*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: Tue, 28 Dec 2010 15:38:00 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/28/t1293550551x2otzlg4sq439wz.htm/, Retrieved Tue, 28 Dec 2010 16:35:52 +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/Dec/28/t1293550551x2otzlg4sq439wz.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

11100 8962 9173 8738 8459 8078 8411 8291 7810 8616 8312 9692 9911 8915 9452 9112 8472 8230 8384 8625 8221 8649 8625 10443 10357 8586 8892 8329 8101 7922 8120 7838 7735 8406 8209 9451 10041 9411 10405 8467 8464 8102 7627 7513 7510 8291 8064 9383 9706 8579 9474 8318 8213 8059 9111 7708 7680 8014 8007 8718 9486 9113 9025 8476 7952 7759 7835 7600 7651 8319 8812 8630

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.135019238273121 beta 0.0440917299700262 gamma 0.0333766681540438 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 9911 9855.39449786325 55.6055021367483 14 8915 8868.50505030804 46.4949496919617 15 9452 9395.41229811428 56.5877018857173 16 9112 9059.56080800653 52.4391919934733 17 8472 8427.54470525155 44.4552947484517 18 8230 8162.79860877957 67.2013912204302 19 8384 8503.52373838579 -119.523738385786 20 8625 8434.15916403987 190.840835960125 21 8221 7985.6692311748 235.330768825194 22 8649 8814.04560710458 -165.045607104577 23 8625 8488.4642483113 136.5357516887 24 10443 9897.66500383773 545.334996162268 25 10357 10207.5800348888 149.419965111239 26 8586 9240.47675450445 -654.476754504447 27 8892 9676.24010234525 -784.240102345255 28 8329 9224.94465761887 -895.944657618873 29 8101 8457.20578773181 -356.205787731811 30 7922 8129.19198695794 -207.19198695794 31 8120 8416.01698300128 -296.01698300128 32 7838 8319.27103852083 -481.271038520834 33 7735 7764.80460021012 -29.8046002101173 34 8406 8527.73234758384 -121.732347583844 35 8209 8198.87235621862 10.1276437813794 36 9451 9584.22169187039 -133.221691870385 37 10041 9768.46277445654 272.537225543463 38 9411 8772.88139397185 638.118606028147 39 10405 9365.22615274824 1039.77384725176 40 8467 9153.64399041275 -686.643990412755 41 8464 8427.654347122 36.3456528779898 42 8102 8157.1888010478 -55.1888010477978 43 7627 8463.12187198599 -836.12187198599 44 7513 8286.0368038243 -773.036803824307 45 7510 7701.40708453483 -191.407084534827 46 8291 8435.09615523769 -144.096155237687 47 8064 8102.12504170216 -38.1250417021565 48 9383 9471.63515753307 -88.6351575330718 49 9706 9668.69038683757 37.3096131624316 50 8579 8645.58256306614 -66.582563066142 51 9474 9143.85912583628 330.140874163722 52 8318 8771.8804255021 -453.880425502099 53 8213 8084.83642706802 128.163572931981 54 8059 7811.31731168935 247.682688310645 55 9111 8124.59311036594 986.406889634055 56 7708 8195.25062554122 -487.250625541223 57 7680 7667.54550318863 12.4544968113705 58 8014 8432.8855319782 -418.885531978196 59 8007 8066.99593374934 -59.9959337493392 60 8718 9433.08858293744 -715.088582937438 61 9486 9546.4609336245 -60.4609336244976 62 9113 8503.83510699378 609.164893006217 63 9025 9105.50922047261 -80.5092204726134 64 8476 8653.71049770796 -177.710497707958 65 7952 8020.66304206782 -68.6630420678202 66 7759 7722.75190740084 36.2480925991576 67 7835 8026.28116891763 -191.281168917627 68 7600 7885.84644121834 -285.846441218339 69 7651 7391.42339227517 259.576607724832 70 8319 8170.81003207372 148.189967926277 71 8812 7888.35690790335 923.643092096655 72 8630 9370.71210645267 -740.712106452673 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 9501.73645841764 8679.82223219945 10323.6506846358 74 8489.1786288639 7659.1375325786 9319.2197251492 75 8987.63864227532 8148.8590064294 9826.41827812125 76 8543.32917791797 7695.19001067107 9391.46834516488 77 7937.90741206751 7079.78014071188 8796.03468342315 78 7653.18781348538 6784.4379865592 8521.93764041155 79 7945.93018360513 7065.91911854136 8825.9412486689 80 7830.40682696975 6938.49318978734 8722.32046415216 81 7393.84156561816 6489.38287100986 8298.30026022646 82 8136.93585747923 7219.28987965724 9054.58183530122 83 7857.95073533312 6926.4768220809 8789.42464858533 84 9163.13648903983 8217.19677350901 10109.0762045706

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293550551x2otzlg4sq439wz/13t0d1293550676.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293550551x2otzlg4sq439wz/13t0d1293550676.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293550551x2otzlg4sq439wz/2w3zy1293550676.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293550551x2otzlg4sq439wz/2w3zy1293550676.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293550551x2otzlg4sq439wz/3w3zy1293550676.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293550551x2otzlg4sq439wz/3w3zy1293550676.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=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