927271969 -0.0106392727196933 61 6.96 7.02275905377812 -0.0627590537781151 62 6.98 6.97627513543449 0.00372486456551524 63 7.02 6.97903404096096 0.0409659590390437 64 7.02 7.00937640879798 0.0106235912020161 65 7.06 7.01724501286739 0.0427549871326089 66 7.02 7.04891246498803 -0.0289124649880312 67 6.94 7.02749779123644 -0.0874977912364425 68 6.97 6.96269056521512 0.00730943478488122 69 6.97 6.96810446407471 0.00189553592528746 70 6.94 6.96950843580252 -0.0295084358025202 71 6.93 6.94765234273359 -0.0176523427335891 72 7 6.93457773423004 0.0654222657699579 73 6.97 6.98303422101293 -0.0130342210129326 74 6.97 6.97338012923232 -0.00338012923232522 75 6.98 6.9708765597588 0.00912344024120237 76 6.92 6.97763404295293 -0.0576340429529267 77 7 6.93494608025819 0.0650539197418087 78 6.94 6.98312974319075 -0.0431297431907538 79 6.97 6.95118471948551 0.0188152805144917 80 6.93 6.96512068426503 -0.0351206842650331 81 6.92 6.9391077519267 -0.0191077519266951 82 6.84 6.92495516155414 -0.0849551615541397 83 6.86 6.86203119194627 -0.00203119194627455 84 6.86 6.86052674350598 -0.000526743505980143 85 6.84 6.86013659896673 -0.0201365989667304 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 86 6.84522196967042 6.75164053250602 6.93880340683482 87 6.84522196967042 6.72876679646096 6.96167714287987 88 6.84522196967042 6.70970027637841 6.98074366296243 89 6.84522196967042 6.6930035366926 6.99744040264824 90 6.84522196967042 6.67796536046255 7.01247857887828 91 6.84522196967042 6.66417198952902 7.02627194981182 92 6.84522196967042 6.65135753947578 7.03908639986506 93 6.84522196967042 6.6393391406628 7.05110479867804 94 6.84522196967042 6.62798463110803 7.06245930823281 95 6.84522196967042 6.61719481503492 7.07324912430591 96 6.84522196967042 6.60689298436513 7.08355095497571 97 6.84522196967042 6.59701836932961 7.09342557001123

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212356983igag30s9h7a8l2f/1vnm61212356565.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212356983igag30s9h7a8l2f/1vnm61212356565.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212356983igag30s9h7a8l2f/2dr9m1212356565.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212356983igag30s9h7a8l2f/2dr9m1212356565.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212356983igag30s9h7a8l2f/3y9vs1212356565.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212356983igag30s9h7a8l2f/3y9vs1212356565.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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')

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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