Maarten Verhaegen 2MAR03 - tweede zit - Oefening 10 - triple additief exponential smoothing model evolutie prijs diesel

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 17 Aug 2008 13:40:03 -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/Aug/17/t12190022382flqf778hz8bvbv.htm/, Retrieved Sun, 17 Aug 2008 19:44:01 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

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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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.779623557136431 beta 0.00737648872348067 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 0.58 0.543976388888889 0.0360236111111109 14 0.57 0.56678526017269 0.00321473982731013 15 0.59 0.592784050117634 -0.00278405011763394 16 0.62 0.623256698023525 -0.00325669802352480 17 0.62 0.622508796260632 -0.00250879626063183 18 0.61 0.608579548533292 0.00142045146670833 19 0.64 0.635638470414827 0.00436152958517311 20 0.65 0.64501540873325 0.00498459126674977 21 0.67 0.664490099757559 0.00550990024244102 22 0.67 0.666489354166652 0.00351064583334781 23 0.69 0.68778346539332 0.00221653460668014 24 0.74 0.736831404056365 0.00316859594363483 25 0.73 0.707495236336884 0.0225047636631156 26 0.74 0.712777698479701 0.0272223015202987 27 0.75 0.756552926934541 -0.00655292693454135 28 0.74 0.784343004705179 -0.0443430047051790 29 0.76 0.751851683187798 0.00814831681220152 30 0.76 0.747281786205614 0.0127182137943862 31 0.78 0.784046726904767 -0.00404672690476737 32 0.79 0.787207216425467 0.00279278357453294 33 0.89 0.80527780135027 0.0847221986497296 34 0.88 0.869236694893582 0.0107633051064182 35 0.88 0.896586121573558 -0.0165861215735575 36 0.84 0.931762909591833 -0.0917629095918326 37 0.76 0.832709230750218 -0.0727092307502176 38 0.77 0.764284780465477 0.00571521953452259 39 0.76 0.78321015808745 -0.0232101580874502 40 0.77 0.788950870961858 -0.0189508709618583 41 0.78 0.787234780841077 -0.00723478084107665 42 0.79 0.771001564819016 0.0189984351809842 43 0.78 0.808326841517319 -0.0283268415173189 44 0.76 0.793284342032865 -0.0332843420328651 45 0.78 0.800295280968893 -0.0202952809688929 46 0.76 0.764488950178656 -0.00448895017865614 47 0.74 0.772240150581619 -0.0322401505816187 48 0.73 0.776875431789645 -0.0468754317896447 49 0.72 0.715504148822393 0.00449585117760709 50 0.71 0.723485576818818 -0.0134855768188176 51 0.73 0.719888744191645 0.0101112558083554 52 0.75 0.751559545173321 -0.00155954517332080 53 0.75 0.765097390427123 -0.0150973904271225 54 0.72 0.747583562459308 -0.0275835624593085 55 0.72 0.736963233516226 -0.0169632335162258 56 0.72 0.728553098183873 -0.00855309818387262 57 0.74 0.756715351008665 -0.0167153510086653 58 0.78 0.726211719179269 0.0537882808207315 59 0.74 0.772645014778041 -0.0326450147780415 60 0.74 0.773100558674985 -0.0331005586749852 61 0.75 0.733229905159572 0.0167700948404280 62 0.78 0.746328920547658 0.0336710794523417 63 0.81 0.784478887565901 0.0255211124340986 64 0.75 0.825462399986536 -0.0754623999865357 65 0.7 0.777846203541177 -0.0778462035411772 66 0.71 0.707745190374723 0.00225480962527691 67 0.71 0.721984552422646 -0.0119845524226465 68 0.73 0.71859446457493 0.0114055354250706 69 0.74 0.759918104592518 -0.0199181045925182 70 0.74 0.741836386053711 -0.00183638605371073 71 0.75 0.72491714358326 0.0250828564167392 72 0.74 0.769671915749024 -0.0296719157490244 73 0.74 0.742877959107356 -0.00287795910735567 74 0.73 0.743683802823674 -0.0136838028236737 75 0.76 0.74214673004863 0.0178532699513699 76 0.8 0.753881730422097 0.0461182695779028 77 0.83 0.800210456126884 0.0297895438731163 78 0.81 0.831979286537432 -0.0219792865374316 79 0.83 0.82434989184064 0.0056501081593604 80 0.88 0.840126975523365 0.0398730244766354 81 0.89 0.89716941185198 -0.0071694118519805 82 0.93 0.89351283916527 0.0364871608347292 83 0.91 0.91312547768583 -0.00312547768583027 84 0.9 0.924381057433586 -0.0243810574335855 85 0.86 0.908206513817093 -0.048206513817093 86 0.88 0.87162089418332 0.00837910581668 87 0.93 0.894690592989276 0.0353094070107237 88 0.98 0.926820117681502 0.0531798823184979 89 0.97 0.975652755636756 -0.00565275563675605 90 1.03 0.968774458260515 0.0612255417394846 91 1.06 1.03297403135202 0.0270259686479786 92 1.06 1.07395274996467 -0.0139527499646692 93 1.08 1.07934933994715 0.000650660052845087 94 1.09 1.09214037223277 -0.00214037223276997 95 1.04 1.07341625367428 -0.0334162536742793 96 1 1.05670587311530 -0.0567058731153010 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 1.01022734738195 0.949993043805336 1.07046165095856 98 1.02411980418284 0.94752950050894 1.10071010785675 99 1.04696857650334 0.956763965315526 1.13717318769116 100 1.05568204497951 0.953501796878194 1.15786229308082 101 1.04995699257963 0.936916697679988 1.16299728747927 102 1.06212455242814 0.93904316726761 1.18520593758867 103 1.07060280409129 0.938112048206995 1.20309355997558 104 1.08087360690523 0.939478177973099 1.22226903583737 105 1.09983948790680 0.949953303940428 1.24972567187317 106 1.11097758155622 0.952947069171049 1.2690080939414 107 1.08651139818089 0.920631226334774 1.25239157002701 108 1.09039452376974 0.916918664263111 1.26387038327638

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t12190022382flqf778hz8bvbv/1c1si1219001999.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t12190022382flqf778hz8bvbv/1c1si1219001999.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t12190022382flqf778hz8bvbv/2i2tk1219001999.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t12190022382flqf778hz8bvbv/2i2tk1219001999.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t12190022382flqf778hz8bvbv/3qt3h1219001999.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/17/t12190022382flqf778hz8bvbv/3qt3h1219001999.ps (open in new window)

Parameters (Session):

par1 = 4 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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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