datareeks-diesel-seda hovhannesian

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 06 Aug 2009 06:29:02 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Aug/06/t12495618716b00l7qbbo4lwyg.htm/, Retrieved Thu, 06 Aug 2009 14:31:11 +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/2009/Aug/06/t12495618716b00l7qbbo4lwyg.htm/}, year = {2009}, } @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 = {2009}, 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:

Dataseries X:

» Textbox « » Textfile « » CSV «

0.9 0.92 0.92 0.95 1.06 1.17 1.23 1.26 1.37 1.37 1.31 1.21 1.2 1.11 1.11 1.11 1.17 1.08 1.05 1.03 1.04 1.02 1.01 1.01 0.98 0.96 0.94 0.99 0.99 0.98 1.02 1.06 1.06 1.06 1.06 1.06 1.04 1.02 1.01 1 1.04 1.09 1.08 1.06 1.06 1.03 0.97 0.98 0.93 0.88 0.86 0.9 0.91 0.93 0.89 0.88 0.83 0.81 0.83 0.8 0.76 0.73 0.74 0.74 0.75 0.74 0.74 0.73 0.71 0.71 0.7 0.75 0.81 0.78 0.75

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 0.740843693108228 beta 0.000554454471247304 gamma 0.450293672392732 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1.2 1.16166475173153 0.0383352482684693 14 1.11 1.11048182758549 -0.000481827585486538 15 1.11 1.12609336529116 -0.016093365291155 16 1.11 1.13552443884904 -0.0255244388490383 17 1.17 1.19875697194969 -0.0287569719496918 18 1.08 1.10112236822382 -0.0211223682238153 19 1.05 1.15936563629937 -0.109365636299373 20 1.03 1.07821459605905 -0.0482145960590488 21 1.04 1.11066661232524 -0.0706666123252446 22 1.02 1.03781221644680 -0.0178122164468011 23 1.01 0.96339143585355 0.0466085641464503 24 1.01 0.914418757946076 0.095581242053924 25 0.98 0.983244042236231 -0.00324404223623131 26 0.96 0.910600003063873 0.0493999969361271 27 0.94 0.958278315643581 -0.0182783156435813 28 0.99 0.960872522070738 0.0291274779292622 29 0.99 1.05367732483681 -0.0636773248368059 30 0.98 0.940818568521542 0.0391814314784582 31 1.02 1.02518372932378 -0.00518372932378131 32 1.06 1.02760156004442 0.0323984399555795 33 1.06 1.11784165612741 -0.0578416561274149 34 1.06 1.06053473495978 -0.000534734959778849 35 1.06 1.00459838939742 0.0554016106025763 36 1.06 0.964093186783026 0.0959068132169737 37 1.04 1.02142595549493 0.0185740445050708 38 1.02 0.967697577674724 0.0523024223252759 39 1.01 1.010201972984 -0.000201972984000598 40 1 1.03373930406097 -0.0337393040609708 41 1.04 1.07040711324789 -0.0304071132478891 42 1.09 0.991828432583796 0.0981715674162041 43 1.08 1.12010601808364 -0.0401060180836366 44 1.06 1.10224633879243 -0.042246338792427 45 1.06 1.12737485710197 -0.0673748571019677 46 1.03 1.06974637423657 -0.0397463742365749 47 0.97 0.991854741482205 -0.0218547414822046 48 0.98 0.903223809009662 0.0767761909903376 49 0.93 0.938657811286493 -0.00865781128649246 50 0.88 0.874271905986817 0.00572809401318297 51 0.86 0.875597507870825 -0.0155975078708248 52 0.9 0.879905971902227 0.0200940280977733 53 0.91 0.949210822775277 -0.0392108227752772 54 0.93 0.882491987697047 0.0475080123029529 55 0.89 0.950131155584487 -0.0601311555844871 56 0.88 0.91391975302273 -0.0339197530227293 57 0.83 0.931794663105861 -0.101794663105861 58 0.81 0.851117320899683 -0.0411173208996831 59 0.83 0.782320831839962 0.0476791681600379 60 0.8 0.76487451614155 0.0351254838584500 61 0.76 0.763981764720434 -0.00398176472043377 62 0.73 0.713830803305864 0.0161691966941364 63 0.74 0.720187805747237 0.0198121942527628 64 0.74 0.750916546259799 -0.0109165462597992 65 0.75 0.780812834208565 -0.0308128342085650 66 0.74 0.733804752048293 0.00619524795170745 67 0.74 0.752581318434594 -0.0125813184345943 68 0.73 0.751333491674163 -0.0213334916741627 69 0.71 0.762536726688223 -0.0525367266882226 70 0.71 0.723925320678525 -0.0139253206785247 71 0.7 0.688004353842362 0.0119956461576380 72 0.75 0.649785394198046 0.100214605801954 73 0.81 0.694768760024662 0.115231239975338 74 0.78 0.734317182243926 0.0456828177560741 75 0.75 0.763043868236371 -0.0130438682363715 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 76 0.766300539025838 0.684440875414117 0.848160202637559 77 0.803330120392207 0.692437594799785 0.91422264598463 78 0.782685360631416 0.652512735377866 0.912857985884966 79 0.795848250483861 0.64500339115471 0.946693109813012 80 0.803949079463282 0.634875134403327 0.973023024523237 81 0.830017545937936 0.640553165666043 1.01948192620983 82 0.836854534862169 0.631619847542009 1.04208922218233 83 0.811702158994556 0.598501216026971 1.02490310196214 84 0.768767639590325 0.552655208550356 0.984880070630294 85 0.738854173038881 0.517318152339675 0.960390193738088 86 0.687996281488051 0.467575105029868 0.908417457946235 87 0.676634038171737 -10.3091842760632 11.6624523524067

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/06/t12495618716b00l7qbbo4lwyg/1h5iw1249561736.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/06/t12495618716b00l7qbbo4lwyg/1h5iw1249561736.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/06/t12495618716b00l7qbbo4lwyg/2x9381249561736.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/06/t12495618716b00l7qbbo4lwyg/2x9381249561736.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/06/t12495618716b00l7qbbo4lwyg/392z21249561736.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/06/t12495618716b00l7qbbo4lwyg/392z21249561736.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')

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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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