ExponentialSmoothingOpg10Oef2Double-GrietjeCordeel

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 28 May 2008 13:02:50 -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/28/t1212001464csym1luerd2f1sk.htm/, Retrieved Wed, 28 May 2008 21:04:24 +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 1.43 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 1.43 1.43 0 20 1.44 1.43 0.01 21 1.48 1.44030577523343 0.0396942247665708 22 1.48 1.48151952631781 -0.00151952631780872 23 1.48 1.48147306296636 -0.00147306296635574 24 1.48 1.48142802034912 -0.00142802034911638 25 1.48 1.48138435502356 -0.00138435502355705 26 1.48 1.48134202487551 -0.00134202487550938 27 1.48 1.48130098907855 -0.00130098907855181 28 1.48 1.48126120805463 -0.00126120805463348 29 1.48 1.48122264343590 -0.00122264343590262 30 1.48 1.4811852580277 -0.00118525802770120 31 1.48 1.48114901577269 -0.00114901577269166 32 1.48 1.48111388171608 -0.00111388171608096 33 1.48 1.48107982197191 -0.00107982197190615 34 1.48 1.48104680369035 -0.00104680369035393 35 1.48 1.48101479502608 -0.00101479502607660 36 1.48 1.48098376510748 -0.00098376510747844 37 1.48 1.48095368400694 -0.000953684006940625 38 1.48 1.48092452271196 -0.000924522711956755 39 1.48 1.48089625309715 -0.000896253097150801 40 1.48 1.48086884789715 -0.00086884789715147 41 1.48 1.48084228068029 -0.000842280680294794 42 1.48 1.48081652582313 -0.000816525823131853 43 1.48 1.48079155848571 -0.000791558485714772 44 1.48 1.48076735458764 -0.000767354587640545 45 1.48 1.48074389078482 -0.00074389078482473 46 1.48 1.48072114444699 -0.000721144446987232 47 1.48 1.48069909363583 -0.000699093635825765 48 1.48 1.48067771708386 -0.000677717083857443 49 1.48 1.48065699417391 -0.000656994173905856 50 1.48 1.48063690491922 -0.000636904919217196 51 1.57 1.48061742994418 0.0893825700558175 52 1.58 1.57335052756652 0.00664947243348424 53 1.58 1.58355385196507 -0.00355385196506863 54 1.58 1.58344518397365 -0.00344518397364957 55 1.58 1.58333983878027 -0.00333983878027455 56 1.59 1.58323771478201 0.00676228521799094 57 1.6 1.59344448871611 0.0065555112838862 58 1.6 1.60364494001542 -0.00364494001542170 59 1.61 1.60353348677702 0.00646651322298353 60 1.61 1.61373121673604 -0.00373121673603971 61 1.61 1.61361712536920 -0.00361712536919589 62 1.62 1.61350652263379 0.00649347736621508 63 1.63 1.62370507708953 0.00629492291047251 64 1.63 1.63389756024176 -0.00389756024176413 65 1.64 1.63377838250249 0.00622161749750894 66 1.64 1.64396862415675 -0.00396862415675203 67 1.64 1.64384727345896 -0.00384727345895963 68 1.64 1.64372963336496 -0.00372963336496168 69 1.64 1.64361559041368 -0.00361559041368387 70 1.65 1.64350503461341 0.00649496538658911 71 1.65 1.65370363456913 -0.00370363456913103 72 1.65 1.65359038659664 -0.00359038659663957 73 1.65 1.65348060146667 -0.00348060146667084 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 1.65337417329408 1.62988940293862 1.67685894364953 75 1.65674834658815 1.62302426516209 1.69047242801422 76 1.66012251988223 1.61818960869147 1.70205543107298 77 1.66349669317630 1.61434659744772 1.71264678890489 78 1.66687086647038 1.61109960479912 1.72264212814164 79 1.67024503976446 1.60824902740447 1.73224105212445 80 1.67361921305853 1.60567821642677 1.74156020969029 81 1.67699338635261 1.60331241590898 1.75067435679624 82 1.68036755964669 1.60110056747518 1.75963455181819 83 1.68374173294076 1.59900613060441 1.76847733527712 84 1.68711590623484 1.59700200317622 1.77722980929345 85 1.69049007952891 1.59506750848748 1.78591265057035

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1212001464csym1luerd2f1sk/1r2ok1212001364.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1212001464csym1luerd2f1sk/1r2ok1212001364.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1212001464csym1luerd2f1sk/2f7hn1212001364.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1212001464csym1luerd2f1sk/2f7hn1212001364.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1212001464csym1luerd2f1sk/3e3h41212001364.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1212001464csym1luerd2f1sk/3e3h41212001364.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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