test

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 15 Apr 2008 14:54:56 -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/Apr/15/t1208292936pmnyvoth3vkfsku.htm/, Retrieved Tue, 15 Apr 2008 22:55:41 +0200

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

13328 12873 14000 13477 14237 13674 13529 14058 12975 14326 14008 16193 14483 14011 15057 14884 15414 14440 14900 15074 14442 15307 14938 17193 15528 14765 15838 15723 16150 15486 15986 15983 15692 16490 15686 18897 16316 15636 17163 16534 16518 16375 16290 16352 15943 16362 16393 19051 16747 16320 17910 16961 17480 17049 16879 17473 16998 17307 17418 20169 17871 17226 19062 17804 19100 18522 18060 18869 18127 18871 18890 21263 19547 18450 20254 19240 20216 19420 19415 20018 18652 19978 19509 21971

Text written by user:

Output produced by software:

Summary of compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.440051506384153 beta 0.000510357792766258 gamma 0.969612467681559 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 14483 13950.0064127244 532.993587275634 14 14011 13710.3180276635 300.681972336470 15 15057 14858.4539887859 198.546011214061 16 14884 14757.8307940628 126.169205937182 17 15414 15346.8791948472 67.1208051528447 18 14440 14409.4965928752 30.503407124801 19 14900 14882.3743789156 17.6256210843821 20 15074 15074.1789431872 -0.178943187207551 21 14442 14462.2002026382 -20.2002026381779 22 15307 15336.5931238976 -29.5931238976373 23 14938 14973.0809767451 -35.0809767451283 24 17193 17227.6015232389 -34.6015232389 25 15528 15796.1793597404 -268.179359740365 26 14765 15019.3832309765 -254.383230976508 27 15838 15923.2660255566 -85.2660255565697 28 15723 15640.7630943440 82.2369056560492 29 16150 16200.2974877907 -50.2974877906745 30 15486 15138.1294300757 347.870569924311 31 15986 15765.315618536 220.684381463989 32 15983 16042.5739394619 -59.5739394618704 33 15692 15349.5587830130 342.44121698697 34 16490 16436.5472822242 53.4527177757809 35 15686 16073.7925925929 -387.79259259293 36 18897 18313.7834502122 583.216549787812 37 16316 16895.902837954 -579.902837953989 38 15636 15936.0503022292 -300.050302229214 39 17163 16983.0463333612 179.953666638754 40 16534 16889.6413325144 -355.641332514424 41 16518 17207.8578450821 -689.85784508209 42 16375 16035.9966343456 339.003365654389 43 16290 16603.8926137903 -313.892613790318 44 16352 16491.7088311061 -139.708831106091 45 15943 15964.7551711965 -21.7551711965316 46 16362 16746.0563229807 -384.05632298073 47 16393 15944.7054354088 448.294564591182 48 19051 19156.3562268122 -105.356226812200 49 16747 16770.4584969018 -23.4584969017887 50 16320 16188.8764249222 131.123575077825 51 17910 17737.8757527059 172.124247294105 52 16961 17327.2676307851 -366.267630785063 53 17480 17460.0099751191 19.9900248809172 54 17049 17134.9256386614 -85.9256386614434 55 16879 17158.8465352252 -279.846535225188 56 17473 17157.4450247844 315.554975215622 57 16998 16867.0219923134 130.978007686619 58 17307 17547.9730593580 -240.973059358035 59 17418 17241.1132802829 176.886719717128 60 20169 20181.7132615435 -12.7132615435003 61 17871 17740.7680291173 130.231970882684 62 17226 17274.8412128557 -48.8412128556665 63 19062 18848.1932548181 213.806745181941 64 17804 18111.7650355630 -307.765035563043 65 19100 18504.8029249481 595.197075051859 66 18522 18340.3783130132 181.621686986797 67 18060 18365.5852249806 -305.585224980576 68 18869 18703.5773108708 165.422689129176 69 18127 18200.9628220797 -73.9628220796694 70 18871 18612.3533893378 258.646610662221 71 18890 18747.3054779328 142.694522067235 72 21263 21783.5634715530 -520.56347155304 73 19547 19028.8903805260 518.109619474024 74 18450 18582.0878468771 -132.087846877093 75 20254 20385.1178385465 -131.117838546452 76 19240 19132.7870737037 107.212926296310 77 20216 20265.7094088722 -49.7094088722079 78 19420 19548.113819717 -128.113819717008 79 19415 19150.0971746056 264.902825394409 80 20018 20037.3628166549 -19.3628166549206 81 18652 19274.9496496976 -622.949649697624 82 19978 19650.4021559322 327.597844067837 83 19509 19746.2597465845 -237.259746584492 84 21971 22352.5260978327 -381.526097832706 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 20131.5438517066 19588.7640742263 20674.3236291868 86 19069.6244112463 18480.392591081 19658.8562314116 87 20990.2274879783 20335.3577824407 21645.0971935158 88 19883.0625592056 19199.8579313300 20566.2671870813 89 20913.9942135405 20173.3622299413 21654.6261971398 90 20146.9728875161 19383.4761703414 20910.4696046907 91 20009.7882003455 19213.0630178783 20806.5133828126 92 20642.3306615502 19795.9350493769 21488.7262737234 93 19519.2896667351 18669.9101677219 20368.6691657482 94 20733.1598560545 19817.2561589593 21649.0635531497 95 20360.6555695005 19426.6869770693 21294.6241619316 96 23101.5535340851 22199.3663440900 24003.7407240801

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208292936pmnyvoth3vkfsku/1ex981208292894.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208292936pmnyvoth3vkfsku/1ex981208292894.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208292936pmnyvoth3vkfsku/2z78x1208292894.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208292936pmnyvoth3vkfsku/2z78x1208292894.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208292936pmnyvoth3vkfsku/3k34v1208292894.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208292936pmnyvoth3vkfsku/3k34v1208292894.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208292936pmnyvoth3vkfsku/43yse1208292894.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208292936pmnyvoth3vkfsku/43yse1208292894.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$fitted[,'xhat'] bitmap(file='test1.png') op <- par(mfrow=c(2,1)) plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing') plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors') par(op) dev.off() bitmap(file='test2.png') p <- predict(fit, par1, prediction.interval=TRUE) np <- length(p[,1]) plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing') dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF') spectrum(myresid,main='Residals Periodogram') cpgram(myresid,main='Residal Cumulative Periodogram') qqnorm(myresid,main='Residual Normal QQ Plot') qqline(myresid) par(op) dev.off() bitmap(file='hist.png') hist(myresid,main="Residual Histogram") grid() dev.off() load(file='createtable') a <- table.start() a<-table.row.start(a) a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'alpha',header=TRUE) a<-table.element(a,fit$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