KDGP2W62

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 20 Jan 2010 15:23:55 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/20/t1264026272gmwaccntdouyzrr.htm/, Retrieved Wed, 20 Jan 2010 23:24:36 +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/2010/Jan/20/t1264026272gmwaccntdouyzrr.htm/}, year = {2010}, } @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 = {2010}, 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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

1 4 -3 -3 0 6 -1 0 -1 1 -4 -1 -1 0 3 0 8 8 8 8 11 13 5 12 13 9 11 7 12 11 10 13 14 10 13 12 13 17 15 6 9 6 11 12 13 11 16 16 19 14 15 12 14 16 13 13 15 12 13 12 15 10 8 11 8 13 9 8 8 6 8 6 12 16

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 0.472554940548756 beta FALSE gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 4 1 3 3 -3 2.41766482164627 -5.41766482164627 4 -3 -0.142479456059871 -2.85752054394013 5 0 -1.49281490681835 1.49281490681835 6 6 -0.787377847276507 6.78737784727651 7 -1 2.42003108782519 -3.42003108782519 8 0 0.803878500443058 -0.803878500443058 9 -1 0.424001743457766 -1.42400174345777 10 1 -0.248917315763244 1.24891731576324 11 -4 0.341264732137568 -4.34126473213757 12 -1 -1.71022136526411 0.710221365264111 13 -1 -1.37460275022527 0.374602750225273 14 0 -1.19758236986317 1.19758236986317 15 3 -0.631658904270241 3.63165890427024 16 0 1.08449945333054 -1.08449945333054 17 8 0.57201387863677 7.42798612136323 18 8 4.08214541861456 3.91785458138544 19 8 5.93354695739982 2.06645304260018 20 8 6.91005955209255 1.08994044790745 21 11 7.42511629565514 3.57488370434486 22 13 9.11444525203054 3.88555474796946 23 5 10.9505833449562 -5.95058334495619 24 12 8.13860578615 3.86139421385 25 13 9.9633266993112 3.03667330068880 26 9 11.3983216703842 -2.39832167038419 27 11 10.264982916019 0.735017083981003 28 7 10.6123188704420 -3.61231887044196 29 12 8.90529974137711 3.09470025862289 30 11 10.3677156381069 0.632284361893129 31 10 10.6665047371512 -0.666504737151188 32 13 10.3515446307112 2.64845536928875 33 14 11.6030853002915 2.39691469970847 34 10 12.7357591837127 -2.73575918371271 35 13 11.4429626652976 1.55703733470236 36 12 12.1787483504301 -0.178748350430105 37 13 12.0942799343194 0.90572006568058 38 17 12.5222824261109 4.47771757388908 39 15 14.6382499880342 0.361750011965803 40 6 14.8091967434322 -8.80919674343221 41 9 10.6463673000573 -1.64636730005731 42 6 9.86836829845731 -3.86836829845731 43 11 8.04035174715913 2.95964825284087 44 12 9.43894815132558 2.56105184867442 45 13 10.6491858554182 2.3508141445818 46 11 11.7600746937522 -0.760074693752227 47 16 11.4008976420335 4.59910235796647 48 16 13.5742261833800 2.42577381661998 49 19 14.7205375850776 4.27946241492240 50 14 16.7428186921419 -2.74281869214190 51 15 15.4466861681408 -0.446686168140765 52 12 15.2356024125111 -3.23560241251106 53 14 13.7066025068275 0.293397493172517 54 16 13.8452489417708 2.15475105822922 55 13 14.8634871999897 -1.86348719998966 56 13 13.9828871169852 -0.982887116985179 57 15 13.5184189538521 1.48158104614789 58 12 14.2185473970327 -2.21854739703269 59 13 13.1701618637233 -0.170161863723312 60 12 13.0897510343279 -1.08975103432788 61 15 12.5747837990881 2.42521620091188 62 10 13.7208316967279 -3.72083169672792 63 8 11.9625342954887 -3.96253429548873 64 11 10.0900191370616 0.909980862938353 65 8 10.520035089648 -2.52003508964799 66 13 9.3291800576786 3.67081994232140 67 9 11.0638441572875 -2.06384415728748 68 8 10.0885644042386 -2.0885644042386 69 8 9.10160297636138 -1.10160297636138 70 6 8.5810350473586 -2.58103504735860 71 8 7.3613541839998 0.6386458160002 72 6 7.66314941961149 -1.66314941961149 73 12 6.87721994450328 5.12278005549672 74 16 9.29801496907289 6.70198503092711 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 75 12.4650711069213 6.26931740694556 18.6608248068970 76 12.4650711069213 5.61236536631645 19.3177768475262 77 12.4650711069213 5.01310572697795 19.9170364868647 78 12.4650711069213 4.45857374038018 20.4715684734624 79 12.4650711069213 3.94003667080402 20.9901055430386 80 12.4650711069213 3.45128032870035 21.4788618851423 81 12.4650711069213 2.9876961407138 21.9424460731288 82 12.4650711069213 2.54575417949872 22.3843880343439 83 12.4650711069213 2.12267968311569 22.8074625307269 84 12.4650711069213 1.71624454679096 23.2138976670516 85 12.4650711069213 1.32462746780535 23.6055147460373 86 12.4650711069213 0.946316984496661 23.9838252293459

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/20/t1264026272gmwaccntdouyzrr/1ud9t1264026232.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1264026272gmwaccntdouyzrr/1ud9t1264026232.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1264026272gmwaccntdouyzrr/2zodk1264026232.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1264026272gmwaccntdouyzrr/2zodk1264026232.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1264026272gmwaccntdouyzrr/3mwh11264026232.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/20/t1264026272gmwaccntdouyzrr/3mwh11264026232.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) 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