Nietje van Santfoort-Exponential Smoothing-verkoop jogging

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 04:27:10 -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/t1211624891yheg3vwzy440xog.htm/, Retrieved Sat, 24 May 2008 12:28:14 +0200

User-defined keywords:

Dataseries X:

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71,42 71,47 71,64 71,55 71,62 71,65 71,65 71,65 71,6 71,7 71,73 71,83 71,83 71,87 71,91 71,99 72,1 72,12 72,12 72,12 72,25 72,59 72,72 72,76 72,76 72,91 73 73,16 73,16 73,11 73,11 73,33 73,51 73,66 73,65 73,65 73,65 73,65 73,71 73,73 73,85 73,77 73,77 73,78 73,88 74,3 74,53 74,71 74,71 74,78 74,9 74,65 74,65 74,53 74,53 74,53 74,65 74,85 74,96 74,96 74,96 75,19 74,98 75,54 75,61 75,59 75,58 75,44 75,37 75,22 75,33 75,33

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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.986964904484443 beta 0.00068148021869358 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 71.64 71.52 0.120000000000005 4 71.55 71.6885165001852 -0.138516500185204 5 71.62 71.6017931216668 0.0182068783331886 6 71.65 71.6697624633511 -0.0197624633511282 7 71.65 71.7002441051719 -0.0502441051719131 8 71.65 71.7006076422472 -0.050607642247158 9 71.6 71.7005783424363 -0.100578342436336 10 71.7 71.651162066589 0.0488379334110363 11 71.73 71.7492472594121 -0.0192472594120829 12 71.83 71.7801218107537 0.0498781892463427 13 71.83 71.8792543018512 -0.0492543018512208 14 71.87 71.8805133750428 -0.0105133750428053 15 71.91 71.9200013120964 -0.0100013120963922 16 71.99 71.9599879104538 0.0300120895461475 17 72.1 72.0394865179847 0.0605134820152955 18 72.12 72.1491296306105 -0.0291296306105409 19 72.12 72.170278544642 -0.0502785446420546 20 72.12 72.1705204055553 -0.0505204055552468 21 72.25 72.1704895783592 0.0795104216408333 22 72.59 72.2988480925824 0.291151907417557 23 72.72 72.636285153517 0.0837148464830619 24 72.76 72.7690454217792 -0.00904542177919154 25 72.76 72.810248476812 -0.0502484768119729 26 72.91 72.8107517655921 0.0992482344078525 27 73 72.9588698157527 0.041130184247308 28 73.16 73.0496550541287 0.110344945871319 29 73.16 73.2088270507859 -0.0488270507858886 30 73.11 73.210869032035 -0.100869032034950 31 73.11 73.161479560017 -0.0514795600170714 32 73.33 73.1608011385312 0.169198861468814 33 73.51 73.3780383768855 0.131961623114506 34 73.66 73.5586125248438 0.101387475156201 35 73.65 73.7090792547003 -0.0590792547003076 36 73.65 73.7011312173181 -0.0511312173181153 37 73.65 73.7009932231853 -0.0509932231852872 38 73.65 73.7009571265267 -0.0509571265266686 39 73.71 73.7009223823898 0.0090776176101599 40 73.73 73.7601459293447 -0.0301459293446555 41 73.85 73.7806369359623 0.0693630640377307 42 73.77 73.8993864801217 -0.129386480121724 43 73.77 73.8218901744475 -0.0518901744475215 44 73.78 73.8208451015222 -0.0408451015222369 45 73.88 73.8306736556465 0.0493263443534744 46 74.3 73.9295314389909 0.370468561009105 47 74.53 74.3455944955873 0.184405504412723 48 74.71 74.5781438759019 0.131856124098135 49 74.71 74.7589175481348 -0.0489175481348099 50 74.78 74.76124104842 0.0187589515799544 51 74.9 74.8303714959978 0.0696285040022246 52 74.65 74.9497552384501 -0.299755238450132 53 74.65 74.7043685763231 -0.0543685763230997 54 74.53 74.7011333695995 -0.171133369599517 55 74.53 74.5825403060316 -0.0525403060316307 56 74.53 74.5809590956652 -0.0509590956652346 57 74.65 74.5809042094992 0.0690957905007963 58 74.85 74.6993857562164 0.150614243783593 59 74.96 74.898424458089 0.0615755419110116 60 74.96 75.0096265016009 -0.0496265016008692 61 74.96 75.0110426522206 -0.0510426522205591 62 75.19 75.0110267807414 0.178973219258623 63 74.98 75.2381488787475 -0.258148878747448 64 75.54 75.0336731768703 0.506326823129697 65 75.61 75.5840487170091 0.0259512829908743 66 75.59 75.6603279128148 -0.0703279128147756 67 75.58 75.641535618981 -0.0615356189809546 68 75.44 75.6313796219147 -0.191379621914663 69 75.37 75.4929434295242 -0.122943429524170 70 75.22 75.4219686658305 -0.201968665830549 71 75.33 75.2728629238033 0.057137076196696 72 75.33 75.3795238859368 -0.0495238859367646 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 75.380880912146 75.1305689297158 75.6311928945761 74 75.4311162757084 75.0793029995007 75.7829295519161 75 75.4813516392708 75.0512675253324 75.9114357532092 76 75.5315870028332 75.0353456941171 76.0278283115493 77 75.5818223663957 75.0271856273964 76.1364591053949 78 75.632057729958 75.0245449078166 76.2395705520996 79 75.6822930935205 75.0260879094345 76.3384982776066 80 75.732528457083 75.0309429579436 76.4341139562223 81 75.7827638206454 75.0385039247087 76.5270237165821 82 75.8329991842078 75.048329164007 76.6176692044087 83 75.8832345477703 75.0600851002218 76.7063839953187 84 75.9334699113327 75.0735124899559 76.7934273327095

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211624891yheg3vwzy440xog/1goxf1211624824.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211624891yheg3vwzy440xog/1goxf1211624824.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211624891yheg3vwzy440xog/22zv41211624824.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211624891yheg3vwzy440xog/22zv41211624824.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211624891yheg3vwzy440xog/3xmx41211624824.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211624891yheg3vwzy440xog/3xmx41211624824.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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