datareeks - exponential Smoothing gemiddelde gokuitgaven - Frederik Verbraken

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 20 May 2011 14:51:38 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/20/t13059028983eiwupje4vfa84r.htm/, Retrieved Fri, 20 May 2011 16:48:20 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

5.81 5.76 5.99 6.12 6.03 6.25 5.80 5.67 5.89 5.91 5.86 6.07 6.27 6.68 6.77 6.71 6.62 6.50 5.89 6.05 6.43 6.47 6.62 6.77 6.70 6.95 6.73 7.07 7.28 7.32 6.76 6.93 6.99 7.16 7.28 7.08 7.34 7.87 6.28 6.30 6.36 6.28 5.89 6.04 5.96 6.10 6.26 6.02 6.25 6.41 6.22 6.57 6.18 6.26 6.10 6.02 6.06 6.35 6.21 6.48 6.74 6.53 6.80 6.75 6.56 6.66 6.18 6.40 6.43 6.54 6.44 6.64 6.82 6.97 7.00 6.91 6.74 6.98 6.37 6.56 6.63 6.87 6.68 6.75 6.84 7.15 7.09 6.97 7.15

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 'Gwilym Jenkins' @ www.wessa.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.790049205367589 beta 0.00443492636579578 gamma 0.910460748484263 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 6.27 6.00513471471907 0.264865285280932 14 6.68 6.64504757277073 0.0349524272292676 15 6.77 6.76683625256194 0.00316374743805969 16 6.71 6.70557576231613 0.00442423768386568 17 6.62 6.60592443261431 0.0140755673856905 18 6.5 6.47849096455569 0.0215090354443106 19 5.89 6.32768873003534 -0.437688730035343 20 6.05 5.83038449164558 0.219615508354418 21 6.43 6.20452293979347 0.225477060206529 22 6.47 6.38565257145608 0.084347428543924 23 6.62 6.3873697161425 0.232630283857501 24 6.77 6.81092562846281 -0.0409256284628086 25 6.7 7.0870432851245 -0.387043285124504 26 6.95 7.19609101986052 -0.246091019860518 27 6.73 7.09083234591805 -0.36083234591805 28 7.07 6.73943662089072 0.330563379109281 29 7.28 6.89194295138071 0.388057048619291 30 7.32 7.04590302294104 0.274096977058964 31 6.76 6.96777018469932 -0.207770184699319 32 6.93 6.76826773051068 0.161732269489317 33 6.99 7.12075248225123 -0.130752482251235 34 7.16 6.98771400797636 0.172285992023641 35 7.28 7.07875433340391 0.201245666596092 36 7.08 7.43942399108796 -0.359423991087963 37 7.34 7.40499384141914 -0.0649938414191356 38 7.87 7.83287524383643 0.0371247561635712 39 6.28 7.93081818628042 -1.65081818628042 40 6.3 6.68681723664301 -0.386817236643013 41 6.36 6.28897084395873 0.0710291560412735 42 6.28 6.19081093903868 0.089189060961318 43 5.89 5.92885085405116 -0.0388508540511632 44 6.04 5.92772634655613 0.112273653443869 45 5.96 6.16205467894051 -0.202054678940506 46 6.1 6.02552669419746 0.0744733058025417 47 6.26 6.04957405308452 0.210425946915479 48 6.02 6.2937208608802 -0.273720860880203 49 6.25 6.33910124086385 -0.0891012408638492 50 6.41 6.69402583507748 -0.284025835077483 51 6.22 6.20952212414486 0.0104778758551411 52 6.57 6.50979860790781 0.0602013920921882 53 6.18 6.54989686954732 -0.369896869547321 54 6.26 6.10725418660603 0.152745813393966 55 6.1 5.872100931875 0.227899068125004 56 6.02 6.10981784742629 -0.0898178474262883 57 6.06 6.12154748840332 -0.0615474884033178 58 6.35 6.14813657946359 0.20186342053641 59 6.21 6.29529171874476 -0.0852917187447568 60 6.48 6.20970817622499 0.270291823775011 61 6.74 6.73716603078734 0.00283396921266199 62 6.53 7.15305644915515 -0.623056449155147 63 6.8 6.44697905104165 0.353020948958346 64 6.75 7.0491669649905 -0.2991669649905 65 6.56 6.71413617678361 -0.154136176783609 66 6.66 6.53552625982474 0.124473740175263 67 6.18 6.26824163141441 -0.0882416314144132 68 6.4 6.19330080279141 0.206699197208589 69 6.43 6.44732049495923 -0.0173204949592334 70 6.54 6.56364382298656 -0.0236438229865579 71 6.44 6.4734637417974 -0.0334637417973935 72 6.64 6.49486693738637 0.14513306261363 73 6.82 6.87579663362076 -0.0557966336207567 74 6.97 7.11880632914136 -0.148806329141363 75 7 6.96674798593013 0.0332520140698707 76 6.91 7.19331361652164 -0.283313616521643 77 6.74 6.89363504515358 -0.15363504515358 78 6.98 6.7661317821046 0.213868217895395 79 6.37 6.50970866641909 -0.139708666419086 80 6.56 6.44929702443397 0.110702975566025 81 6.63 6.58383231703029 0.0461676829697142 82 6.87 6.75097395552786 0.119026044472145 83 6.68 6.76622330712744 -0.0862233071274359 84 6.75 6.78091928977597 -0.0309192897759702 85 6.84 6.98648794517266 -0.146487945172659 86 7.15 7.13965760133986 0.0103423986601392 87 7.09 7.14616507889787 -0.0561650788978687 88 6.97 7.23992776665109 -0.269927766651091 89 7.15 6.97235483920058 0.177645160799422 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 90 7.17723772571819 6.64228893620205 7.71218651523433 91 6.66776459804395 5.99977804862465 7.33575114746325 92 6.76795963906842 5.96670505720956 7.56921422092729 93 6.80194437657832 5.88941528190521 7.71447347125144 94 6.9481678402962 5.92362926253406 7.97270641805833 95 6.82686785262107 5.73053982230424 7.9231958829379 96 6.9204993858277 5.72996163878806 8.11103713286734 97 7.13134225719529 5.8337376635858 8.42894685080478 98 7.44090466706791 6.02349583822046 8.85831349591536 99 7.4239771976113 5.94573975052716 8.90221464469544 100 7.52226019523222 5.96485581234178 9.07966457812267 101 7.55324235889449 -9.28715915209915 24.3936438698881

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/20/t13059028983eiwupje4vfa84r/1is661305903096.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13059028983eiwupje4vfa84r/1is661305903096.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13059028983eiwupje4vfa84r/2de071305903096.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13059028983eiwupje4vfa84r/2de071305903096.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13059028983eiwupje4vfa84r/3m6bf1305903096.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13059028983eiwupje4vfa84r/3m6bf1305903096.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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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