Workshop 9-10

*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, 04 Dec 2009 15:11:18 -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/04/t1259964750iaya3f6sv89rdv9.htm/, Retrieved Fri, 04 Dec 2009 23:12:33 +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/04/t1259964750iaya3f6sv89rdv9.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:

WS 9-10

Dataseries X:

» Textbox « » Textfile « » CSV «

5.7 6.1 6 5.9 5.8 5.7 5.6 5.4 5.4 5.5 5.6 5.7 5.9 6.1 6 5.8 5.8 5.7 5.5 5.3 5.2 5.2 5 5.1 5.1 5.2 4.9 4.8 4.5 4.5 4.4 4.4 4.2 4.1 3.9 3.8 3.9 4.2 4.1 3.8 3.6 3.7 3.5 3.4 3.1 3.1 3.1 3.2 3.3 3.5 3.6 3.5 3.3 3.2 3.1 3.2 3 3 3.1 3.4

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.795617759934405 beta 0.115622092346912 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 5.9 5.91141206844105 -0.0114120684410484 14 6.1 6.09959501506799 0.000404984932013797 15 6 6.00157408438233 -0.00157408438233375 16 5.8 5.81031371087173 -0.0103137108717304 17 5.8 5.82842033663677 -0.028420336636767 18 5.7 5.74202426512985 -0.0420242651298519 19 5.5 5.45947408374793 0.0405259162520668 20 5.3 5.27415719418642 0.0258428058135802 21 5.2 5.28338773530909 -0.0833877353090866 22 5.2 5.29816326227001 -0.0981632622700124 23 5 5.28991767617873 -0.289917676178727 24 5.1 5.09300016320327 0.00699983679672567 25 5.1 5.22129803504218 -0.121298035042178 26 5.2 5.23686392003097 -0.0368639200309691 27 4.9 5.05919557120876 -0.159195571208759 28 4.8 4.69830756726449 0.101692432735510 29 4.5 4.73103257316789 -0.231032573167893 30 4.5 4.40926848263627 0.0907315173637349 31 4.4 4.22730752354078 0.172692476459217 32 4.4 4.13339342179269 0.266606578207315 33 4.2 4.28455429904767 -0.0845542990476673 34 4.1 4.24486578898424 -0.14486578898424 35 3.9 4.10933651747807 -0.209336517478072 36 3.8 3.97489505508343 -0.174895055083426 37 3.9 3.84515059473186 0.0548494052681359 38 4.2 3.93673989363645 0.263260106363548 39 4.1 3.98650169833447 0.113498301665525 40 3.8 3.93018633909184 -0.130186339091839 41 3.6 3.71434602817831 -0.114346028178310 42 3.7 3.55385174913284 0.146148250867164 43 3.5 3.47219720812245 0.0278027918775474 44 3.4 3.30884476441603 0.0911552355839738 45 3.1 3.25237280793271 -0.152372807932715 46 3.1 3.10534363273615 -0.00534363273615002 47 3.1 3.04774695106348 0.0522530489365201 48 3.2 3.11468517381809 0.0853148261819148 49 3.3 3.25102718156222 0.0489728184377793 50 3.5 3.38743863026519 0.112561369734810 51 3.6 3.33044526200662 0.269554737993377 52 3.5 3.4035720801344 0.0964279198655986 53 3.3 3.43178898730854 -0.131788987308539 54 3.2 3.36210769613620 -0.162107696136195 55 3.1 3.05799001604015 0.0420099839598529 56 3.2 2.95932910718225 0.240670892817750 57 3 3.02065973935298 -0.0206597393529750 58 3 3.06029592031758 -0.060295920317579 59 3.1 3.01938236342738 0.0806176365726174 60 3.4 3.1688183551414 0.231181644858601 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 3.49002179107176 3.22406804667539 3.75597553546813 62 3.67924954757116 3.31512459120152 4.04337450394081 63 3.61599089835826 3.17194885142785 4.06003294528867 64 3.46938596262686 2.95739418129983 3.9813777439539 65 3.39585861786705 2.81026355476833 3.98145368096577 66 3.45969461501472 2.77920701553256 4.14018221449687 67 3.36690773552337 2.61838644778714 4.11542902325959 68 3.31106711822 2.48810996930822 4.13402426713179 69 3.14138399121592 2.27297395993347 4.00979402249837 70 3.21440228855856 2.23757635421557 4.19122822290154 71 3.28245842628467 2.19353601591677 4.37138083665256 72 3.42532446035466 -123.777322913226 130.627971833935

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259964750iaya3f6sv89rdv9/17kx41259964676.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259964750iaya3f6sv89rdv9/17kx41259964676.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259964750iaya3f6sv89rdv9/2aqmm1259964676.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259964750iaya3f6sv89rdv9/2aqmm1259964676.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259964750iaya3f6sv89rdv9/3mips1259964676.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259964750iaya3f6sv89rdv9/3mips1259964676.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')

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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