Michiel van Schaik - Exponential Smoothing - Gemiddelde consumptieprijs hotelkamer

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 28 May 2008 09:46:46 -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/May/28/t1211989669tuub98ag5xx4r12.htm/, Retrieved Wed, 28 May 2008 17:47:52 +0200

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

65,05 65,84 66,6 67,55 68,07 69,06 69,06 69,11 69,29 69,38 69,28 69,75 69,9 70,21 70,48 71,55 72,18 72,64 72,77 72,74 73,13 73,44 73,34 73,34 73,81 74,26 74,72 75,11 75,26 75,89 75,91 76,43 76,56 76,76 76,76 76,56 76,82 77,09 77,51 77,76 77,86 77,89 77,94 77,99 78,17 78,91 78,87 78,88 79,08 79,41 79,51 79,73 80,38 80,56 80,46 80,45 80,58 80,68 80,52 81,49 81,66 81,95 82,3 82,4 83,14 83,17 83,11 83,21 83,33 83,88 83,8 83,73

Text written by user:

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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.917656813396868 beta 0.0281982938785126 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 69.9 68.0280291666667 1.87197083333331 14 70.21 70.1097524439018 0.100247556098211 15 70.48 70.5228191591618 -0.0428191591618372 16 71.55 71.5855750578989 -0.0355750578988676 17 72.18 72.2048913359693 -0.0248913359692864 18 72.64 72.6829508405107 -0.0429508405107413 19 72.77 72.819576506402 -0.0495765064019906 20 72.74 72.7696725588243 -0.0296725588243021 21 73.13 73.1435157866442 -0.0135157866442341 22 73.44 73.4722523138908 -0.0322523138907655 23 73.34 73.4212939002112 -0.0812939002111506 24 73.34 73.436145217428 -0.0961452174280453 25 73.81 73.8711076112687 -0.0611076112687385 26 74.26 74.0224412100544 0.237558789945581 27 74.72 74.5426873273149 0.177312672685119 28 75.11 75.8066967954683 -0.696696795468341 29 75.26 75.8017541082026 -0.541754108202568 30 75.89 75.7721935356235 0.117806464376542 31 75.91 76.0281231170997 -0.118123117099742 32 76.43 75.8875115810087 0.542488418991283 33 76.56 76.7730937913862 -0.213093791386186 34 76.76 76.8973401886155 -0.137340188615454 35 76.76 76.7233864500827 0.0366135499172628 36 76.56 76.8257419725764 -0.265741972576421 37 76.82 77.0840978456703 -0.264097845670292 38 77.09 77.0446365573425 0.0453634426575462 39 77.51 77.3494664733912 0.160533526608802 40 77.76 78.491589561936 -0.731589561936005 41 77.86 78.431962709569 -0.571962709569021 42 77.89 78.3927865840641 -0.502786584064097 43 77.94 78.0075341024115 -0.0675341024115284 44 77.99 77.9167884083721 0.0732115916278957 45 78.17 78.2464209483747 -0.0764209483747322 46 78.91 78.4427629540263 0.467237045973690 47 78.87 78.7940108450253 0.0759891549747493 48 78.88 78.8647049456004 0.0152950543995871 49 79.08 79.345466161293 -0.265466161293062 50 79.41 79.2945702677283 0.115429732271693 51 79.51 79.6393325341397 -0.129332534139706 52 79.73 80.4006491921818 -0.67064919218177 53 80.38 80.3703171768239 0.0096828231761208 54 80.56 80.8458673950013 -0.285867395001333 55 80.46 80.6764046146996 -0.216404614699641 56 80.45 80.4376763564789 0.0123236435211425 57 80.58 80.6745779044181 -0.0945779044181023 58 80.68 80.8740192199891 -0.194019219989102 59 80.52 80.5441279248172 -0.0241279248171793 60 81.49 80.4732442238735 1.01675577612649 61 81.66 81.8310911402325 -0.171091140232477 62 81.95 81.8818126102876 0.0681873897124063 63 82.3 82.145494955383 0.154505044617025 64 82.4 83.1124748864526 -0.712474886452625 65 83.14 83.0884711708567 0.051528829143308 66 83.17 83.567857163918 -0.397857163918033 67 83.11 83.288220157795 -0.178220157794911 68 83.21 83.0912285768618 0.118771423138156 69 83.33 83.407626758217 -0.077626758217022 70 83.88 83.605490444982 0.274509555018000 71 83.8 83.7227163318945 0.0772836681054514 72 83.73 83.836406682311 -0.106406682310975 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 84.0425047949956 83.2831187358906 84.8018908541005 74 84.2510993667296 83.2070457558424 85.2951529776167 75 84.4387195131186 83.1612322464884 85.7162067797488 76 85.167931672716 83.6836080000961 86.6522553453358 77 85.854486871398 84.1798079932701 87.5291657495258 78 86.2420908101048 84.3882451552578 88.0959364649517 79 86.3484384474797 84.323451503598 88.3734253913613 80 86.3468614254291 84.1567000537753 88.537022797083 81 86.5424371609503 84.1916457832809 88.8932285386198 82 86.8468813070568 84.3389769664646 89.354785647649 83 86.6952078249575 84.0329397447405 89.3574759051745 84 86.7200992247252 83.9056270173981 89.5345714320524

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211989669tuub98ag5xx4r12/1yp7s1211989595.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211989669tuub98ag5xx4r12/1yp7s1211989595.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211989669tuub98ag5xx4r12/2rfny1211989595.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211989669tuub98ag5xx4r12/2rfny1211989595.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211989669tuub98ag5xx4r12/3wsvz1211989595.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211989669tuub98ag5xx4r12/3wsvz1211989595.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