Exponential Smoothing - Bruin Brood - Nhu Truong

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 06:35:37 -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/t1211891783xl6pnebwql635ox.htm/, Retrieved Tue, 27 May 2008 14:36:23 +0200

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Dataseries X:

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1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.44 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.57 1.58 1.58 1.58 1.58 1.59 1.6 1.6 1.61 1.61 1.61 1.62 1.63 1.63 1.64 1.64 1.64 1.64 1.64 1.65 1.65 1.65 1.65

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 1 beta 0.0305775233429336 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 1.43 1.43 0 4 1.43 1.43 0 5 1.43 1.43 0 6 1.43 1.43 0 7 1.43 1.43 0 8 1.43 1.43 0 9 1.43 1.43 0 10 1.43 1.43 0 11 1.43 1.43 0 12 1.43 1.43 0 13 1.43 1.43 0 14 1.43 1.43 0 15 1.43 1.43 0 16 1.43 1.43 0 17 1.43 1.43 0 18 1.43 1.43 0 19 1.44 1.43 0.01 20 1.48 1.44030577523343 0.0396942247665708 21 1.48 1.48151952631781 -0.00151952631780872 22 1.48 1.48147306296636 -0.00147306296635574 23 1.48 1.48142802034912 -0.00142802034911638 24 1.48 1.48138435502356 -0.00138435502355705 25 1.48 1.48134202487551 -0.00134202487550938 26 1.48 1.48130098907855 -0.00130098907855181 27 1.48 1.48126120805463 -0.00126120805463348 28 1.48 1.48122264343590 -0.00122264343590262 29 1.48 1.4811852580277 -0.00118525802770120 30 1.48 1.48114901577269 -0.00114901577269166 31 1.48 1.48111388171608 -0.00111388171608096 32 1.48 1.48107982197191 -0.00107982197190615 33 1.48 1.48104680369035 -0.00104680369035393 34 1.48 1.48101479502608 -0.00101479502607660 35 1.48 1.48098376510748 -0.00098376510747844 36 1.48 1.48095368400694 -0.000953684006940625 37 1.48 1.48092452271196 -0.000924522711956755 38 1.48 1.48089625309715 -0.000896253097150801 39 1.48 1.48086884789715 -0.00086884789715147 40 1.48 1.48084228068029 -0.000842280680294794 41 1.48 1.48081652582313 -0.000816525823131853 42 1.48 1.48079155848571 -0.000791558485714772 43 1.48 1.48076735458764 -0.000767354587640545 44 1.48 1.48074389078482 -0.00074389078482473 45 1.48 1.48072114444699 -0.000721144446987232 46 1.48 1.48069909363583 -0.000699093635825765 47 1.48 1.48067771708386 -0.000677717083857443 48 1.48 1.48065699417391 -0.000656994173905856 49 1.48 1.48063690491922 -0.000636904919217196 50 1.57 1.48061742994418 0.0893825700558175 51 1.58 1.57335052756652 0.00664947243348424 52 1.58 1.58355385196507 -0.00355385196506863 53 1.58 1.58344518397365 -0.00344518397364957 54 1.58 1.58333983878027 -0.00333983878027455 55 1.59 1.58323771478201 0.00676228521799094 56 1.6 1.59344448871611 0.0065555112838862 57 1.6 1.60364494001542 -0.00364494001542170 58 1.61 1.60353348677702 0.00646651322298353 59 1.61 1.61373121673604 -0.00373121673603971 60 1.61 1.61361712536920 -0.00361712536919589 61 1.62 1.61350652263379 0.00649347736621508 62 1.63 1.62370507708953 0.00629492291047251 63 1.63 1.63389756024176 -0.00389756024176413 64 1.64 1.63377838250249 0.00622161749750894 65 1.64 1.64396862415675 -0.00396862415675203 66 1.64 1.64384727345896 -0.00384727345895963 67 1.64 1.64372963336496 -0.00372963336496168 68 1.64 1.64361559041368 -0.00361559041368387 69 1.65 1.64350503461341 0.00649496538658911 70 1.65 1.65370363456913 -0.00370363456913103 71 1.65 1.65359038659664 -0.00359038659663957 72 1.65 1.65348060146667 -0.00348060146667084 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 1.65337417329408 1.62972271901860 1.67702562756956 74 1.65674834658815 1.62278490739932 1.69071178577698 75 1.66012251988223 1.61789198849296 1.7023530512715 76 1.66349669317630 1.61399775304764 1.71299563330497 77 1.66687086647038 1.61070376645881 1.72303796648196 78 1.67024503976446 1.60780900869406 1.73268107083486 79 1.67361921305853 1.60519600299749 1.74204242311957 80 1.67699338635261 1.60278946282922 1.751197309876 81 1.68036755964669 1.60053796742486 1.76019715186851 82 1.68374173294076 1.59840471691591 1.76907874896562 83 1.68711590623484 1.59636241682374 1.77786939564593 84 1.69049007952891 1.59439024369165 1.78658991536618

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211891783xl6pnebwql635ox/1nm1n1211891731.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211891783xl6pnebwql635ox/1nm1n1211891731.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211891783xl6pnebwql635ox/28tda1211891731.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211891783xl6pnebwql635ox/28tda1211891731.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211891783xl6pnebwql635ox/3ov591211891731.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211891783xl6pnebwql635ox/3ov591211891731.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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