Experimental smoothing

*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 09:09:28 -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/t1260547842x4g7q2wengswca0.htm/, Retrieved Fri, 11 Dec 2009 17:10:46 +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/t1260547842x4g7q2wengswca0.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 «

8.3 8.2 8 7.9 7.6 7.6 8.3 8.4 8.4 8.4 8.4 8.6 8.9 8.8 8.3 7.5 7.2 7.4 8.8 9.3 9.3 8.7 8.2 8.3 8.5 8.6 8.5 8.2 8.1 7.9 8.6 8.7 8.7 8.5 8.4 8.5 8.7 8.7 8.6 8.5 8.3 8 8.2 8.1 8.1 8 7.9 7.9 8 8 7.9 8 7.7 7.2 7.5 7.3 7 7 7 7.2 7.3 7.1 6.8 6.4 6.1 6.5 7.7 7.9 7.5 6.9 6.6 6.9

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 1 beta 0.00352340646797870 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 8.9 8.9503140766282 -0.0503140766281973 14 8.8 8.75795932726792 0.0420406727320852 15 8.3 8.24431609483113 0.0556839051688698 16 7.5 7.47242442055062 0.0275755794493833 17 7.2 7.21280290290433 -0.0128029029043333 18 7.4 7.43515757080091 -0.0351575708009104 19 8.8 8.52584202748093 0.274157972519067 20 9.3 8.87231887352567 0.427681126474331 21 9.3 9.27959758617377 0.0204024138262309 22 8.7 9.32643992965158 -0.626439929651577 23 8.2 8.75478518261489 -0.554785182614888 24 8.3 8.43891041178834 -0.138910411788343 25 8.5 8.59475462049406 -0.094754620494058 26 8.6 8.36299111548783 0.237008884512170 27 8.5 8.05591476094622 0.444085239053775 28 8.2 7.65199645704296 0.548003542957042 29 8.1 7.88615538355202 0.213844616447984 30 7.9 8.36500928681314 -0.465009286813141 31 8.6 9.1018164327324 -0.501816432732401 32 8.7 8.66959313245035 0.0304068675496527 33 8.7 8.67938324687388 0.0206167531261219 34 8.5 8.72320812946758 -0.223208129467581 35 8.4 8.55246176408234 -0.152461764082336 36 8.5 8.64419427175929 -0.144194271759291 37 8.7 8.80129428351827 -0.101294283518273 38 8.7 8.55921000776276 0.140789992237234 39 8.6 8.14893696013846 0.451063039861536 40 8.5 7.74143841171686 0.758561588283137 41 8.3 8.17435734841297 0.125642651587032 42 8 8.57110904648884 -0.571109046488839 43 8.2 9.21638133958279 -1.01638133958279 44 8.1 8.26501134402285 -0.165011344022849 45 8.1 8.07920682225726 0.0207931777427444 46 8 8.12001412938259 -0.120014129382588 47 7.9 8.047902750705 -0.147902750704992 48 7.9 8.12814290430106 -0.228142904301055 49 8 8.17832367553149 -0.178323675531486 50 8 7.8687471945272 0.131252805472799 51 7.9 7.49160739937399 0.40839260062601 52 8 7.10981833012476 0.890181669875243 53 7.7 7.69230919079451 0.00769080920548859 54 7.2 7.95013065469094 -0.750130654690939 55 7.5 8.29281845025857 -0.792818450258565 56 7.3 7.55771594955604 -0.257715949556043 57 7 7.27936065334012 -0.279360653340116 58 7 7.01493489161981 -0.0149348916198146 59 7 7.0396898750571 -0.0396898750571033 60 7.2 7.20002038019794 -2.03801979425933e-05 61 7.3 7.45181192963172 -0.151811929631722 62 7.1 7.17843657501434 -0.0784365750143401 63 6.8 6.64681466808213 0.153185331917874 64 6.4 6.11776161784542 0.282238382154585 65 6.1 6.15119200601735 -0.0511920060173523 66 6.5 6.29534094252554 0.204659057474462 67 7.7 7.48479564088605 0.215204359113954 68 7.9 7.75911270846598 0.140887291534019 69 7.5 7.87825668532496 -0.378256685324959 70 6.9 7.51644954893393 -0.616449548933926 71 6.6 6.93842614275394 -0.338426142753939 72 6.9 6.78728807549504 0.112711924504959 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 7.14019920194742 6.4386641445697 7.84173425932513 74 7.02047820979466 6.03563731703855 8.00531910255077 75 6.57174683025305 5.41176544746876 7.73172821303735 76 5.91158718057025 4.65243889532976 7.17073546581075 77 5.68049355811327 4.27973758039145 7.08124953583509 78 5.86118225218876 4.2519304014519 7.47043410292563 79 6.74739575051795 4.76288125687701 8.73191024415889 80 6.79704533811296 4.67454019895298 8.91955047727293 81 6.77598705786248 4.54268364007111 9.00929047565385 82 6.78909796112338 4.43972061737682 9.13847530486994 83 6.82627032087783 4.3574481894979 9.29509245225776 84 7.02004704166552 -71.2401196924339 85.2802137757649

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260547842x4g7q2wengswca0/1egkz1260547766.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260547842x4g7q2wengswca0/1egkz1260547766.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260547842x4g7q2wengswca0/27n4e1260547766.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260547842x4g7q2wengswca0/27n4e1260547766.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260547842x4g7q2wengswca0/3c5a71260547766.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260547842x4g7q2wengswca0/3c5a71260547766.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