Exponentional smooting - Blue Jeans (D) - Alexia Versluys

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 12:33:40 -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/t121199973749jn8196mprxx2i.htm/, Retrieved Wed, 28 May 2008 20:35:37 +0200

User-defined keywords:

Exponentional smooting - Blue Jeans (D) - Alexia Versluys

Dataseries X:

» Textbox « » Textfile « » CSV «

44,13 44,13 44,17 44,14 44,15 44,14 44,14 44,14 44,19 44,29 44,29 44,29 44,29 44,27 44,26 44,33 44,32 44,34 44,34 44,34 44,37 44,47 44,51 44,51 44,51 44,52 44,7 44,84 44,9 44,95 44,94 44,94 44,91 45,28 45,36 45,34 45,34 45,34 45,44 45,62 45,75 45,77 45,77 45,77 46,09 46,25 46,35 46,34 46,34 46,28 46,59 46,42 46,29 46,29 46,29 46,3 46,52 46,66 46,67 46,72 46,72 46,72 46,76 46,89 47,04 47,02 47,02 47,18 47,22 47,8 47,88 47,91

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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.0607904611895088 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 44.17 44.13 0.0399999999999991 4 44.14 44.1724316184476 -0.0324316184475819 5 44.15 44.140460085405 0.00953991459496706 6 44.14 44.151040021213 -0.0110400212129633 7 44.14 44.1403688932319 -0.000368893231886602 8 44.14 44.1403464680422 -0.000346468042188519 9 44.19 44.1403254060901 0.0496745939098773 10 44.29 44.1933451475633 0.0966548524367 11 44.29 44.2992208406191 -0.00922084061913608 12 44.29 44.2986603014653 -0.00866030146534058 13 44.29 44.2981338377452 -0.0081338377452198 14 44.27 44.2976393779974 -0.0276393779974455 15 44.26 44.275959167462 -0.0159591674620003 16 44.33 44.2649890023118 0.0650109976882192 17 44.32 44.3389410508436 -0.0189410508436367 18 44.34 44.3277896156274 0.0122103843725654 19 44.34 44.3485318905248 -0.00853189052475045 20 44.34 44.3480132329649 -0.0080132329649274 21 44.37 44.3475261048374 0.0224738951626193 22 44.47 44.378892303289 0.0911076967109707 23 44.51 44.48443078219 0.0255692178099949 24 44.51 44.5259851467329 -0.0159851467329304 25 44.51 44.5250134022909 -0.0150134022908546 26 44.52 44.5241007306416 -0.0041007306415608 27 44.7 44.5338514453347 0.166148554665348 28 44.84 44.7239516925987 0.116048307401272 29 44.9 44.8710063227259 0.0289936772740802 30 44.95 44.932768861739 0.0172311382610175 31 44.94 44.9838163505807 -0.0438163505806983 32 44.94 44.9711527344213 -0.031152734421255 33 44.91 44.9692589453285 -0.0592589453284731 34 45.28 44.9356565667123 0.344343433287655 35 45.36 45.3265893628295 0.0334106371705118 36 45.34 45.4086204108717 -0.0686204108717092 37 45.34 45.3844489444478 -0.044448944447808 38 45.34 45.3817468726154 -0.0417468726154411 39 45.44 45.3792090609759 0.0607909390240664 40 45.62 45.4829045701953 0.137095429804653 41 45.75 45.6712386646001 0.0787613353998609 42 45.77 45.806026602503 -0.0360266025030000 43 45.77 45.8238365287218 -0.053836528721753 44 45.77 45.8205637813119 -0.0505637813119151 45 46.09 45.8174899857265 0.272510014273522 46 46.25 46.1540559951729 0.0959440048270679 47 46.35 46.3198884754747 0.0301115245252674 48 46.34 46.4217189689377 -0.0817189689377429 49 46.34 46.4067512351281 -0.0667512351280877 50 46.28 46.4026933967597 -0.122693396759686 51 46.59 46.3352348085858 0.254765191414251 52 46.42 46.6607221020669 -0.240722102066862 53 46.29 46.4760884944637 -0.186088494463711 54 46.29 46.3347760890632 -0.0447760890631983 55 46.29 46.3320541299588 -0.0420541299587782 56 46.3 46.3294976400037 -0.0294976400036688 57 46.52 46.3377044648638 0.18229553513617 58 46.66 46.5687862945176 0.0912137054824385 59 46.67 46.7143312177406 -0.0443312177406341 60 46.72 46.7216363025691 -0.00163630256909642 61 46.72 46.7715368309813 -0.05153683098127 62 46.72 46.7684038832577 -0.0484038832576701 63 46.76 46.7654613888711 -0.00546138887107617 64 46.89 46.8051293885229 0.084870611477136 65 47.04 46.940288712136 0.0997112878640039 66 47.02 47.0963502073110 -0.0763502073110445 67 47.02 47.0717088429967 -0.0517088429966961 68 47.18 47.0685654385834 0.111434561416644 69 47.22 47.2353395969643 -0.0153395969643242 70 47.8 47.2744070957904 0.525592904209603 71 47.88 47.8863581308352 -0.00635813083523118 72 47.91 47.9659716171295 -0.0559716171294653 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 47.9925690767106 47.7743263116889 48.2108118417324 74 48.0751381534213 47.7569766974649 48.3932996093776 75 48.1577072301319 47.7562817034759 48.5591327567879 76 48.2402763068425 47.7630665422695 48.7174860714156 77 48.3228453835532 47.7739019796855 48.8717887874209 78 48.4054144602638 47.7870912535795 49.0237376669481 79 48.4879835369744 47.801663369733 49.1743037042159 80 48.5705526136851 47.8170101507149 49.3240950766553 81 48.6531216903957 47.8327265214252 49.4735168593662 82 48.7356907671063 47.8485304816955 49.6228510525171 83 48.818259843817 47.8642191264183 49.7723005612157 84 48.9008289205276 47.8796427380228 49.9220151030324

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t121199973749jn8196mprxx2i/16t9r1211999614.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t121199973749jn8196mprxx2i/16t9r1211999614.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t121199973749jn8196mprxx2i/2xe9o1211999614.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t121199973749jn8196mprxx2i/2xe9o1211999614.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t121199973749jn8196mprxx2i/35nt01211999614.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t121199973749jn8196mprxx2i/35nt01211999614.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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