Exponential Smoothing (double)

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 10:32:24 -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/t1211387645f1vbuubv2a7vgk2.htm/, Retrieved Wed, 21 May 2008 18:34:05 +0200

User-defined keywords:

Dataseries X:

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1,74 1,73 1,74 1,73 1,74 1,73 1,73 1,74 1,75 1,73 1,74 1,74 1,74 1,74 1,76 1,76 1,78 1,77 1,78 1,79 1,83 1,82 1,84 1,83 1,83 1,84 1,83 1,83 1,83 1,83 1,83 1,84 1,83 1,84 1,84 1,83 1,84 1,85 1,85 1,85 1,85 1,84 1,84 1,85 1,84 1,84 1,84 1,84 1,85 1,84 1,85 1,84 1,84 1,84 1,84 1,84 1,83 1,83 1,82 1,83 1,83 1,83 1,87 1,87 1,86 1,87 1,87 1,89 1,89 1,88 1,88 1,87

Text written by user:

Gem prijzen kattenvoeding Veronique Van Hoof 2MAR02

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 4 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.693896710109591 beta 0.271603477614666 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 1.74 1.72 0.02 4 1.73 1.72764722939361 0.0023527706063855 5 1.74 1.72349251871511 0.0165074812848909 6 1.73 1.73227079370045 -0.0022707937004538 7 1.73 1.72759092086314 0.00240907913685695 8 1.74 1.72661242291169 0.0133875770883110 9 1.75 1.73577495506788 0.0142250449321175 10 1.73 1.74819952307874 -0.0181995230787360 11 1.74 1.73469482127879 0.00530517872120995 12 1.74 1.73849979396211 0.00150020603789147 13 1.74 1.73994724458865 5.27554113460837e-05 14 1.74 1.74040025652331 -0.000400256523308773 15 1.76 1.74046349071743 0.0195365092825661 16 1.76 1.75804272463928 0.00195727536072088 17 1.78 1.76379266340678 0.0162073365932180 18 1.77 1.78248518457670 -0.0124851845767042 19 1.78 1.77891504239262 0.00108495760738236 20 1.79 1.78496565350041 0.00503434649959145 21 1.83 1.79470552947009 0.0352944705299103 22 1.82 1.83209456985453 -0.0120945698545276 23 1.84 1.83432111082120 0.00567888917879644 24 1.83 1.84995086702208 -0.0199508670220838 25 1.83 1.84403618435771 -0.0140361843577095 26 1.84 1.83958035442521 0.000419645574785132 27 1.83 1.84523446572714 -0.0152344657271390 28 1.83 1.83715508077651 -0.00715508077650862 29 1.83 1.83333347388457 -0.00333347388457295 30 1.83 1.83153542508809 -0.00153542508809079 31 1.83 1.83069566291604 -0.000695662916037731 32 1.84 1.83030750100823 0.00969249899176705 33 1.83 1.83895434496447 -0.00895434496446645 34 1.84 1.83297462677470 0.0070253732253025 35 1.84 1.83940721774109 0.000592782258908242 36 1.83 1.84148797356433 -0.0114879735643276 37 1.84 1.83302085449042 0.00697914550957779 38 1.85 1.83868333156758 0.0113166684324235 39 1.85 1.84948839472618 0.000511605273818549 40 1.85 1.85289227967143 -0.00289227967142947 41 1.85 1.85338912725869 -0.00338912725868989 42 1.84 1.85290248288576 -0.0129024828857593 43 1.84 1.84338288900617 -0.00338288900616757 44 1.85 1.839831354638 0.0101686453619994 45 1.84 1.84759961668816 -0.00759961668815512 46 1.84 1.84160628022538 -0.00160628022537623 47 1.84 1.83946897300022 0.000531026999779804 48 1.84 1.83891481610293 0.00108518389706735 49 1.85 1.83894970577581 0.0110502942241912 50 1.84 1.84798194376471 -0.00798194376470795 51 1.85 1.84230345931456 0.00769654068543923 52 1.84 1.84895475033369 -0.0089547503336862 53 1.84 1.84236411042691 -0.00236411042690521 54 1.84 1.83990114236575 9.88576342497716e-05 55 1.84 1.83916585091961 0.000834149080393587 56 1.84 1.83909798349480 0.000902016505203607 57 1.83 1.83924720737657 -0.00924720737656792 58 1.83 1.83061114548168 -0.000611145481683284 59 1.82 1.82785243913769 -0.00785243913769329 60 1.83 1.81858911489473 0.0114108851052719 61 1.83 1.82484309768759 0.00515690231241028 62 1.83 1.82772935674984 0.00227064325015691 63 1.87 1.82904078637849 0.0409592136215124 64 1.87 1.86491745605406 0.00508254394593965 65 1.86 1.87685730309485 -0.0168573030948458 66 1.87 1.87039615487893 -0.000396154878934629 67 1.87 1.87528268202066 -0.00528268202065929 68 1.89 1.87578286465797 0.0142171353420339 69 1.89 1.89249333540501 -0.00249333540500984 70 1.88 1.89713855961866 -0.0171385596186620 71 1.88 1.88839149641372 -0.00839149641371684 72 1.87 1.88413249023575 -0.0141324902357505 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 1.87322635095749 1.85100001091685 1.89545269099813 74 1.87212670015948 1.84248504640327 1.90176835391569 75 1.87102704936147 1.83301266106515 1.90904143765778 76 1.86992739856345 1.82272038749492 1.91713440963198 77 1.86882774776544 1.81169679618181 1.92595869934907 78 1.86772809696742 1.80000425785574 1.93545193607911 79 1.86662844616941 1.78768977616825 1.94556711617057 80 1.86552879537140 1.77479057407830 1.95626701666449 81 1.86442914457338 1.76133721767474 1.96752107147202 82 1.86332949377537 1.74735549303263 1.97930349451811 83 1.86222984297735 1.73286760491986 1.99159208103485 84 1.86113019217934 1.71789298257730 2.00436740178139

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/21/t1211387645f1vbuubv2a7vgk2/14l3c1211387537.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/21/t1211387645f1vbuubv2a7vgk2/14l3c1211387537.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/21/t1211387645f1vbuubv2a7vgk2/2s5qh1211387537.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/21/t1211387645f1vbuubv2a7vgk2/2s5qh1211387537.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/21/t1211387645f1vbuubv2a7vgk2/31r101211387537.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/21/t1211387645f1vbuubv2a7vgk2/31r101211387537.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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Software written by Ed van Stee & Patrick Wessa

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