Tinneke Hermans - opgave 10 oef 2 - prijzen broodjes - double smoothing additiefmodel

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 02:30:14 -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/t1211963523zgmkt5wovcnt22x.htm/, Retrieved Wed, 28 May 2008 10:32:03 +0200

User-defined keywords:

Dataseries X:

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4,07 4,08 4,09 4,08 4,09 4,12 4,14 4,14 4,14 4,14 4,14 4,23 4,29 4,32 4,33 4,35 4,35 4,35 4,35 4,36 4,36 4,38 4,4 4,4 4,4 4,43 4,44 4,46 4,47 4,49 4,49 4,57 4,62 4,64 4,66 4,67 4,68 4,72 4,74 4,75 4,76 4,77 4,76 4,77 4,77 4,78 4,81 4,81 4,85 4,92 4,96 4,95 4,96 4,97 5 5 5,01 5,01 5,02 5,04 5,04 5,19 5,22 5,22 5,22 5,24 5,28 5,34 5,36 5,38 5,39 5,41 5,44 5,51 5,55 5,56 5,57 5,58 5,58 5,59 5,61 5,63 5,64 5,64

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 0.0348836110569791 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 4.09 4.09 0 4 4.08 4.1 -0.0199999999999996 5 4.09 4.08930232777886 0.000697672221139811 6 4.12 4.09932666510527 0.0206733348947328 7 4.14 4.13004782567899 0.00995217432101292 8 4.14 4.15039499345717 -0.0103949934571714 9 4.14 4.15003237854847 -0.0100323785484715 10 4.14 4.14968241295721 -0.0096824129572104 11 4.14 4.14934465542952 -0.00934465542951823 12 4.23 4.14901868010405 0.0809813198959475 13 4.29 4.24184360097018 0.0481563990298151 14 4.32 4.30352347006384 0.0164765299361553 15 4.33 4.33409823092571 -0.00409823092570694 16 4.35 4.34395526983207 0.00604473016792717 17 4.35 4.36416613184819 -0.0141661318481949 18 4.35 4.36367196601462 -0.0136719660146207 19 4.35 4.36319503846978 -0.0131950384697825 20 4.36 4.36273474787992 -0.00273474787992001 21 4.36 4.37263934999854 -0.0126393499985387 22 4.38 4.37219844382918 0.0078015561708229 23 4.4 4.39247059028028 0.00752940971972205 24 4.4 4.41273324328043 -0.0127332432804304 25 4.4 4.41228906177434 -0.0122890617743421 26 4.43 4.41186037492315 0.0181396250768486 27 4.44 4.44249315054905 -0.00249315054904997 28 4.46 4.45240618045499 0.0075938195450087 29 4.47 4.47267108030244 -0.00267108030243612 30 4.49 4.48257790337606 0.00742209662393645 31 4.49 4.50283681290792 -0.0128368129079206 32 4.57 4.50238901851923 0.0676109814807706 33 4.62 4.58474753370039 0.0352524662996148 34 4.64 4.63597726702358 0.00402273297641909 35 4.66 4.65611759447612 0.00388240552388464 36 4.67 4.67625302680038 -0.00625302680037709 37 4.68 4.68603489864554 -0.00603489864554341 38 4.72 4.69582437958842 0.0241756204115759 39 4.74 4.73666771252792 0.00333228747207759 40 4.75 4.75678395474803 -0.00678395474802862 41 4.76 4.76654730590917 -0.0065473059091703 42 4.77 4.77631891223636 -0.00631891223636405 43 4.76 4.78609848575961 -0.0260984857596069 44 4.77 4.77518807633319 -0.00518807633319263 45 4.77 4.78500709749625 -0.0150070974962517 46 4.78 4.7844835957441 -0.00448359574409807 47 4.81 4.79432719173403 0.0156728082659745 48 4.81 4.82487391588174 -0.0148739158817452 49 4.85 4.82435505998523 0.025644940014768 50 4.92 4.86524964809829 0.0547503519017134 51 4.96 4.93715953807926 0.0228404619207412 52 4.95 4.97795629586926 -0.0279562958692638 53 4.96 4.96698107931757 -0.0069810793175673 54 4.97 4.97673755406189 -0.00673755406189525 55 5 4.98650252384652 0.0134974761534759 56 5 5.01697336455491 -0.0169733645549135 57 5.01 5.01638127230745 -0.00638127230745145 58 5.01 5.02615867048623 -0.0161586704862291 59 5.02 5.02559499770979 -0.00559499770978977 60 5.04 5.03539982398582 0.00460017601418361 61 5.04 5.05556029473669 -0.0155602947366891 62 5.19 5.05501749546716 0.134982504532838 63 5.22 5.20972617265478 0.0102738273452161 64 5.22 5.24008456085196 -0.0200845608519602 65 5.22 5.23938393884295 -0.0193839388429504 66 5.24 5.2387077570596 0.00129224294039965 67 5.28 5.25875283515972 0.0212471648402754 68 5.34 5.29949401299408 0.0405059870059237 69 5.36 5.36090700809027 -0.000907008090269557 70 5.38 5.38087536837282 -0.000875368372823537 71 5.39 5.40084483236297 -0.0108448323629746 72 5.41 5.41046652544885 -0.000466525448845623 73 5.44 5.43045025135654 0.00954974864345992 74 5.51 5.46078338107391 0.0492166189260885 75 5.55 5.53250023446607 0.0174997655339322 76 5.56 5.57311068948054 -0.0131106894805422 77 5.57 5.58265334128801 -0.0126533412880132 78 5.58 5.59221194705195 -0.0122119470519522 79 5.58 5.60178595024074 -0.0217859502407425 80 5.59 5.60102597762604 -0.0110259776260380 81 5.61 5.61064135171101 -0.000641351711007765 82 5.63 5.63061897904737 -0.000618979047371404 83 5.64 5.65059738682303 -0.0105973868230302 84 5.64 5.66022771170287 -0.0202277117028746 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 5.65952209607526 5.61019181607674 5.70885237607378 86 5.67904419215052 5.60805340991579 5.75003497438525 87 5.69856628822578 5.6101097093639 5.78702286708766 88 5.71808838430104 5.61419408945801 5.82198267914406 89 5.7376104803763 5.61948348064934 5.85573748010325 90 5.75713257645156 5.62556366117943 5.88870149172368 91 5.77665467252681 5.63219318583796 5.92111615921567 92 5.79617676860207 5.63921774367152 5.95313579353263 93 5.81569886467733 5.64653224560157 5.98486548375309 94 5.83522096075259 5.65406171568152 6.01638020582366 95 5.85474305682785 5.66175072761762 6.04773538603808 96 5.87426515290311 5.66955714470954 6.07897316109669

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211963523zgmkt5wovcnt22x/14p6v1211963407.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211963523zgmkt5wovcnt22x/14p6v1211963407.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211963523zgmkt5wovcnt22x/2p4bf1211963407.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211963523zgmkt5wovcnt22x/2p4bf1211963407.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211963523zgmkt5wovcnt22x/3kjyc1211963407.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211963523zgmkt5wovcnt22x/3kjyc1211963407.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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