verbetering workshop

*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: Sun, 06 Dec 2009 06:43:35 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/06/t1260107036xwmn8ubfj3os24w.htm/, Retrieved Sun, 06 Dec 2009 14:44:00 +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/2009/Dec/06/t1260107036xwmn8ubfj3os24w.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 «

3922 3759 4138 4634 3995 4308 4143 4429 5219 4929 5755 5592 4163 4962 5208 4755 4491 5732 5731 5040 6102 4904 5369 5578 4619 4731 5011 5299 4146 4625 4736 4219 5116 4205 4121 5103 4300 4578 3809 5526 4247 3830 4394 4826 4409 4569 4106 4794 3914 3793 4405 4022 4100 4788 3163 3585 3903 4178 3863 4187

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 0.153124352600844 beta 0.64835715407674 gamma 0.543887574114765 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 4163 3809.25532525683 353.744674743175 14 4962 4623.30104637635 338.698953623653 15 5208 4987.44965139763 220.550348602374 16 4755 4699.41752520211 55.5824747978932 17 4491 4605.22202565029 -114.222025650291 18 5732 6044.20055930014 -312.200559300143 19 5731 5007.38980934768 723.610190652324 20 5040 5595.93871963285 -555.938719632854 21 6102 6525.74862527719 -423.748625277191 22 4904 6150.55087063321 -1246.55087063321 23 5369 6907.54106634089 -1538.54106634089 24 5578 6217.85663114186 -639.856631141858 25 4619 4460.93557534072 158.064424659277 26 4731 5028.49176635032 -297.491766350323 27 5011 4889.65987490575 121.340125094252 28 5299 4207.645304464 1091.35469553600 29 4146 4010.59027844513 135.409721554869 30 4625 5031.09249709813 -406.092497098133 31 4736 4331.47143083952 404.528569160483 32 4219 4099.06455095694 119.935449043064 33 5116 4789.86665914226 326.133340857742 34 4205 4203.14513747064 1.85486252936244 35 4121 4814.87712682466 -693.877126824658 36 5103 4708.97500899456 394.024991005437 37 4300 3815.68257017946 484.317429820537 38 4578 4333.83748008552 244.162519914482 39 3809 4694.03209120716 -885.03209120716 40 5526 4443.30592014669 1082.69407985331 41 4247 3962.3920460763 284.607953923701 42 3830 4894.83659840055 -1064.83659840055 43 4394 4554.95919865592 -160.959198655923 44 4826 4136.4518895516 689.5481104484 45 4409 5122.0030255261 -713.003025526104 46 4569 4220.23158550852 348.768414491485 47 4106 4595.92563024681 -489.925630246812 48 4794 5093.42662327743 -299.426623277429 49 3914 4102.13492992989 -188.134929929887 50 3793 4314.85636478824 -521.856364788238 51 4405 3883.69342205548 521.306577944524 52 4022 4671.04335751626 -649.04335751626 53 4100 3500.46975717676 599.530242823237 54 4788 3678.1784112647 1109.82158873530 55 3163 4129.96135401951 -966.961354019506 56 3585 3955.69970968602 -370.699709686025 57 3903 3970.3231208981 -67.323120898102 58 4178 3633.40940200503 544.590597994973 59 3863 3616.41364518351 246.586354816492 60 4187 4237.98411175221 -50.9841117522137 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 3495.09324525687 2770.91623440958 4219.27025610418 62 3622.76617238188 2835.3145729812 4410.21777178255 63 3843.02080535391 2929.60353023945 4756.43808046838 64 4052.54437980923 2945.58080244219 5159.50795717628 65 3685.71996648461 2448.93562964016 4922.50430332907 66 4024.5438726263 2463.53257254199 5585.55517271061 67 3334.36266726677 1760.67973675347 4908.04559778008 68 3595.91148700847 1653.36943638253 5538.45353763440 69 3868.91119061594 1481.46237789757 6256.36000333432 70 3897.59781883445 1154.34468632382 6640.85095134508 71 3683.24978231974 742.314523967259 6624.18504067222 72 4114.84521166860 519.630799709684 7710.05962362753

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/06/t1260107036xwmn8ubfj3os24w/1u1ib1260107013.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260107036xwmn8ubfj3os24w/1u1ib1260107013.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260107036xwmn8ubfj3os24w/2ldua1260107013.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260107036xwmn8ubfj3os24w/2ldua1260107013.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260107036xwmn8ubfj3os24w/33sfa1260107013.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/06/t1260107036xwmn8ubfj3os24w/33sfa1260107013.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$fitted[,'xhat'] bitmap(file='test1.png') op <- par(mfrow=c(2,1)) plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing') plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors') par(op) dev.off() bitmap(file='test2.png') p <- predict(fit, par1, prediction.interval=TRUE) np <- length(p[,1]) plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing') dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF') spectrum(myresid,main='Residals Periodogram') cpgram(myresid,main='Residal Cumulative Periodogram') qqnorm(myresid,main='Residual Normal QQ Plot') qqline(myresid) par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'alpha',header=TRUE) a<-table.element(a,fit$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