module Exponential Smoothing -Time Series Analysis (new) - goudkoers te brussel

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 29 May 2008 12:59:02 -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/29/t1212087600w6kp7yi0pfypf7t.htm/, Retrieved Thu, 29 May 2008 19:00:04 +0000

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

10236 10893 10756 10940 10997 10827 10166 10186 10457 10368 10244 10511 10812 10738 10171 9721 9897 9828 9924 10371 10846 10413 10709 10662 10570 10297 10635 10872 10296 10383 10431 10574 10653 10805 10872 10625 10407 10463 10556 10646 10702 11353 11346 11451 11964 12574 13031 13812 14544 14931 14886 16005 17064 15168 16050 15839 15137 14954 15648 15305 15579 16348 15928 16171 15937 15713 15594 15683 16438 17032 17696 17745

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 0.7740580389191 beta 0.0233317689039484 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 10812 10920.0551455554 -108.055145555360 14 10738 10768.0070828160 -30.007082816026 15 10171 10156.2936485080 14.7063514919719 16 9721 9703.45150271692 17.54849728308 17 9897 9875.64504069516 21.3549593048374 18 9828 9802.23944815749 25.7605518425116 19 9924 9925.69474894115 -1.69474894114501 20 10371 10404.1371366797 -33.137136679743 21 10846 10856.4696915348 -10.4696915348159 22 10413 10350.9907448230 62.0092551770394 23 10709 10632.9209962772 76.0790037228471 24 10662 10610.3352401593 51.6647598406635 25 10570 11021.3949629194 -451.394962919412 26 10297 10617.5002892705 -320.500289270507 27 10635 9801.84290402755 833.15709597245 28 10872 9975.9195173201 896.080482679901 29 10296 10865.8636989703 -569.863698970299 30 10383 10341.7026001367 41.2973998633333 31 10431 10487.3761114264 -56.3761114263925 32 10574 10951.6135144414 -377.613514441362 33 10653 11160.4413436224 -507.441343622368 34 10805 10285.9948531293 519.005146870748 35 10872 10935.1365574079 -63.1365574079264 36 10625 10799.4126465267 -174.412646526654 37 10407 10916.1111901584 -509.111190158443 38 10463 10491.9685123756 -28.9685123755607 39 10556 10147.4295947097 408.570405290346 40 10646 9995.5940031531 650.405996846908 41 10702 10353.7617773491 348.238222650894 42 11353 10685.5011588257 667.498841174334 43 11346 11317.1199596909 28.8800403091282 44 11451 11828.4726973284 -377.472697328396 45 11964 12066.1079164284 -102.107916428353 46 12574 11728.1716539189 845.82834608114 47 13031 12547.4314616023 483.56853839774 48 13812 12829.1155601624 982.884439837619 49 14544 13872.7694725202 671.23052747978 50 14931 14588.8458552917 342.154144708347 51 14886 14625.9389543208 260.061045679249 52 16005 14320.4167296740 1684.58327032598 53 17064 15402.5665528891 1661.43344711093 54 15168 17001.7396022744 -1833.73960227444 55 16050 15610.0889008407 439.911099159297 56 15839 16582.5158785322 -743.515878532206 57 15137 16910.8253601221 -1773.82536012207 58 14954 15515.8897181854 -561.889718185401 59 15648 15199.6018931586 448.398106841354 60 15305 15576.9985206996 -271.998520699552 61 15579 15596.8681645326 -17.8681645326051 62 16348 15701.9913755013 646.008624498674 63 15928 15927.4080528217 0.591947178261762 64 16171 15685.9521902165 485.047809783482 65 15937 15778.5474661450 158.452533854954 66 15713 15380.3011200495 332.698879950489 67 15594 16176.9310734336 -582.93107343364 68 15683 16046.9900869157 -363.990086915701 69 16438 16371.854286068 66.14571393199 70 17032 16691.2449586921 340.755041307923 71 17696 17358.3267908446 337.673209155368 72 17745 17479.5206287904 265.479371209582 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 18035.8073164737 16851.6072288515 19220.0074040958 74 18360.5850072049 16842.8921805296 19878.2778338802 75 17896.2226439474 16131.7336592897 19660.7116286052 76 17752.2191062614 15752.7761785235 19751.6620339993 77 17360.6160218346 15170.2007170725 19551.0313265967 78 16832.6816875727 14484.0917808659 19181.2715942795 79 17177.5725440508 14583.4594009380 19771.6856871637 80 17585.9231183630 14744.3603468841 20427.4858898418 81 18382.4658160619 15240.5850586050 21524.3465735188 82 18756.8449002525 15380.719191855 22132.9706086501 83 19200.1464416233 15579.7587474632 22820.5341357834 84 19025.7396416940 15462.9984260664 22588.4808573215

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212087600w6kp7yi0pfypf7t/18ibg1212087536.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212087600w6kp7yi0pfypf7t/18ibg1212087536.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212087600w6kp7yi0pfypf7t/277c51212087536.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212087600w6kp7yi0pfypf7t/277c51212087536.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212087600w6kp7yi0pfypf7t/3tjsl1212087536.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/29/t1212087600w6kp7yi0pfypf7t/3tjsl1212087536.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=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