*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 17 Jan 2010 05:31:49 -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/17/t1263731998ujzkqj7amo6i1d0.htm/, Retrieved Sun, 17 Jan 2010 13:40:02 +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/17/t1263731998ujzkqj7amo6i1d0.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 «

3,81 3,95 3,99 4 4,06 4,16 4,19 4,2 4,2 4,2 4,2 4,2 4,23 4,38 4,43 4,44 4,44 4,44 4,44 4,44 4,45 4,45 4,45 4,45 4,45 4,45 4,45 4,45 4,46 4,46 4,46 4,48 4,58 4,67 4,68 4,68 4,69 4,69 4,69 4,69 4,69 4,69 4,69 4,73 4,78 4,79 4,79 4,8 4,8 4,81 5,16 5,26 5,29 5,29 5,29 5,3 5,3 5,3 5,3 5,3 5,3 5,3 5,3 5,35 5,44 5,47 5,47 5,48 5,48 5,48 5,48 5,48

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 0.344199179309432 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 3.99 4.09 -0.0999999999999996 4 4 4.09558008206906 -0.0955800820690573 5 4.06 4.07268149626256 -0.0126814962625597 6 4.16 4.12831653565657 0.0316834643434296 7 4.19 4.23922195808126 -0.049221958081259 8 4.2 4.25227980050569 -0.0522798005056861 9 4.2 4.24428513607717 -0.0442851360771686 10 4.2 4.2290422285838 -0.0290422285838003 11 4.2 4.21904591733994 -0.0190459173399393 12 4.2 4.21249032822234 -0.0124903282223370 13 4.23 4.2081911674989 0.0218088325010974 14 4.38 4.24569774974748 0.134302250252522 15 4.43 4.44192447406381 -0.0119244740638056 16 4.44 4.48782007987735 -0.0478200798773463 17 4.44 4.48136044762905 -0.041360447629053 18 4.44 4.46712421549926 -0.0271242154992626 19 4.44 4.457788082785 -0.0177880827850041 20 4.44 4.45166543928892 -0.0116654392889171 21 4.45 4.44765020465939 0.00234979534061175 22 4.45 4.45845900228717 -0.00845900228717156 23 4.45 4.45554742064215 -0.00554742064215041 24 4.45 4.45363800300984 -0.00363800300983819 25 4.45 4.45238580535953 -0.00238580535952693 26 4.45 4.45156461311279 -0.00156461311278555 27 4.45 4.45102607456343 -0.00102607456342785 28 4.45 4.45067290054079 -0.000672900540785726 29 4.46 4.45044128872689 0.00955871127310903 30 4.46 4.46373138930235 -0.00373138930235051 31 4.46 4.4624470481668 -0.00244704816679775 32 4.48 4.46160477619606 0.0183952238039451 33 4.58 4.48793639713259 0.0920636028674133 34 4.67 4.61962461368382 0.0503753863161807 35 4.68 4.72696378031124 -0.0469637803112448 36 4.68 4.72079888567085 -0.0407988856708457 37 4.69 4.7067559427062 -0.0167559427062001 38 4.69 4.71098856097817 -0.0209885609781715 39 4.69 4.7037643155146 -0.0137643155145986 40 4.69 4.69902664941072 -0.00902664941071762 41 4.69 4.69591968409163 -0.00591968409163446 42 4.69 4.69388213368552 -0.00388213368552304 43 4.69 4.692545906457 -0.00254590645699615 44 4.73 4.6916696075439 0.0383303924561007 45 4.78 4.7448628971699 0.0351371028301015 46 4.79 4.80695705912733 -0.0169570591273303 47 4.79 4.8111204532922 -0.0211204532922018 48 4.8 4.80385081060238 -0.00385081060238246 49 4.8 4.81252536475337 -0.0125253647533663 50 4.81 4.80821414448471 0.0017858555152932 51 5.16 4.81882883448744 0.341171165512565 52 5.26 5.2862596696609 -0.0262596696609032 53 5.29 5.37722111291468 -0.0872211129146834 54 5.29 5.37719967743099 -0.087199677430994 55 5.29 5.3471856200232 -0.0571856200231986 56 5.3 5.32750237654291 -0.0275023765429125 57 5.3 5.32803608110778 -0.0280360811077829 58 5.3 5.31838608499943 -0.0183860849994311 59 5.3 5.31205760963191 -0.0120576096319134 60 5.3 5.30790739029218 -0.0079073902921758 61 5.3 5.30518567304313 -0.00518567304312967 62 5.3 5.30340076863752 -0.00340076863751726 63 5.3 5.30223022686346 -0.00223022686346219 64 5.35 5.30146258460738 0.048537415392615 65 5.44 5.36816912315132 0.0718308768486766 66 5.47 5.48289325201172 -0.0128932520117164 67 5.47 5.50845540525065 -0.0384554052506534 68 5.48 5.49521908632337 -0.0152190863233663 69 5.48 5.49998068930103 -0.0199806893010246 70 5.48 5.49310335244158 -0.0131033524415756 71 5.48 5.48859318928498 -0.00859318928498265 72 5.48 5.48563542058544 -0.00563542058544098 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 5.48369571344487 5.37345934272625 5.59393208416349 74 5.48739142688974 5.30270449487177 5.6720783589077 75 5.49108714033461 5.22888302230759 5.75329125836162 76 5.49478285377948 5.14988192509285 5.8396837824661 77 5.49847856722434 5.06534394683796 5.93161318761073 78 5.50217428066921 4.97531829556631 6.02903026577212 79 5.50586999411408 4.8799699039905 6.13177008423767 80 5.50956570755895 4.77949306464286 6.23963835047504 81 5.51326142100382 4.67408203874077 6.35244080326687 82 5.51695713444869 4.56392081767855 6.46999345121882 83 5.52065284789356 4.4491800280983 6.59212566768881 84 5.52434856133843 4.33001662830207 6.71868049437478

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/17/t1263731998ujzkqj7amo6i1d0/1655y1263731507.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/17/t1263731998ujzkqj7amo6i1d0/1655y1263731507.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/17/t1263731998ujzkqj7amo6i1d0/2kvil1263731507.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/17/t1263731998ujzkqj7amo6i1d0/2kvil1263731507.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/17/t1263731998ujzkqj7amo6i1d0/3v3rc1263731507.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/17/t1263731998ujzkqj7amo6i1d0/3v3rc1263731507.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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