Tijdreeks B stap 27

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 04 Aug 2010 16:00:42 +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/Aug/04/t1280937623dr3wcsdzf5ci0zw.htm/, Retrieved Wed, 04 Aug 2010 18:00:27 +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/2010/Aug/04/t1280937623dr3wcsdzf5ci0zw.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:

Bogaerts Yannik

Dataseries X:

» Textbox « » Textfile « » CSV «

83 82 81 79 77 76 77 79 80 80 81 83 83 76 77 72 64 70 69 78 84 91 96 101 99 98 98 97 92 106 100 107 111 115 117 120 117 108 111 118 113 129 122 135 146 151 147 151 156 144 151 159 148 170 163 179 184 192 197 199 205 194 200 211 211 230 229 236 239 250 254 254 264 258 264 277 274 284 279 290 287 297 302 294

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.469691048112616 beta 0.300455994256597 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 83 86.5926816239316 -3.59268162393161 14 76 77.5833956371879 -1.58339563718788 15 77 76.794402138584 0.205597861416024 16 72 70.3746971481254 1.62530285187455 17 64 61.3928467108587 2.60715328914131 18 70 66.9484213269438 3.05157867305624 19 69 75.018381899208 -6.01838189920794 20 78 73.7289401577997 4.27105984220033 21 84 77.0417620915322 6.95823790846778 22 91 81.6403510817023 9.3596489182977 23 96 90.0627089352497 5.93729106475028 24 101 98.6738286415736 2.32617135842639 25 99 101.803545958472 -2.80354595847177 26 98 97.890680625728 0.109319374271934 27 98 102.744566298714 -4.74456629871405 28 97 97.9532280513072 -0.953228051307178 29 92 91.1175949528343 0.882405047165733 30 106 98.692000620699 7.30799937930114 31 100 107.145202148465 -7.14520214846502 32 107 113.817987072556 -6.81798707255635 33 111 114.817415673438 -3.81741567343757 34 115 115.577588247146 -0.577588247145613 35 117 116.064571883904 0.935428116096247 36 120 118.252446005486 1.74755399451405 37 117 116.149495340168 0.850504659832467 38 108 113.772726932398 -5.77272693239794 39 111 110.734829441275 0.265170558725416 40 118 108.459102250088 9.54089774991193 41 113 107.158867329643 5.8411326703568 42 129 120.802624769529 8.1973752304714 43 122 122.467137667288 -0.467137667287886 44 135 133.850734844355 1.14926515564494 45 146 142.708550944563 3.29144905543666 46 151 152.054027295175 -1.05402729517451 47 147 156.580586273897 -9.58058627389698 48 151 156.236812945517 -5.23681294551687 49 156 151.368962831473 4.63103716852675 50 144 148.780340552410 -4.7803405524096 51 151 151.075379051861 -0.0753790518606365 52 159 155.175510954643 3.82448904535673 53 148 150.038414410777 -2.03841441077736 54 170 160.928885128604 9.07111487139568 55 163 158.230349884092 4.76965011590769 56 179 173.491268513331 5.50873148666875 57 184 186.708376833063 -2.70837683306266 58 192 191.260309901062 0.739690098938382 59 197 192.689749636653 4.31025036334708 60 199 203.716313693272 -4.71631369327176 61 205 206.941794185064 -1.94179418506357 62 194 197.963313758854 -3.96331375885367 63 200 204.940765425902 -4.9407654259021 64 211 209.940773082206 1.05922691779378 65 211 201.122438786339 9.87756121366084 66 230 225.909550961025 4.09044903897453 67 229 220.295988854545 8.70401114545461 68 236 240.057458559765 -4.05745855976522 69 239 245.334487401686 -6.33448740168612 70 250 250.410767879563 -0.41076787956257 71 254 253.42995185048 0.570048149520062 72 254 257.621689750201 -3.62168975020074 73 264 262.69591386934 1.30408613066021 74 258 254.491283941411 3.5087160585891 75 264 265.835713240551 -1.83571324055060 76 277 277.289958841612 -0.289958841612020 77 274 274.137939662596 -0.137939662595841 78 284 291.362074898671 -7.36207489867076 79 279 281.409952410558 -2.40995241055839 80 290 286.209326499249 3.79067350075098 81 287 292.098119231321 -5.09811923132111 82 297 299.204085676986 -2.20408567698553 83 302 299.955597586206 2.04440241379399 84 294 300.879471159033 -6.87947115903336 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 304.838545394674 295.685693040981 313.991397748368 86 294.809316128952 284.084094669302 305.534537588601 87 298.795162221134 286.051654261088 311.53867018118 88 309.314039898841 294.174312088511 324.453767709172 89 303.802434953038 285.947176423893 321.657693482183 90 314.703407908807 293.858013100900 335.548802716715 91 309.317360248233 285.240216865131 333.394503631335 92 317.359030181487 289.833004384508 344.885055978467 93 315.040740993757 283.867241584663 346.214240402851 94 325.082604339094 290.077454234522 360.087754443665 95 328.440034716885 289.430557738399 367.449511695371 96 322.700419509781 279.523340649142 365.87749837042

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/04/t1280937623dr3wcsdzf5ci0zw/1dlk21280937640.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/04/t1280937623dr3wcsdzf5ci0zw/1dlk21280937640.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/04/t1280937623dr3wcsdzf5ci0zw/2dlk21280937640.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/04/t1280937623dr3wcsdzf5ci0zw/2dlk21280937640.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/04/t1280937623dr3wcsdzf5ci0zw/3dlk21280937640.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/04/t1280937623dr3wcsdzf5ci0zw/3dlk21280937640.ps (open in new window)

Parameters (Session):

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