Exponential Smoothing personenwagens

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 24 May 2008 08:24:00 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/24/t1211639236s8srvcvlbkk9hzn.htm/, Retrieved Sat, 24 May 2008 16:27:16 +0200

User-defined keywords:

Pieter Van den Broeck

Dataseries X:

» Textbox « » Textfile « » CSV «

41086 39690 43129 37863 35953 29133 24693 22205 21725 27192 21790 13253 37702 30364 32609 30212 29965 28352 25814 22414 20506 28806 22228 13971 36845 35338 35022 34777 26887 23970 22780 17351 21382 24561 17409 11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698

Text written by user:

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 7 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.269020114715571 beta 0.000794515688686379 gamma 0.647545306845453 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 37702 39185.4976388889 -1483.49763888889 14 30364 31314.6139080394 -950.613908039413 15 32609 33267.3834347094 -658.383434709365 16 30212 30598.0864468339 -386.086446833942 17 29965 30082.9186368187 -117.918636818729 18 28352 28311.201491138 40.7985088619971 19 25814 25711.1495038309 102.850496169132 20 22414 22088.4793992713 325.52060072868 21 20506 19881.5316087857 624.468391214261 22 28806 27980.1819281694 825.818071830643 23 22228 21483.9675393312 744.032460668841 24 13971 13659.7018726830 311.298127316957 25 36845 37372.9275490279 -527.927549027881 26 35338 30011.4193196546 5326.58068034544 27 35022 33792.6186356465 1229.38136435346 28 34777 31761.8746560918 3015.12534390822 29 26887 32291.1799993497 -5404.17999934965 30 23970 29173.8934320634 -5203.89343206336 31 22780 25192.5782927589 -2412.57829275888 32 17351 20998.3614692089 -3647.36146920886 33 21382 17863.0390220109 3518.96097798915 34 24561 26835.1979309961 -2274.19793099609 35 17409 19465.1661502300 -2056.16615023002 36 11514 10681.0225058456 832.977494154407 37 31514 34135.7240364325 -2621.72403643249 38 27071 28980.0578886706 -1909.05788867064 39 29462 28871.7267237739 590.273276226129 40 26105 27510.5626871544 -1405.56268715436 41 22397 22860.697502806 -463.697502806011 42 23843 21163.6595544619 2679.34044553812 43 21705 20622.3815018554 1082.61849814457 44 18089 16782.7547694398 1306.24523056019 45 20764 18372.0239310598 2391.97606894016 46 25316 24298.4575906626 1017.54240933738 47 17704 17917.4827076927 -213.482707692710 48 15548 10997.3153833767 4550.68461662326 49 28029 33818.39481305 -5789.39481305002 50 29383 28148.7169794256 1234.28302057439 51 36438 30070.539730284 6367.46026971597 52 32034 29321.567935672 2712.43206432803 53 22679 26228.9581711376 -3549.95817113758 54 24319 25192.3351898115 -873.335189811492 55 18004 22941.7075003799 -4937.7075003799 56 17537 17589.2453249500 -52.2453249499558 57 20366 19327.5867784097 1038.4132215903 58 22782 24239.6284255707 -1457.62842557074 59 19169 16609.8787474887 2559.12125251132 60 13807 12691.0661661607 1115.93383383932 61 29743 29693.3795670639 49.6204329361317 62 25591 28920.0192473718 -3329.01924737185 63 29096 32043.8970469941 -2947.89704699406 64 26482 27056.7588683261 -574.758868326102 65 22405 20112.8026182902 2292.19738170978 66 27044 21913.2754015566 5130.72459844344 67 17970 19353.7820862739 -1383.78208627392 68 18730 17270.4163455993 1459.58365440071 69 19684 19932.5701622099 -248.570162209897 70 19785 23317.474294791 -3532.474294791 71 18479 17030.9743077252 1448.02569227476 72 10698 12130.0213606700 -1432.02136066998 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 27941.4961756975 22858.4634009577 33024.5289504373 74 25554.8664488476 20290.8298297964 30818.9030678989 75 29754.7638644571 24315.4701865658 35194.0575423484 76 26684.6518599747 21075.3090185416 32293.9947014077 77 21253.1678553488 15478.5234435578 27027.8122671398 78 23780.8973765077 17845.3021254164 29716.492627599 79 16756.7539072204 10664.2135355910 22849.2942788498 80 16391.0467279594 10145.2647890146 22636.8286669043 81 17851.196481407 11455.6101210898 24246.7828417242 82 19747.8076738444 13205.6177399642 26289.9976077246 83 16769.1005314344 10083.2971312688 23454.9039316000 84 10115.0445220695 3288.4288761486 16941.6601679904

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211639236s8srvcvlbkk9hzn/10t1t1211639029.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211639236s8srvcvlbkk9hzn/10t1t1211639029.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211639236s8srvcvlbkk9hzn/2grlh1211639029.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211639236s8srvcvlbkk9hzn/2grlh1211639029.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211639236s8srvcvlbkk9hzn/3z4261211639029.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211639236s8srvcvlbkk9hzn/3z4261211639029.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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=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