Gemiddelde prijs inktjet printer (exponential smoothing) - Sanne Dangez

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 21 May 2008 08:38:30 -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/21/t1211380795agtqcd3z19265r4.htm/, Retrieved Wed, 21 May 2008 16:39:56 +0200

User-defined keywords:

Dataseries X:

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58,1 57,9 57,3 55,9 55 55,9 56,6 57,3 56,2 57,7 56,8 57,9 58,3 58,2 56,9 57,1 56,7 54,2 54,2 52,1 51,5 51,8 53 52,4 52,41 52,36 52,94 52,34 51,84 51,42 50,85 50,66 51,53 51,59 52,32 51,98 51,17 50,57 49,84 50,12 49,08 48,57 47,22 46,78 46,04 45,05 44,42 44,09 44,46 44,34 43,04 42,87 42,32 42,49 41,94 41,6 41,42 41,12 41,28 40,21 39,69 39,16 38,8 38,44 37,02 36,75 35,95 36,29 36,35 36,07 36,6 36,5

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 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.00765387410320782 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 57.3 57.7 -0.399999999999999 4 55.9 57.0969384503587 -1.19693845035872 5 55 55.6877772341504 -0.687777234150381 6 55.9 54.7825130737891 1.11748692621086 7 56.6 55.6910661780343 0.908933821965661 8 57.3 56.3980230430758 0.901976956924187 9 56.2 57.1049266611481 -0.904926661148096 10 57.7 55.998000466411 1.70199953358896 11 56.8 57.5110273565649 -0.711027356564855 12 57.9 56.6055852426938 1.29441475730624 13 58.3 57.7154925302835 0.584507469716478 14 58.2 58.1199662768691 0.0800337231308887 15 56.9 58.02057884491 -1.12057884490997 16 57.1 56.7120020755083 0.387997924491692 17 56.7 56.9149717627747 -0.214971762774674 18 54.2 56.5133263959667 -2.31332639596666 19 54.2 53.9956204869723 0.204379513027703 20 52.1 53.9971847820343 -1.89718478203429 21 51.5 51.8826639685621 -0.382663968562078 22 51.8 51.2797351067229 0.52026489327713 23 53 51.5837171487163 1.41628285128368 24 52.4 52.7945571993546 -0.394557199354587 25 52.41 52.1915373082242 0.218462691775784 26 52.36 52.2032093941633 0.15679060583669 27 52.94 52.154409449721 0.785590550279046 28 52.34 52.7404222608895 -0.400422260889449 29 51.84 52.1373574793165 -0.297357479316489 30 51.42 51.6350815426062 -0.21508154260615 31 50.85 51.2134353355571 -0.363435335557121 32 50.66 50.6406536472541 0.0193463527458846 33 51.53 50.4508017218024 1.07919827819762 34 51.59 51.3290617695561 0.260938230443898 35 52.32 51.3910589579206 0.928941042079359 36 51.98 52.128168955706 -0.148168955706019 37 51.17 51.787034889173 -0.617034889173034 38 50.57 50.972312181814 -0.402312181814018 39 49.84 50.3692329350242 -0.529232935024226 40 50.12 49.6351822527683 0.484817747231709 41 49.08 49.9188929867686 -0.838892986768592 42 48.57 48.8724722054618 -0.302472205461804 43 47.22 48.3601571212815 -1.14015712128148 44 46.78 47.0014305022173 -0.221430502217316 45 46.04 46.5597357010307 -0.519735701030733 46 45.05 45.8157577094081 -0.765757709408106 47 44.42 44.8198966963067 -0.399896696306726 48 44.09 44.1868359373389 -0.0968359373389092 49 44.46 43.8560947672659 0.603905232734142 50 44.34 44.2307169818875 0.109283018112535 51 43.04 44.1115534203497 -1.07155342034972 52 42.87 42.8033518853755 0.066648114624499 53 42.32 42.6338620016541 -0.313862001654051 54 42.49 42.0814597414076 0.408540258592389 55 41.94 42.254586657113 -0.314586657112976 56 41.6 41.7021788504449 -0.102178850444879 57 41.42 41.3613967863876 0.0586032136124359 58 41.12 41.1818453280066 -0.0618453280066049 59 41.28 40.8813719716522 0.398628028347844 60 40.21 41.0444230203952 -0.83442302039515 61 39.69 39.9680364516482 -0.278036451648227 62 39.16 39.4459083956512 -0.285908395651205 63 38.8 38.9137200887858 -0.113720088785840 64 38.44 38.5528496895433 -0.112849689543268 65 37.02 38.1919859522269 -1.17198595222691 66 36.75 36.7630157192978 -0.0130157192978473 67 35.95 36.492916098621 -0.542916098620978 68 36.29 35.6887606871535 0.601239312846467 69 36.35 36.0333624971600 0.316637502840045 70 36.07 36.0957860007430 -0.0257860007430466 71 36.6 35.8155886379397 0.784411362060268 72 36.5 36.3515924237501 0.148407576249930 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 36.2527283166546 34.8202151292343 37.685241504075 74 36.0054566333093 33.9718093634157 38.0391039032028 75 35.7581849499639 33.2579605621709 38.2584093377570 76 35.5109132666186 32.6128903585449 38.4089361746923 77 35.2636415832732 32.0112261718845 38.516056994662 78 35.0163698999279 31.4400072061354 38.5927325937203 79 34.7690982165825 30.8915642664627 38.6466321667024 80 34.5218265332372 30.3609198184378 38.6827332480366 81 34.2745548498918 29.8446297926227 38.704479907161 82 34.0272831665465 29.3401962315425 38.7143701015504 83 33.7800114832011 28.8457406262526 38.7142823401497 84 33.5327397998558 28.359809169735 38.7056704299765

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/21/t1211380795agtqcd3z19265r4/1s1mp1211380703.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/21/t1211380795agtqcd3z19265r4/1s1mp1211380703.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/21/t1211380795agtqcd3z19265r4/2lzvf1211380703.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/21/t1211380795agtqcd3z19265r4/2lzvf1211380703.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/21/t1211380795agtqcd3z19265r4/31wjo1211380703.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/21/t1211380795agtqcd3z19265r4/31wjo1211380703.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')

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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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