Workshop 9 verbetering 3 link 4

*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 11 Dec 2009 08:39:25 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/11/t1260546026yawwqc4z2wsu2nk.htm/, Retrieved Fri, 11 Dec 2009 16:40:30 +0100

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/Dec/11/t1260546026yawwqc4z2wsu2nk.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:

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8 8,1 7,7 7,5 7,6 7,8 7,8 7,8 7,5 7,5 7,1 7,5 7,5 7,6 7,7 7,7 7,9 8,1 8,2 8,2 8,2 7,9 7,3 6,9 6,6 6,7 6,9 7 7,1 7,2 7,1 6,9 7 6,8 6,4 6,7 6,6 6,4 6,3 6,2 6,5 6,8 6,8 6,4 6,1 5,8 6,1 7,2 7,3 6,9 6,1 5,8 6,2 7,1 7,7 7,9 7,7 7,4 7,5 8

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.928337978024088 beta 1 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 7.5 7.43325688014239 0.0667431198576134 14 7.6 7.64602125144062 -0.0460212514406226 15 7.7 7.69906398705166 0.000936012948344889 16 7.7 7.69656461879542 0.00343538120457598 17 7.9 7.92064255850776 -0.0206425585077596 18 8.1 8.14661417062053 -0.046614170620531 19 8.2 7.94549565282806 0.254504347171943 20 8.2 8.4488881479485 -0.248888147948495 21 8.2 7.91500604288992 0.284993957110078 22 7.9 8.42638631490673 -0.526386314906732 23 7.3 7.27394660241382 0.0260533975861774 24 6.9 7.47803073148591 -0.578030731485913 25 6.6 6.17914539632137 0.420854603678625 26 6.7 6.26918029161326 0.430819708386739 27 6.9 6.76782900282106 0.132170997178936 28 7 7.01981194650812 -0.0198119465081223 29 7.1 7.3134137817753 -0.213413781775293 30 7.2 7.26479021842537 -0.0647902184253724 31 7.1 6.99337732623124 0.106622673768758 32 6.9 7.0957641453048 -0.195764145304794 33 7 6.5174601913346 0.482539808665398 34 6.8 7.17307514272357 -0.373075142723573 35 6.4 6.40077979247309 -0.000779792473089458 36 6.7 6.6156503985121 0.0843496014879035 37 6.6 6.74098316599545 -0.140983165995448 38 6.4 6.5277804195043 -0.127780419504296 39 6.3 6.18269556698019 0.117304433019809 40 6.2 6.10055251175049 0.099447488249515 41 6.5 6.26663944286728 0.233360557132715 42 6.8 6.83850075057714 -0.0385007505771426 43 6.8 6.84306011460125 -0.0430601146012544 44 6.4 6.87990404816121 -0.479904048161212 45 6.1 5.93047515652366 0.169524843476341 46 5.8 5.79828809105899 0.00171190894101247 47 6.1 5.34941704155298 0.750582958447024 48 7.2 6.87829798701684 0.321702012983159 49 7.3 8.06166693068413 -0.761666930684131 50 6.9 7.55654300690666 -0.656543006906658 51 6.1 6.52680899013502 -0.426808990135024 52 5.8 5.22457717449504 0.575422825504956 53 6.2 5.55278970809034 0.647210291909664 54 7.1 6.58764776321892 0.512352236781081 55 7.7 7.71005243133236 -0.0100524313323644 56 7.9 8.3741390179299 -0.474139017929902 57 7.7 8.07813183944 -0.378131839440006 58 7.4 7.51196918249704 -0.111969182497037 59 7.5 6.95373052001372 0.546269479986283 60 8 8.12546755984644 -0.125467559846438 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 8.20151286668224 7.52306513965207 8.87996059371241 62 8.51264718611941 7.0722899912208 9.95300438101802 63 8.83089587875789 6.4282129691002 11.2335787884156 64 9.11400177850221 5.59820715857465 12.6297963984298 65 9.56613371179337 4.71560112149303 14.4166663020937 66 10.0444149510147 3.6786053407488 16.4102245612807 67 10.1079857462893 2.38053297835026 17.8354385142284 68 10.2431052859799 1.04192280396469 19.4442877679952 69 10.3165490133721 -0.356197216814968 20.9892952435592 70 10.3838903553653 -1.79408248812996 22.5618631988605 71 10.2732534107119 -3.21287793298523 23.7593847544091 72 10.8697099394555 -5.15857384168304 26.8979937205941

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260546026yawwqc4z2wsu2nk/1s2kp1260545962.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260546026yawwqc4z2wsu2nk/1s2kp1260545962.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260546026yawwqc4z2wsu2nk/29cvl1260545962.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260546026yawwqc4z2wsu2nk/29cvl1260545962.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260546026yawwqc4z2wsu2nk/37svd1260545962.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260546026yawwqc4z2wsu2nk/37svd1260545962.ps (open in new window)

Parameters (Session):

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

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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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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