Opgave10: Exponential Smoothing Gemiddelede Prijs Zakje Frieten - Dave Florus

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 24 May 2008 11:55:28 -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/24/t1211651891ejanves0wlxq7u2.htm/, Retrieved Sat, 24 May 2008 19:58:11 +0200

User-defined keywords:

Exponential Smoothing, Gemiddelede Prijs, Zakje Frieten

Dataseries X:

» Textbox « » Textfile « » CSV «

1,72 1,73 1,73 1,73 1,73 1,73 1,74 1,74 1,74 1,74 1,75 1,75 1,75 1,75 1,75 1,76 1,77 1,77 1,78 1,78 1,78 1,79 1,8 1,8 1,82 1,83 1,85 1,86 1,86 1,87 1,88 1,88 1,89 1,9 1,9 1,9 1,9 1,92 1,92 1,93 1,93 1,93 1,94 1,94 1,95 1,96 1,96 1,96 1,96 1,97 1,97 1,98 1,99 1,99 1,99 2 2 2,01 2,01 2,01 2,02 2,02 2,02 2,02 2,03 2,03 2,03 2,04 2,04 2,05 2,06 2,06

Text written by user:

Exponential Smoothing Gemiddelede Prijs Zakje Frieten

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 0.823465303952612 beta 0.208609164233188 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 1.73 1.74 -0.01 4 1.73 1.74004752287215 -0.0100475228721482 5 1.73 1.73832992462616 -0.00832992462615989 6 1.73 1.73659577442420 -0.00659577442419734 7 1.74 1.73515659872669 0.00484340127331162 8 1.74 1.74396919845957 -0.00396919845956822 9 1.74 1.74484308960228 -0.00484308960228019 10 1.74 1.74416540411147 -0.0041654041114656 11 1.75 1.7433302259573 0.00666977404269975 12 1.75 1.75256319092666 -0.00256319092665946 13 1.75 1.75375281847946 -0.00375281847946218 14 1.75 1.75331816081959 -0.00331816081959224 15 1.75 1.75267142700324 -0.00267142700323908 16 1.76 1.75209835187991 0.00790164812009131 17 1.77 1.76158920142454 0.00841079857545779 18 1.77 1.77294414594316 -0.00294414594315939 19 1.78 1.77444293514032 0.0055570648596821 20 1.78 1.78389678246284 -0.00389678246283864 21 1.78 1.78489631584824 -0.00489631584823513 22 1.79 1.7842316672398 0.00576833276019961 23 1.8 1.79333988483575 0.0066601151642467 24 1.8 1.80432654492613 -0.00432654492613116 25 1.82 1.80552284731643 0.0144771526835714 26 1.83 1.82469026243535 0.00530973756464626 27 1.85 1.83722074878604 0.0127792512139626 28 1.86 1.85809737102094 0.00190262897905535 29 1.86 1.87034431041034 -0.0103443104103431 30 1.87 1.87072934957296 -0.000729349572960558 31 1.88 1.8789066859575 0.00109331404249802 32 1.88 1.88877273470998 -0.00877273470998063 33 1.89 1.88900743312716 0.000992566872841438 34 1.9 1.89745402410877 0.00254597589123184 35 1.9 1.90761714739129 -0.00761714739129471 36 1.9 1.90810279934356 -0.00810279934355829 37 1.9 1.90679661537381 -0.0067966153738126 38 1.92 1.90539848962291 0.0146015103770907 39 1.92 1.92412926062266 -0.00412926062266039 40 1.93 1.92672655725138 0.0032734427486234 41 1.93 1.93598204314233 -0.00598204314233208 42 1.93 1.93658834775013 -0.0065883477501325 43 1.94 1.93556361930304 0.00443638069696162 44 1.94 1.94437946438025 -0.00437946438024794 45 1.95 1.94518345197072 0.00481654802928144 46 1.96 1.95438743493788 0.00561256506211794 47 1.96 1.96521105025904 -0.00521105025904189 48 1.96 1.96622662713385 -0.00622662713385091 49 1.96 1.96533628668080 -0.00533628668080288 50 1.97 1.96426243051930 0.00573756948070425 51 1.97 1.97329312419399 -0.00329312419399108 52 1.98 1.97432165415032 0.00567834584967808 53 1.99 1.98371331834131 0.00628668165869328 54 1.99 1.99468586728306 -0.00468586728306164 55 1.99 1.99581795330601 -0.00581795330600521 56 2 1.99501838373458 0.00498161626541593 57 2 2.00396763904480 -0.00396763904480357 58 2.01 2.00486592251835 0.00513407748165084 59 2.01 2.01414109795477 -0.00414109795477291 60 2.01 2.01506712044935 -0.00506712044934599 61 2.02 2.01436015339232 0.00563984660767547 62 2.02 2.02343882865304 -0.00343882865303691 63 2.02 2.02445079956112 -0.00445079956111849 64 2.02 2.02386487846795 -0.00386487846794559 65 2.03 2.02309752493279 0.0069024750672142 66 2.03 2.03238243724317 -0.00238243724317400 67 2.03 2.03361228560719 -0.00361228560719029 68 2.04 2.03320886939132 0.00679113060867831 69 2.04 2.04253890224645 -0.00253890224645481 70 2.05 2.04374983801696 0.00625016198303863 71 2.06 2.05327193111571 0.00672806888429323 72 2.06 2.06434332784589 -0.00434332784588998 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 2.06555170618276 2.05345201127048 2.07765140109504 74 2.07033666430440 2.05326572274391 2.08740760586490 75 2.07512162242605 2.05296735755028 2.09727588730183 76 2.0799065805477 2.05246161227888 2.10735154881653 77 2.08469153866935 2.05171727618984 2.11766580114886 78 2.08947649679100 2.05072499349639 2.12822800008560 79 2.09426145491265 2.04948425318137 2.13903865664392 80 2.09904641303429 2.04799840822533 2.15009441784325 81 2.10383137115594 2.04627251037064 2.16139023194125 82 2.10861632927759 2.04431229191059 2.17292036664459 83 2.11340128739924 2.04212366438617 2.18467891041230 84 2.11818624552089 2.03971246732700 2.19666002371478

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211651891ejanves0wlxq7u2/1ms2r1211651723.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211651891ejanves0wlxq7u2/1ms2r1211651723.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211651891ejanves0wlxq7u2/262la1211651723.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211651891ejanves0wlxq7u2/262la1211651723.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211651891ejanves0wlxq7u2/3p5f01211651723.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211651891ejanves0wlxq7u2/3p5f01211651723.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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