Thomas van den Bosch opgave 10

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 19 Aug 2009 09:48:41 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Aug/19/t1250696958uq78q214238v0l8.htm/, Retrieved Wed, 19 Aug 2009 17:49:18 +0200

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Aug/19/t1250696958uq78q214238v0l8.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

5.93 5.9 5.9 5.94 5.86 5.92 5.9 5.91 5.84 5.84 5.83 5.82 5.8 5.91 5.92 5.96 5.9 5.92 6.09 6.31 6.25 6.23 6.22 6.19 6.15 6.12 6.13 6.1 6.05 6.07 6.09 6.17 6.12 6.12 6.13 6.19 6.24 6.41 6.5 6.53 6.58 6.53 6.51 6.51 6.49 6.49 6.49 6.53 6.65 6.61 6.52 6.62 6.6 6.61 6.63 6.62 6.6 6.59 6.59 6.52 6.52 6.61 6.59 6.6 6.48 6.53 6.56 6.56 6.49 6.45 6.44 6.43

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 4.7857361519868e-19 gamma 0.0425143406904243 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 5.8 5.78963818082616 0.0103618191738422 14 5.91 5.90047551080801 0.009524489191989 15 5.92 5.9013860743668 0.0186139256331979 16 5.96 5.94178014400469 0.0182198559953131 17 5.9 5.88287899074986 0.0171210092501433 18 5.92 5.90372735952147 0.0162726404785287 19 6.09 6.08159483867765 0.00840516132235436 20 6.31 6.12066975345772 0.189330246542281 21 6.25 6.24890594824382 0.00109405175618171 22 6.23 6.26319341225341 -0.0331934122534143 23 6.22 6.23162127244342 -0.0116212724434224 24 6.19 6.22247541860107 -0.0324754186010647 25 6.15 6.17526655614421 -0.0252665561442118 26 6.12 6.25563038306529 -0.135630383065286 27 6.13 6.11054729248438 0.0194527075156152 28 6.1 6.15202033872586 -0.0520203387258569 29 6.05 6.02072030059814 0.0292796994018572 30 6.07 6.0534471252742 0.0165528747257984 31 6.09 6.23530632444558 -0.145306324445584 32 6.17 6.12066975345772 0.0493302465422811 33 6.12 6.11059359745032 0.0094064025496765 34 6.12 6.13323029168604 -0.0132302916860390 35 6.13 6.12185633709093 0.00814366290906676 36 6.19 6.13265526258602 0.0573447374139757 37 6.24 6.17526655614421 0.064733443855788 38 6.41 6.34695592164573 0.063044078354272 39 6.5 6.39938897464676 0.100611025353238 40 6.53 6.52244353894887 0.0075564610511325 41 6.58 6.4440900379893 0.135909962010696 42 6.53 6.58245696426719 -0.0524569642671864 43 6.51 6.70668821413392 -0.196688214133925 44 6.51 6.54173984835998 -0.031739848359984 45 6.49 6.44649502080595 0.0435049791940454 46 6.49 6.50312532714703 -0.0131253271470317 47 6.49 6.49106566509476 -0.00106566509475581 48 6.53 6.49193588664619 0.0380641133538147 49 6.65 6.51364252679656 0.136357473203437 50 6.61 6.76299448628996 -0.152994486289963 51 6.52 6.59859013475875 -0.0785901347587474 52 6.62 6.5424664146366 0.077533585363402 53 6.6 6.53270230860606 0.0672976913939412 54 6.61 6.60241959970088 0.00758040029911644 55 6.63 6.78866767321016 -0.158667673210159 56 6.62 6.66204558976063 -0.0420455897606313 57 6.6 6.55516901071513 0.0448309892848693 58 6.59 6.61309412147327 -0.0230941214732727 59 6.59 6.59085196996065 -0.000851969960653953 60 6.52 6.59173605999623 -0.0717360599962289 61 6.52 6.50369029236561 0.0163097076343881 62 6.61 6.63107981945155 -0.0210798194515460 63 6.59 6.59859013475875 -0.00859013475874715 64 6.6 6.61254647954365 -0.0125464795436550 65 6.48 6.51301069291345 -0.0330106929134448 66 6.53 6.4826437870987 0.0473562129013008 67 6.56 6.70668821413392 -0.146688214133925 68 6.56 6.59186724061025 -0.0318672406102536 69 6.49 6.49589228894649 -0.0058922889464883 70 6.45 6.50312532714703 -0.0531253271470318 71 6.44 6.4511511431484 -0.0111511431483962 72 6.43 6.44203579997116 -0.0120357999711631 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 6.41412018248705 6.27555728754022 6.55268307743388 74 6.52364058212744 6.32623473093106 6.72104643332383 75 6.5125756536247 6.27203861455407 6.75311269269533 76 6.53503357640983 6.25720238121926 6.81286477160041 77 6.4490460006004 6.14240650998267 6.75568549121813 78 6.45174761683724 6.11577670956435 6.78771852411013 79 6.62649961359506 6.25537821787811 6.997621009312 80 6.65853628491367 6.26150543568457 7.05556713414277 81 6.59324075469554 6.17724117740592 7.00924033198517 82 6.60633679368521 6.16797946172117 7.04469412564926 83 6.6071538527127 6.1483113493641 7.06599635606128 84 6.60885563473971 -2.63681263971161 15.8545239091910

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250696958uq78q214238v0l8/1qoes1250696916.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250696958uq78q214238v0l8/1qoes1250696916.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250696958uq78q214238v0l8/24b7o1250696916.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250696958uq78q214238v0l8/24b7o1250696916.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250696958uq78q214238v0l8/3qvd51250696916.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250696958uq78q214238v0l8/3qvd51250696916.ps (open in new window)

Parameters (Session):

par1 = 0 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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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