opgave10bW.Verlinden

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 05 Jun 2009 09:15:35 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/05/t1244214964c8ocxo4a8s5tu11.htm/, Retrieved Fri, 05 Jun 2009 17:16:08 +0200

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/Jun/05/t1244214964c8ocxo4a8s5tu11.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 «

665272 661735 621014 574889 677734 717075 653612 690697 665864 830701 789303 617808 805775 909449 599973 955874 799494 876097 823300 900079 860754 923882 1121084 741757 966066 901978 648659 852732 706036 835792 722489 714262 739459 816834 743082 683375 1006000 866000 644000 703000 699000 713000 688000 672000 600000 847000 697000 687000 973000 796000 658000 709000 798000 820000 776000 699000 828433 942131 792916 864942 982689 948143 874863 735794 854605 1284216 961585 818379 1079498 1095091 1008925 967118 1127715

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 0.380224313860241 beta 0.020939568714286 gamma 0.880171901277375 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 805775 718406.610576923 87368.3894230766 14 909449 855318.560498585 54130.4395014151 15 599973 565823.522498264 34149.4775017363 16 955874 939221.834291656 16652.1657083437 17 799494 788115.031147029 11378.9688529712 18 876097 866794.826659712 9302.17334028834 19 823300 832958.785445379 -9658.78544537851 20 900079 866931.71768106 33147.2823189399 21 860754 862257.467477854 -1503.46747785353 22 923882 1028513.23116823 -104631.231168231 23 1121084 942539.224061432 178544.775938568 24 741757 844808.604152631 -103051.604152631 25 966066 1044312.97979541 -78246.9797954111 26 901978 1100442.50086780 -198464.500867802 27 648659 702314.000881889 -53655.0008818891 28 852732 1030391.96910099 -177659.969100993 29 706036 798589.326908614 -92553.3269086143 30 835792 831854.08061852 3937.91938148078 31 722489 780827.78945107 -58338.7894510698 32 714262 814447.67097411 -100185.67097411 33 739459 733918.296857974 5540.70314202609 34 816834 840394.978828436 -23560.9788284361 35 743082 934166.10519183 -191084.105191829 36 683375 533782.461942105 149592.538057895 37 1006000 836393.182487073 169606.817512927 38 866000 916670.082232239 -50670.0822322386 39 644000 650395.315443437 -6395.31544343662 40 703000 925836.78545995 -222836.785459951 41 699000 719963.649440517 -20963.6494405171 42 713000 830335.752865224 -117335.752865224 43 688000 695510.556683143 -7510.55668314267 44 672000 722318.200373803 -50318.2003738035 45 6e+05 715510.875149156 -115510.875149156 46 847000 756208.310089609 90791.6899103915 47 697000 799106.889516008 -102106.889516008 48 687000 616138.369267380 70861.6307326205 49 973000 896846.420744103 76153.579255897 50 796000 817797.778014666 -21797.7780146664 51 658000 583253.840951776 74746.1590482239 52 709000 768723.085689035 -59723.0856890354 53 798000 733538.66792899 64461.33207101 54 820000 823044.97564338 -3044.97564338031 55 776000 791721.926199214 -15721.9261992142 56 699000 792125.435374473 -93125.4353744728 57 828433 733207.727490098 95225.2725099018 58 942131 967979.09934044 -25848.0993404402 59 792916 861778.795188115 -68862.795188115 60 864942 786549.417135278 78392.5828647225 61 982689 1073810.70527378 -91121.705273784 62 948143 877197.749264459 70945.250735541 63 874863 730792.14045647 144070.859543529 64 735794 870027.637357362 -134233.637357362 65 854605 874424.516599558 -19819.5165995579 66 1284216 894557.15164276 389658.84835724 67 961585 1008258.11815969 -46673.118159687 68 818379 957046.350818993 -138667.350818993 69 1079498 985574.381487375 93923.6185126251 70 1095091 1155808.68664253 -60717.686642533 71 1008925 1014612.07056818 -5687.07056818123 72 967118 1045962.64545584 -78844.6454558376 73 1127715 1181944.89242415 -54229.892424149 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 1089039.80016631 885163.542839536 1292916.05749309 75 956256.616263905 737558.258814116 1174954.97371369 76 888455.013744392 655319.908595503 1121590.11889328 77 1006933.25931018 759668.593381235 1254197.92523912 78 1258762.27110654 997615.273317035 1519909.26889604 79 983966.35431306 709137.197970299 1258795.51065582 80 898372.707613736 610023.931315839 1186721.48391163 81 1105665.53106342 803929.09157613 1407401.97055071 82 1154241.34589083 839224.011204752 1469258.68057691 83 1065045.99193226 736833.540739452 1393258.44312507 84 1057591.29930868 716251.843017712 1398930.75559965 85 1236548.00642188 882134.653580146 1590961.35926360

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244214964c8ocxo4a8s5tu11/1oa861244214933.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244214964c8ocxo4a8s5tu11/1oa861244214933.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244214964c8ocxo4a8s5tu11/2tmfs1244214933.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244214964c8ocxo4a8s5tu11/2tmfs1244214933.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244214964c8ocxo4a8s5tu11/3rtbo1244214933.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244214964c8ocxo4a8s5tu11/3rtbo1244214933.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