Nicky Van Calster 2MAR04b-Opgave 10, pond

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 08:06:29 -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/t1211983633du02jwfknwjmc3x.htm/, Retrieved Wed, 28 May 2008 16:07:13 +0200

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Dataseries X:

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0,70291 0,6885 0,67127 0,66502 0,65825 0,65025 0,65779 0,66014 0,64683 0,64587 0,63702 0,62651 0,61834 0,61466 0,61063 0,59802 0,60151 0,62927 0,62304 0,6071 0,60773 0,58933 0,60039 0,61342 0,6348 0,634 0,62915 0,62168 0,61328 0,6089 0,60857 0,62672 0,62291 0,62393 0,61838 0,62012 0,61659 0,6116 0,61573 0,61407 0,62823 0,64405 0,6387 0,63633 0,63059 0,62994 0,63709 0,64217 0,65711 0,66977 0,68255 0,68902 0,71322 0,70224 0,70045 0,69919 0,69693 0,69763 0,69278 0,70196 0,69215 0,6769 0,67124 0,66532 0,67157 0,66428 0,66576 0,66942 0,6813 0,69144 0,69862 0,695 0,69867 0,68968 0,69233 0,68293 0,68399 0,66895 0,68756 0,68527 0,6776 0,68137 0,67933 0,67922 0,68598 0,68297 0,68935 0,69463 0,6833 0,68666 0,68782 0,67669 0,67511 0,67254 0,67397 0,67286 0,66341 0,668 0,68021 0,67934 0,68136 0,67562 0,6744 0,67766 0,68887 0,69614 0,70896 0,72064 0,74725

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 0.17436144158383 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 0.67127 0.67409 -0.00281999999999993 4 0.66502 0.656368300734734 0.00865169926526632 5 0.65825 0.651626823490775 0.00662317650922484 6 0.65025 0.646011650094788 0.00423834990521221 7 0.65779 0.638750654894197 0.0190393451058027 8 0.66014 0.649610382553657 0.0105296174463428 9 0.64683 0.653796341830928 -0.00696634183092759 10 0.64587 0.639271680426721 0.00659831957327861 11 0.63702 0.639462172939549 -0.00244217293954907 12 0.62651 0.630186352145212 -0.00367635214521222 13 0.61834 0.619035338085403 -0.00069533808540323 14 0.61466 0.610744097934444 0.00391590206555581 15 0.61063 0.607746880263696 0.00288311973630440 16 0.59802 0.604219585177176 -0.00619958517717645 17 0.60151 0.590528616568462 0.0109813834315378 18 0.62927 0.59593334641417 0.0333366535858300 19 0.62304 0.629505973390976 -0.00646597339097599 20 0.6071 0.622148556949283 -0.0150485569492829 21 0.60773 0.603584668865849 0.00414533113415061 22 0.58933 0.604937454778242 -0.0156074547782422 23 0.60039 0.583816116463654 0.0165738835363465 24 0.61342 0.597765962689693 0.0156540373103066 25 0.6348 0.613525423201725 0.0212745767982746 26 0.634 0.638614889081359 -0.00461488908135854 27 0.62915 0.637010230368383 -0.00786023036838346 28 0.62168 0.630789709270171 -0.00910970927017107 29 0.61328 0.621731327229414 -0.00845132722941444 30 0.6089 0.611857741630397 -0.00295774163039719 31 0.60857 0.606962025535889 0.00160797446411154 32 0.62672 0.606912394281481 0.0198076057185190 33 0.62291 0.628516076968886 -0.00560607696888615 34 0.62393 0.623728593306961 0.000201406693038808 35 0.61838 0.624783710868304 -0.00640371086830405 36 0.62012 0.61811715060982 0.00200284939017947 37 0.61659 0.620206370316768 -0.00361637031676754 38 0.6116 0.616045814775035 -0.00444581477503492 39 0.61573 0.610280636101845 0.00544936389815476 40 0.61407 0.615360795046842 -0.00129079504684237 41 0.62823 0.613475730161686 0.0147542698383143 42 0.64405 0.630208305920211 0.0138416940797891 43 0.6387 0.648441763653925 -0.00974176365392532 44 0.63633 0.641393175699658 -0.00506317569965808 45 0.63059 0.638140353085673 -0.00755035308567331 46 0.62994 0.631083862637188 -0.00114386263718835 47 0.63709 0.630234417098794 0.00685558290120558 48 0.64217 0.638579766416346 0.00359023358365396 49 0.65711 0.644285764719615 0.0128242352803853 50 0.66977 0.661461816870313 0.00830818312968717 51 0.68255 0.675570443657748 0.00697955634225245 52 0.68902 0.689567409163198 -0.000547409163198287 53 0.71322 0.695941962112367 0.0172780378876332 54 0.70224 0.723154585706195 -0.0209145857061945 55 0.70045 0.708527888392334 -0.00807788839233392 56 0.69919 0.705329416127293 -0.0061394161272933 57 0.69693 0.702998938680855 -0.00606893868085534 58 0.69763 0.699680749783578 -0.00205074978357767 59 0.69278 0.700023178094985 -0.00724317809498531 60 0.70196 0.693910247120695 0.00804975287930487 61 0.69215 0.704493813637124 -0.0123438136371243 62 0.6769 0.692531528496713 -0.0156315284967133 63 0.67124 0.674555992653868 -0.00331599265386762 64 0.66532 0.668317811394458 -0.00299781139445776 65 0.67157 0.661875108678124 0.00969489132187618 66 0.66428 0.669815523905005 -0.00553552390500467 67 0.66576 0.661560341977006 0.00419965802299371 68 0.66942 0.663772600404055 0.0056473995959454 69 0.6813 0.668417289138804 0.0128827108611964 70 0.69144 0.68254353717607 0.00889646282393064 71 0.69862 0.694234737259047 0.00438526274095308 72 0.695 0.702179357992283 -0.00717935799228342 73 0.69867 0.697307554783102 0.00136244521689766 74 0.68968 0.7012151126952 -0.0115351126951998 75 0.69233 0.690213833816833 0.00211616618316735 76 0.68293 0.693232811603161 -0.0103028116031607 77 0.68399 0.682036398519667 0.00195360148033297 78 0.66895 0.683437031290058 -0.0144870312900581 79 0.68756 0.665871051630054 0.0216889483699463 80 0.68527 0.688262767934275 -0.00299276793427461 81 0.6776 0.685450944602929 -0.00785094460292879 82 0.68137 0.676412042584167 0.00495795741583283 83 0.67933 0.681046519186503 -0.00171651918650317 84 0.67922 0.678707224426638 0.000512775573361934 85 0.68598 0.678686632714819 0.00729336728518148 86 0.68297 0.686718314748663 -0.00374831474866311 87 0.68935 0.683054753185576 0.00629524681442384 88 0.69463 0.690532401495265 0.00409759850473479 89 0.6833 0.696526864677582 -0.0132268646775824 90 0.68666 0.682890609484765 0.00376939051523506 91 0.68782 0.686907845848894 0.000912154151106126 92 0.67669 0.688226890361627 -0.0115368903616273 93 0.67511 0.67508530152678 2.4698473220619e-05 94 0.67254 0.673509607988175 -0.000969607988175025 95 0.67397 0.670770545741586 0.00319945425841428 96 0.67286 0.672758407198364 0.000101592801635797 97 0.66341 0.671666121065712 -0.00825612106571205 98 0.668 0.660776571894804 0.00722342810519616 99 0.68021 0.666626059232403 0.0135839407675969 100 0.67934 0.68120457472703 -0.0018645747270305 101 0.68136 0.680009464789685 0.00135053521031514 102 0.67562 0.682264946055865 -0.00664494605586496 103 0.6744 0.675366323682318 -0.000966323682317638 104 0.67766 0.673977834092032 0.00368216590796788 105 0.68887 0.677879861847896 0.0109901381521037 106 0.69614 0.691006118179302 0.00513388182069752 107 0.70896 0.69917126921448 0.00978873078551967 108 0.72064 0.71369804642552 0.00694195357448035 109 0.74725 0.726588455458174 0.020661544541826 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 110 0.756801032149835 0.738209036180096 0.775393028119574 111 0.76635206429967 0.73767500408719 0.79502912451215 112 0.775903096449506 0.737809107480094 0.813997085418918 113 0.785454128599341 0.737988198245236 0.832920058953446 114 0.795005160749176 0.738005344788993 0.85200497670936 115 0.804556192899012 0.737772489709751 0.871339896088272 116 0.814107225048847 0.7372483666678 0.890966083429893 117 0.823658257198682 0.736413429786843 0.910903084610521 118 0.833209289348517 0.735259261283947 0.931159317413088 119 0.842760321498353 0.733783507608649 0.951737135388057 120 0.852311353648188 0.731987243828285 0.97263546346809 121 0.861862385798023 0.72987351541957 0.993851256176476

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211983633du02jwfknwjmc3x/1a2661211983581.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211983633du02jwfknwjmc3x/1a2661211983581.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211983633du02jwfknwjmc3x/2rrhq1211983581.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211983633du02jwfknwjmc3x/2rrhq1211983581.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211983633du02jwfknwjmc3x/3sko41211983581.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211983633du02jwfknwjmc3x/3sko41211983581.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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