Verbetering opgave 10.2

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 02 Jun 2008 02:06:45 -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/02/t1212394033fxya8smp2flydoe.htm/, Retrieved Mon, 02 Jun 2008 08:07:13 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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10236 10893 10756 10940 10997 10827 10166 10186 10457 10368 10244 10511 10812 10738 10171 9721 9897 9828 9924 10371 10846 10413 10709 10662 10570 10297 10635 10872 10296 10383 10431 10574 10653 10805 10872 10625 10407 10463 10556 10646 10702 11353 11346 11451 11964 12574 13031 13812 14544 14931 14886 16005 17064 15168 16050 15839 15137 14954 15648 15305 15579 16348 15928 16171 15937 15713 15594 15683 16438 17032 17696 17745 19394

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 0.989310479959063 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 10893 10236 657 3 10756 10885.9769853331 -129.976985333104 4 10940 10757.3893915896 182.610608410421 5 10997 10938.0479802417 58.9520197582915 6 10827 10996.3698312033 -169.369831203339 7 10166 10828.8104822050 -662.810482204979 8 10186 10173.0851259329 12.9148740671262 9 10457 10185.8619461948 271.138053805167 10 10368 10454.1016643400 -86.101664339989 11 10244 10368.9203854665 -124.920385466521 12 10511 10245.3353389640 265.664661036035 13 10812 10508.1601722817 303.839827718313 14 10738 10808.7520980724 -70.7520980723712 15 10171 10738.7563059703 -567.756305970282 16 9721 10177.0690424110 -456.069042411038 17 9897 9725.8751591689 171.124840831097 18 9828 9895.17075758443 -67.1707575844339 19 9924 9828.71802315936 95.281976840637 20 10371 9922.98148139902 448.018518600978 21 10846 10366.2108970667 479.789102933297 22 10413 10840.8712847688 -427.871284768771 23 10709 10417.5737386735 291.426261326524 24 10662 10705.8847931391 -43.8847931390956 25 10570 10662.4691073758 -92.469107375753 26 10297 10570.9884503765 -273.988450376461 27 10635 10299.9288050313 335.071194968716 28 10872 10631.4182497462 240.581750253759 29 10296 10869.4282965592 -573.428296559179 30 10383 10302.1296732681 80.8703267318906 31 10431 10382.1355350217 48.8644649783182 32 10574 10430.4776623223 143.522337677676 33 10653 10572.4658150951 80.5341849049273 34 10805 10652.1391282165 152.860871783521 35 10872 10803.3659906476 68.634009352405 36 10625 10871.2663353815 -246.266335381537 37 10407 10627.6324689275 -220.632468927470 38 10463 10409.3584551983 53.6415448017178 39 10556 10462.4265976318 93.5734023681853 40 10646 10554.9997452401 91.0002547599142 41 10702 10645.0272509530 56.9727490469868 42 11353 10701.3909886573 651.609011342725 43 11346 11346.0346124144 -0.0346124143961788 44 11451 11346.0003699901 104.999630009903 45 11964 11449.8776043507 514.122395649281 46 12574 11958.5042783482 615.495721651787 47 13031 12567.4206461483 463.579353851708 48 13812 13026.0445592064 785.955440793563 49 14544 13803.5985135644 740.401486435647 50 14931 14536.0854634724 394.914536527593 51 14886 14926.7785531473 -40.778553147331 52 16005 14886.4359031611 1118.56409683889 53 17064 15993.0430866698 1070.95691333023 54 15168 17052.5519846120 -1884.55198461198 55 16050 15188.1449562077 861.855043792302 56 15839 16040.787183237 -201.787183237 57 15137 15841.1570081392 -704.157008139216 58 14954 15144.5271004505 -190.527100450470 59 15648 14956.0366432586 691.963356741393 60 15305 15640.6032438305 -335.603243830519 61 15579 15308.5874376007 270.412562399270 62 16348 15576.1094194949 771.890580505087 63 15928 16339.7488601703 -411.748860170281 64 16171 15932.4013976926 238.598602307376 65 15937 16168.4494954589 -231.449495458895 66 15713 15939.4740840202 -226.474084020172 67 15594 15715.4208992599 -121.420899259887 68 15683 15595.2979311360 87.7020688639732 69 16438 15682.0625069772 755.937493022753 70 17032 16429.9193910186 602.080608981363 71 17696 17025.5640472640 670.435952735967 72 17745 17688.8333614471 56.1666385529352 73 19394 17744.3996055916 1649.60039440844 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 19376.3665635244 18398.0401003495 20354.6930266994 75 19376.3665635244 18000.1789529033 20752.5541741456 76 19376.3665635244 17693.9094286453 21058.8236984036 77 19376.3665635244 17435.3792678976 21317.3538591512 78 19376.3665635244 17207.4494713184 21545.2836557304 79 19376.3665635244 17001.2937174959 21751.4394095530 80 19376.3665635244 16811.6559180479 21941.077209001 81 19376.3665635244 16635.1058378547 22117.6272891942 82 19376.3665635244 16469.2580280242 22283.4750990246 83 19376.3665635244 16312.3741176694 22440.3590093795 84 19376.3665635244 16163.1408666062 22589.5922604427 85 19376.3665635244 16020.5374483259 22732.195678723

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212394033fxya8smp2flydoe/14fy81212393999.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212394033fxya8smp2flydoe/14fy81212393999.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212394033fxya8smp2flydoe/24k6p1212393999.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212394033fxya8smp2flydoe/24k6p1212393999.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212394033fxya8smp2flydoe/3e99l1212393999.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/02/t1212394033fxya8smp2flydoe/3e99l1212393999.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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