Opgave 10 - Exponential smoothing: Goudkoers - Talia Vereycken

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 07 Jun 2009 10:02:40 -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/07/t124439065335rg8zjhzxer62h.htm/, Retrieved Sun, 07 Jun 2009 18:04:13 +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/07/t124439065335rg8zjhzxer62h.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 «

10.812 10.738 10.171 9.721 9.897 9.828 9.924 10.371 10.846 10.413 10.709 10.662 10.570 10.297 10.635 10.872 10.296 10.383 10.431 10.574 10.653 10.805 10.872 10.625 10.407 10.463 10.556 10.646 10.702 11.353 11.346 11.451 11.964 12.574 13.031 13.812 14.544 14.931 14.886 16.005 17.064 15.168 16.050 15.839 15.137 14.954 15.648 15.305 15.579 16.348 15.928 16.171 15.937 15.713 15.594 15.683 16.438 17.032 17.696 17.745 19.394 20.148 20.108 18.584 18.441 18.391 19.178 18.079 18.483 19.644 19.195 19.650 20.830

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 10.171 10.738 -0.567 4 9.721 10.171 -0.449999999999999 5 9.897 9.721 0.176 6 9.828 9.897 -0.0690000000000008 7 9.924 9.828 0.096 8 10.371 9.924 0.447000000000001 9 10.846 10.371 0.475 10 10.413 10.846 -0.433 11 10.709 10.413 0.295999999999999 12 10.662 10.709 -0.0469999999999988 13 10.57 10.662 -0.0920000000000005 14 10.297 10.57 -0.273000000000000 15 10.635 10.297 0.337999999999999 16 10.872 10.635 0.237 17 10.296 10.872 -0.576 18 10.383 10.296 0.0869999999999997 19 10.431 10.383 0.048 20 10.574 10.431 0.143000000000001 21 10.653 10.574 0.0790000000000006 22 10.805 10.653 0.151999999999999 23 10.872 10.805 0.0670000000000002 24 10.625 10.872 -0.247 25 10.407 10.625 -0.218 26 10.463 10.407 0.0559999999999992 27 10.556 10.463 0.093 28 10.646 10.556 0.0900000000000016 29 10.702 10.646 0.0559999999999992 30 11.353 10.702 0.651 31 11.346 11.353 -0.00699999999999967 32 11.451 11.346 0.105000000000000 33 11.964 11.451 0.513 34 12.574 11.964 0.61 35 13.031 12.574 0.457000000000001 36 13.812 13.031 0.780999999999999 37 14.544 13.812 0.732000000000001 38 14.931 14.544 0.386999999999999 39 14.886 14.931 -0.0449999999999999 40 16.005 14.886 1.119 41 17.064 16.005 1.059 42 15.168 17.064 -1.896 43 16.05 15.168 0.882000000000001 44 15.839 16.05 -0.211000000000000 45 15.137 15.839 -0.702 46 14.954 15.137 -0.183 47 15.648 14.954 0.693999999999999 48 15.305 15.648 -0.343 49 15.579 15.305 0.274000000000001 50 16.348 15.579 0.768999999999998 51 15.928 16.348 -0.419999999999998 52 16.171 15.928 0.242999999999999 53 15.937 16.171 -0.234 54 15.713 15.937 -0.224 55 15.594 15.713 -0.119000000000000 56 15.683 15.594 0.0890000000000004 57 16.438 15.683 0.754999999999999 58 17.032 16.438 0.594000000000001 59 17.696 17.032 0.664000000000001 60 17.745 17.696 0.0489999999999995 61 19.394 17.745 1.64900000000000 62 20.148 19.394 0.754000000000001 63 20.108 20.148 -0.0399999999999991 64 18.584 20.108 -1.524 65 18.441 18.584 -0.143000000000001 66 18.391 18.441 -0.0500000000000007 67 19.178 18.391 0.787000000000003 68 18.079 19.178 -1.099 69 18.483 18.079 0.404 70 19.644 18.483 1.16100000000000 71 19.195 19.644 -0.448999999999998 72 19.65 19.195 0.454999999999998 73 20.83 19.65 1.18 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 20.83 19.6756783694299 21.9843216305701 75 20.83 19.1975426947072 22.4624573052928 76 20.83 18.8306562875769 22.8293437124231 77 20.83 18.5213567388599 23.1386432611401 78 20.83 18.2488583661469 23.4111416338531 79 20.83 18.0025010060459 23.6574989939541 80 20.83 17.7759520325290 23.8840479674710 81 20.83 17.5650853894144 24.0949146105856 82 20.83 17.3670351082898 24.2929648917102 83 20.83 17.1797144949991 24.4802855050008 84 20.83 17.0015482640079 24.6584517359921 85 20.83 16.8313125751538 24.8286874248462

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t124439065335rg8zjhzxer62h/17z541244390555.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t124439065335rg8zjhzxer62h/17z541244390555.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t124439065335rg8zjhzxer62h/2cl2d1244390555.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t124439065335rg8zjhzxer62h/2cl2d1244390555.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t124439065335rg8zjhzxer62h/35nzv1244390555.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t124439065335rg8zjhzxer62h/35nzv1244390555.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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