Exponential Smoothing - verkoopcijfers X - Lehaen Joni

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 26 May 2010 20:15:37 +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/May/26/t12749049710yax9lqw3pobgfc.htm/, Retrieved Wed, 26 May 2010 22:16:11 +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/May/26/t12749049710yax9lqw3pobgfc.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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

154 96 73 49 36 59 95 169 210 278 298 245 200 118 90 79 78 91 167 169 289 347 375 203 223 104 107 85 75 99 135 211 335 460 488 326 346 261 224 141 148 145 223 272 445 560 612 467 518 404 300 210 196 186 247 343 464 680 711 610 613 392 273 322 189 257 324 404 677 858 895 664 628 308 324 248 272

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 0.665421046338253 beta 0.000770639574476133 gamma 0.646362889708687 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 200 174.888900211549 25.1110997884505 14 118 113.442480703907 4.55751929609274 15 90 88.9411140246669 1.05888597533313 16 79 77.4939342549065 1.50606574509352 17 78 76.4037008872773 1.59629911272273 18 91 91.3597275152543 -0.359727515254335 19 167 120.885421468935 46.1145785310648 20 169 268.487229560383 -99.4872295603834 21 289 253.415738639192 35.5842613608075 22 347 368.383920418892 -21.383920418892 23 375 378.934325820553 -3.93432582055277 24 203 308.713097295575 -105.713097295575 25 223 199.106304451831 23.8936955481693 26 104 124.603942701796 -20.6039427017963 27 107 84.2636953404822 22.7363046595178 28 85 85.8858200729584 -0.885820072958381 29 75 82.9186970356463 -7.91869703564635 30 99 91.0798157909288 7.92018420907122 31 135 136.197133275263 -1.19713327526318 32 211 201.603632069602 9.39636793039784 33 335 298.735180252139 36.2648197478606 34 460 411.347516366038 48.6524836339619 35 488 478.231771575 9.76822842500002 36 326 358.967935841707 -32.9679358417073 37 346 316.461163698796 29.5388363012036 38 261 181.382180831354 79.6178191686458 39 224 192.520962063871 31.4790379361294 40 141 173.826130322579 -32.8261303225794 41 148 143.726403380052 4.27359661994774 42 145 177.386175713433 -32.3861757134329 43 223 214.689021941814 8.3109780581864 44 272 329.627395624004 -57.627395624004 45 445 422.774894319884 22.2251056801161 46 560 555.192114150232 4.8078858497679 47 612 588.966663517296 23.0333364827039 48 467 435.039741417224 31.9602585827760 49 518 444.375118213835 73.6248817861647 50 404 279.402756500690 124.597243499310 51 300 285.267840835805 14.7321591641948 52 210 221.491527417580 -11.4915274175803 53 196 212.812424030486 -16.8124240304861 54 186 231.005870534258 -45.0058705342578 55 247 291.589575589157 -44.5895755891567 56 343 371.639438220566 -28.6394382205659 57 464 539.197984617746 -75.1979846177461 58 680 614.377516312488 65.622483687512 59 711 697.349078392747 13.6509216072531 60 610 511.305691974145 98.6943080258552 61 613 570.266149531425 42.7338504685746 62 392 352.415447323278 39.5845526767223 63 273 280.599741530896 -7.59974153089615 64 322 202.334592276207 119.665407723793 65 189 278.325554955421 -89.3255549554209 66 257 242.856303616285 14.1436963837146 67 324 369.618094190125 -45.6180941901252 68 404 489.926685592868 -85.9266855928677 69 677 650.060339504961 26.939660495039 70 858 884.038735958918 -26.0387359589176 71 895 901.01453409839 -6.01453409839064 72 664 669.215155406219 -5.21515540621851 73 628 643.787384815201 -15.7873848152011 74 308 375.268172582017 -67.2681725820173 75 324 238.262947583285 85.7370524167154 76 248 238.047612286582 9.95238771341752 77 272 201.921349726258 70.0786502737423 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 78 305.759388145103 223.019235979670 388.499540310536 79 429.331810249379 309.072930190873 549.590690307884 80 610.240403522688 437.340052910974 783.140754134402 81 963.978867408961 692.927529472112 1235.03020534581 82 1253.94371274631 900.279835560756 1607.60758993187 83 1307.37129379048 935.358591187613 1679.38399639335 84 973.021471580121 688.080808287364 1257.96213487288 85 935.416102800596 655.225795585457 1215.60641001573 86 531.583281547937 355.432887870354 707.73367522552 87 424.70352552675 267.8237132179 581.5833378356 88 324.425494357226 185.228592563105 463.622396151347 89 281.182226090519 170.228887566324 392.135564614713

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/26/t12749049710yax9lqw3pobgfc/1kbc51274904932.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/26/t12749049710yax9lqw3pobgfc/1kbc51274904932.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/26/t12749049710yax9lqw3pobgfc/2v2t81274904932.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/26/t12749049710yax9lqw3pobgfc/2v2t81274904932.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/26/t12749049710yax9lqw3pobgfc/3v2t81274904932.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/26/t12749049710yax9lqw3pobgfc/3v2t81274904932.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=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