Exponential Smoothing - Verkoop vrouwenkleding VS 2000-2008 - Amelie Barratt

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 05 Jun 2009 06:24:42 -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/05/t1244204767cfgt3fwjfecjit9.htm/, Retrieved Fri, 05 Jun 2009 14:26:07 +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/05/t1244204767cfgt3fwjfecjit9.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 «

461683 731993 522673 572709 382812 942567 802385 272643 992660 672651 122826 493878 801948 742156 612673 662804 572750 202510 652313 492663 292397 382618 872790 913865 221989 842162 142783 112683 862759 392482 602262 542540 982375 112533 622742 883970 562056 322091 832619 82723 872811 562534 112447 342593 422622 682787 602944 84298 942258 722391 662901 3007 452988 12759 942577 52626 882755 22968 433067 904437 812315 32428 53073 403145 243133 313018 32720 922852 192947 693108 33335 944749 962536 292541 953227 193417 73378 433219 962953 632986 333186 733212 463421 495024 752596 22640 123421 243440 623653 413304 852981 613232 493203 253344 803665 574904 132570 132785 393406 333452 583642 893230 272991 373159 133072 653091 373307

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 0.00263339025737825 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 731993 461683 270310 3 522673 462394.831720472 60278.1682795281 4 572709 462553.567661552 110155.432338448 5 382812 462843.649903869 -80031.6499038692 6 942567 462632.895336730 479934.10466327 7 802385 463896.749132134 338488.250867866 8 272643 464788.120794207 -192145.120794207 9 992660 464282.127705104 528377.872294896 10 672651 465673.55284622 206977.44715378 11 122826 466218.605239052 -343392.605239052 12 493878 465314.31849796 28563.6815020404 13 801948 465389.537818542 336558.462181458 14 742156 466275.827593889 275880.172406111 15 612673 467002.327752107 145670.672247893 16 662804 467385.93548119 195418.064518810 17 572750 467900.54750841 104849.452491590 18 202510 468176.657035093 -265666.657035093 19 652313 467477.053048746 184835.946951254 20 492663 467963.798230661 24699.2017693392 21 292397 468028.840867965 -175631.840867965 22 382618 467566.333689338 -84948.3336893381 23 872790 467342.63157502 405447.36842498 24 913865 468410.33272491 445454.66727509 25 221989 469583.388705816 -247594.388705816 26 842162 468931.376054817 373230.623945183 27 142783 469914.237943669 -327131.237943669 28 112683 469052.773728784 -356369.773728784 29 862759 468114.313038623 394644.686961377 30 392482 469153.566512393 -76671.5665123927 31 602262 468951.660356121 133310.339643879 32 542540 469302.718505747 73237.281494253 33 982375 469495.580849311 512879.419150689 34 112533 470846.192514912 -358313.192514912 35 622742 469902.614044653 152839.385955347 36 883970 470305.099794572 413664.900205428 37 562056 471394.440912592 90661.559087408 38 322091 471633.188179012 -149542.188179012 39 832619 471239.385237594 361379.614762406 40 82723 472191.038794324 -389468.038794324 41 872811 471165.417455403 401645.582544597 42 562534 472223.107019395 90310.8929806048 43 112447 472460.930845105 -360013.930845105 44 342593 471512.873667097 -128919.873667097 45 422622 471173.3773278 -48551.3773278001 46 682787 471045.522603763 211741.477396237 47 602944 471603.120547421 131340.879452579 48 84298 471948.992339767 -387650.992339767 49 942258 470928.155993276 471329.844006724 50 722391 472169.351412495 250221.648587505 51 662901 472828.282664071 190072.717335929 52 3007 473328.818306096 -470321.818306096 53 452988 472090.277411937 -19102.2774119367 54 12759 472039.973660706 -459280.973660706 55 942577 470830.507619269 471746.492380731 56 52626 472072.800236257 -419446.800236257 57 882755 470968.233119026 411786.766880974 58 22968 472052.628379048 -449084.628379048 59 433067 470870.013293936 -37803.0132939362 60 904437 470770.463207028 433666.536792972 61 812315 471912.47643997 340402.52356003 62 32428 472808.8891291 -440380.8891291 63 53073 471649.194386132 -418576.194386132 64 403145 470546.919913865 -67401.9199138649 65 243133 470369.424354635 -227236.424354635 66 313018 469771.022168618 -156753.022168618 67 32720 469358.230287225 -436638.230287225 68 922852 468208.391425587 454643.608574413 69 192947 469405.645474987 -276458.645474987 70 693108 468677.621971425 224430.378028575 71 33335 469268.634742385 -435933.634742385 72 944749 468120.651355791 476628.348644209 73 962536 469375.799805501 493160.200194499 74 292541 470674.48307202 -178133.483072020 75 953227 470205.388093185 483021.611906815 76 193417 471477.372500084 -278060.372500084 77 73378 470745.131024179 -397367.131024179 78 433219 469698.708292737 -36479.7082927374 79 962953 469602.642984327 493350.357015673 80 632986 470901.827007966 162084.172992034 81 333186 471328.657889999 -138142.657889999 82 733212 470964.874360583 262247.125639417 83 463421 471655.473386267 -8234.47338626737 84 495024 471633.788804277 23390.2111957227 85 752596 471695.384358558 280900.615641442 86 22640 472435.10530308 -449795.10530308 87 123421 471250.619254958 -347829.619254958 88 243440 470334.648124385 -226894.648124385 89 623653 469737.145968563 153915.854031437 90 413304 470142.466479025 -56838.4664790252 91 852981 469992.788615155 382988.211384845 92 613232 471001.346039707 142230.653960293 93 493203 471375.894858146 21827.1051418538 94 253344 471433.374144174 -218089.374144174 95 803665 470859.059711065 332805.940288935 96 574904 471735.467631819 103168.532368181 97 132570 472007.150639825 -339437.150639825 98 132785 471113.280154338 -338328.280154338 99 393406 470222.329757584 -76816.3297575843 100 333452 470020.042383193 -136568.042383193 101 583642 469660.405430912 113981.594569088 102 893230 469960.563451571 423269.436548429 103 272991 471075.197062023 -198084.197062023 104 373159 470553.56406734 -97394.5640673396 105 133072 470297.086171203 -337225.086171203 106 653091 469409.040914736 183681.959085264 107 373307 469892.747196248 -96585.7471962476 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 108 469638.399230579 -117973.028170112 1057249.82663127 109 469638.399230579 -117975.065634063 1057251.86409522 110 469638.399230579 -117977.103090949 1057253.90155211 111 469638.399230579 -117979.140540771 1057255.93900193 112 469638.399230579 -117981.177983528 1057257.97644469 113 469638.399230579 -117983.215419221 1057260.01388038 114 469638.399230579 -117985.252847849 1057262.05130901 115 469638.399230579 -117987.290269414 1057264.08873057 116 469638.399230579 -117989.327683914 1057266.12614507 117 469638.399230579 -117991.365091350 1057268.16355251 118 469638.399230579 -117993.402491722 1057270.20095288 119 469638.399230579 -117995.43988503 1057272.23834619

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244204767cfgt3fwjfecjit9/1i6oz1244204676.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244204767cfgt3fwjfecjit9/1i6oz1244204676.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244204767cfgt3fwjfecjit9/2hmw41244204676.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244204767cfgt3fwjfecjit9/2hmw41244204676.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244204767cfgt3fwjfecjit9/3isq21244204676.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244204767cfgt3fwjfecjit9/3isq21244204676.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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