Exponential Smoothing Eigen Reeks Dimitri Troquay

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 11:41:08 -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/t12119965418pl9dsca2pyrtwk.htm/, Retrieved Wed, 28 May 2008 19:42:21 +0200

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

8,16 8,43 8,43 8,43 8,43 8,43 8,43 8,43 8,43 8,43 8,43 8,43 8,43 8,43 8,68 8,68 8,68 8,68 8,68 8,68 8,68 8,68 8,68 8,68 8,68 8,68 8,92 8,92 8,92 8,92 8,92 8,92 8,92 8,92 8,92 8,92 8,92 8,92 9,3 9,3 9,3 9,3 9,3 9,3 9,3 9,3 9,3 9,3 9,3 9,3 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,6 9,9 9,9 9,9 9,9 9,9 9,9 9,9 9,9 9,9 9,9 9,9 9,9 10,2 10,2 10,2 10,2 10,2 10,2 10,2 10,2 10,2 10,2

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 4 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.286867200485029 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 8.43 8.7 -0.270000000000000 4 8.43 8.62254585586904 -0.192545855869042 5 8.43 8.5673107652309 -0.137310765230897 6 8.43 8.52792081041265 -0.0979208104126528 7 8.43 8.49983054166035 -0.06983054166035 8 8.43 8.47979844966589 -0.0497984496658912 9 8.43 8.46551290782174 -0.035512907821742 10 8.43 8.45532541937384 -0.0253254193738357 11 8.43 8.44806038721696 -0.0180603872169556 12 8.43 8.44287945449635 -0.0128794544963515 13 8.43 8.4391847614412 -0.00918476144120817 14 8.43 8.43654995463945 -0.0065499546394463 15 8.68 8.43467098748872 0.245329012511275 16 8.68 8.75504783450559 -0.0750478345055914 17 8.68 8.7335190723185 -0.0535190723185082 18 8.68 8.71816620586994 -0.0381662058699419 19 8.68 8.7072175732389 -0.0272175732388966 20 8.68 8.69940974419986 -0.0194097441998586 21 8.68 8.69384172521911 -0.0138417252191143 22 8.68 8.68987098825562 -0.00987098825562427 23 8.68 8.68703932548871 -0.00703932548871222 24 8.68 8.68501997389246 -0.00501997389246256 25 8.68 8.68357990803542 -0.00357990803542307 26 8.68 8.6825529498393 -0.00255294983930732 27 8.92 8.68182059226593 0.238179407734073 28 8.92 8.99014645217578 -0.0701464521757824 29 8.92 8.97002373581616 -0.0500237358161595 30 8.92 8.95567356676477 -0.0356735667647747 31 8.92 8.94543999053565 -0.0254399905356486 32 8.92 8.93814209167032 -0.0181420916703203 33 8.92 8.93293772062191 -0.0129377206219132 34 8.92 8.92922631292645 -0.00922631292644738 35 8.92 8.92657958636644 -0.0065795863664384 36 8.92 8.92469211884515 -0.0046921188451492 37 8.92 8.9233461038477 -0.00334610384769896 38 8.92 8.92238621640438 -0.00238621640437664 39 9.3 8.9217016891847 0.3782983108153 40 9.3 9.4102230665565 -0.110223066556502 41 9.3 9.37860368402456 -0.0786036840245625 42 9.3 9.35605486524063 -0.0560548652406272 43 9.3 9.33997456297548 -0.0399745629754822 44 9.3 9.3285071720041 -0.0285071720040939 45 9.3 9.32032939937753 -0.0203293993775340 46 9.3 9.31449756149056 -0.0144975614905594 47 9.3 9.3103386866119 -0.0103386866119024 48 9.3 9.30737285652686 -0.00737285652685493 49 9.3 9.30525782581542 -0.00525782581541812 50 9.3 9.30374952804311 -0.00374952804311057 51 9.6 9.30267391143024 0.297326088569756 52 9.6 9.68796701408941 -0.0879670140894131 53 9.6 9.66273216302256 -0.0627321630225559 54 9.6 9.6447363630359 -0.0447363630359057 55 9.6 9.63190296781191 -0.0319029678119129 56 9.6 9.62275105274855 -0.0227510527485464 57 9.6 9.61622452193848 -0.0162245219384829 58 9.6 9.61157023875078 -0.0115702387507817 59 9.6 9.6082511167514 -0.00825111675140278 60 9.6 9.60588414198805 -0.00588414198805154 61 9.6 9.60419617464868 -0.00419617464868338 62 9.6 9.60299242977447 -0.00299242977446923 63 9.9 9.60213399982242 0.297866000177581 64 9.9 9.98758198541304 -0.0875819854130349 65 9.9 9.96245758644468 -0.0624575864446779 66 9.9 9.94454055347224 -0.0445405534722401 67 9.9 9.9317633295896 -0.0317633295896051 68 9.9 9.92265147215215 -0.0226514721521518 69 9.9 9.916153507749 -0.0161535077489994 70 9.9 9.91151959620303 -0.0115195962030317 71 9.9 9.90821500188955 -0.00821500188954971 72 9.9 9.90585838729552 -0.00585838729551469 73 9.9 9.9041778081327 -0.00417780813269353 74 9.9 9.9029793320095 -0.00297933200950418 75 10.2 9.90212465937662 0.297875340623376 76 10.2 10.2875753244348 -0.0875753244347752 77 10.2 10.2624528362826 -0.0624528362826027 78 10.2 10.2445371659759 -0.0445371659758624 79 10.2 10.2317609138548 -0.0317609138548303 80 10.2 10.2226497494124 -0.022649749412448 81 10.2 10.2161522792068 -0.0161522792068123 82 10.2 10.2115187200893 -0.0115187200893008 83 10.2 10.2082143771041 -0.0082143771041121 84 10.2 10.2058579417405 -0.005857941740528 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 10.2041774903928 10.0147294817858 10.3936254989998 86 10.2083549807856 9.89960545233274 10.5171045092385 87 10.2125324711785 9.78333061101376 10.6417343313431 88 10.2167099615713 9.6613168476271 10.7721030755154 89 10.2208874519641 9.5324289123498 10.9093459915784 90 10.2250649423569 9.3964140793711 11.0537158053427 91 10.2292424327497 9.25331730570405 11.2051675597954 92 10.2334199231425 9.10329381067171 11.3635460356134 93 10.2375974135354 8.94653782974394 11.5286569973268 94 10.2417749039282 8.78325292029629 11.7002968875601 95 10.245952394321 8.61363910321953 11.8782656854225 96 10.2501298847138 8.43788739919723 12.0623723702304

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t12119965418pl9dsca2pyrtwk/1k8mj1211996461.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t12119965418pl9dsca2pyrtwk/1k8mj1211996461.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t12119965418pl9dsca2pyrtwk/2nt3t1211996461.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t12119965418pl9dsca2pyrtwk/2nt3t1211996461.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t12119965418pl9dsca2pyrtwk/3j95u1211996461.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t12119965418pl9dsca2pyrtwk/3j95u1211996461.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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