SHW WS9

*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: Sun, 06 Dec 2009 03:49:38 -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/06/t1260096854rze5jmj7qc00g2w.htm/, Retrieved Sun, 06 Dec 2009 11:54:18 +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/06/t1260096854rze5jmj7qc00g2w.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 «

1.4 1.2 1 1.7 2.4 2 2.1 2 1.8 2.7 2.3 1.9 2 2.3 2.8 2.4 2.3 2.7 2.7 2.9 3 2.2 2.3 2.8 2.8 2.8 2.2 2.6 2.8 2.5 2.4 2.3 1.9 1.7 2 2.1 1.7 1.8 1.8 1.8 1.3 1.3 1.3 1.2 1.4 2.2 2.9 3.1 3.5 3.6 4.4 4.1 5.1 5.8 5.9 5.4 5.5 4.8 3.2 2.7

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 0.83662597434103 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 2 1.70232491037523 0.297675089624768 14 2.3 2.23686640268501 0.0631335973149865 15 2.8 2.7491238604665 0.0508761395334987 16 2.4 2.41659124317405 -0.0165912431740511 17 2.3 2.37223843724851 -0.0722384372485143 18 2.7 2.73103950620319 -0.0310395062031872 19 2.7 2.82295149719121 -0.122951497191213 20 2.9 2.55182330868504 0.348176691314956 21 3 2.45709285416430 0.542907145835697 22 2.2 4.2256732282077 -2.02567322820770 23 2.3 2.18720589040239 0.112794109597607 24 2.8 1.90912398194133 0.890876018058667 25 2.8 2.84410496376943 -0.0441049637694317 26 2.8 3.13266827637733 -0.332668276377328 27 2.2 3.4070774219412 -1.20707742194120 28 2.6 2.07407062628186 0.525929373718139 29 2.8 2.46993914146424 0.330060858535761 30 2.5 3.24338176325385 -0.743381763253854 31 2.4 2.72229363595367 -0.322293635953673 32 2.3 2.36951056594137 -0.0695105659413673 33 1.9 2.02765849303223 -0.127658493032229 34 1.7 2.37245071415674 -0.672450714156736 35 2 1.82378794550119 0.176212054498808 36 2.1 1.73276166901427 0.367238330985731 37 1.7 2.07974523935379 -0.379745239353789 38 1.8 1.95290492841483 -0.152904928414835 39 1.8 2.05760562817595 -0.257605628175954 40 1.8 1.80471362847849 -0.00471362847849477 41 1.3 1.75991270057602 -0.45991270057602 42 1.3 1.54717044569962 -0.247170445699625 43 1.3 1.45490996364744 -0.154909963647439 44 1.2 1.32675459201488 -0.126754592014876 45 1.4 1.08653358163036 0.313466418369639 46 2.2 1.59754817254623 0.602451827453774 47 2.9 2.27412525993367 0.62587474006633 48 3.1 2.47557148397502 0.62442851602498 49 3.5 2.84488006942854 0.655119930571456 50 3.6 3.79389676589506 -0.193896765895060 51 4.4 4.00053141843505 0.399468581564948 52 4.1 4.26881251901869 -0.168812519018687 53 5.1 3.75298431879364 1.34701568120636 54 5.8 5.48543602683377 0.314563973166227 55 5.9 6.11769357806188 -0.217693578061883 56 5.4 5.76151131186642 -0.361511311866418 57 5.5 4.95742305463946 0.542576945360539 58 4.8 6.30278933425556 -1.50278933425556 59 3.2 5.33004462506922 -2.13004462506922 60 2.7 3.12041799431657 -0.420417994316566 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 2.62604682917858 1.33954459577247 3.9125490625847 62 2.83427593187052 1.11464541097857 4.55390645276247 63 3.20892447903329 1.04094454475208 5.3769044133145 64 3.10684805552705 0.769832198229048 5.44386391282505 65 2.98430971978455 0.517888224088255 5.45073121548084 66 3.26094305278603 0.413772819594682 6.10811328597738 67 3.44350181674455 0.302389567315443 6.58461406617367 68 3.34863588555818 0.149546384376985 6.54772538673937 69 3.14337834327917 -0.0136688797499414 6.30042556630829 70 3.44986001815668 -0.115342532700712 7.01506256901407 71 3.47000455992472 -0.222852876854585 7.16286199670402 72 3.29557716932162 -18.9742467079709 25.5654010466141

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260096854rze5jmj7qc00g2w/17g8d1260096576.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260096854rze5jmj7qc00g2w/17g8d1260096576.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260096854rze5jmj7qc00g2w/20kwc1260096576.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260096854rze5jmj7qc00g2w/20kwc1260096576.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260096854rze5jmj7qc00g2w/3jrzu1260096576.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260096854rze5jmj7qc00g2w/3jrzu1260096576.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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by