Exponential smoothing eigen reeks - Lotte Kenis

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 16 Jan 2009 04:53:00 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jan/16/t1232106818p0sze147chxti43.htm/, Retrieved Fri, 16 Jan 2009 12:53:42 +0100

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/Jan/16/t1232106818p0sze147chxti43.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 «

1.82 1.76 1.79 1.74 1.78 1.80 1.80 1.80 1.79 1.82 1.82 1.83 1.77 1.77 1.77 1.77 1.74 1.78 1.78 1.78 1.78 1.81 1.84 1.80 1.78 1.76 1.74 1.72 1.73 1.77 1.81 1.83 1.87 1.89 1.82 1.79 1.79 1.82 1.82 1.81 1.81 1.78 1.80 1.79 1.83 1.82 1.80 1.82 1.84 1.82 1.81 1.79 1.87 1.89 1.92 1.9 1.91 1.95 2.04 1.99 1.94 1.93 1.89 1.87 1.89 1.9 1.93 1.94 1.88 1.89 1.92 1.91 1.89 1.89 1.98 2.02 2.02 1.99 1.97 1.96 1.95 1.98 2.00 2.00

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.861637420509336 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1.77 1.77745734897717 -0.00745734897717387 14 1.77 1.77268467088063 -0.00268467088062585 15 1.77 1.77161150337079 -0.00161150337079419 16 1.77 1.77104998553188 -0.00104998553187574 17 1.74 1.73973643083105 0.000263569168945654 18 1.78 1.78037847553123 -0.000378475531233047 19 1.78 1.79001781681592 -0.0100178168159186 20 1.78 1.78304280903269 -0.00304280903268928 21 1.78 1.77094153418063 0.00905846581936887 22 1.81 1.80813754652268 0.00186245347732417 23 1.84 1.81016317643645 0.0298368235635522 24 1.8 1.84853826298730 -0.0485382629872955 25 1.78 1.74808959897233 0.0319104010276676 26 1.76 1.77790481937347 -0.0179048193734692 27 1.74 1.76385981307807 -0.0238598130780718 28 1.72 1.74419229237287 -0.0241922923728668 29 1.73 1.69391691168240 0.0360830883176047 30 1.77 1.76498608380562 0.00501391619438141 31 1.81 1.77787945451679 0.0321205454832139 32 1.83 1.80821452926487 0.0217854707351273 33 1.87 1.81896892069814 0.051031079301856 34 1.89 1.89265728742304 -0.00265728742304017 35 1.82 1.89478931838934 -0.0747893183893358 36 1.79 1.83200622154673 -0.0420062215467327 37 1.79 1.74835918563097 0.0416408143690263 38 1.82 1.77963330729428 0.0403666927057238 39 1.82 1.8149504002141 0.00504959978590103 40 1.81 1.82014248623299 -0.0101424862329915 41 1.81 1.78909725436703 0.020902745632968 42 1.78 1.84437618055992 -0.0643761805599243 43 1.8 1.80129378200306 -0.00129378200306007 44 1.79 1.80137036464926 -0.011370364649262 45 1.83 1.78752316055545 0.0424768394445474 46 1.82 1.84586514170359 -0.025865141703592 47 1.8 1.81786387509542 -0.0178638750954161 48 1.82 1.80849015592034 0.0115098440796599 49 1.84 1.78184107938412 0.0581589206158759 50 1.82 1.82694988812251 -0.00694988812251118 51 1.81 1.81660670969448 -0.00660670969448174 52 1.79 1.80965282491897 -0.0196528249189702 53 1.87 1.77485203234714 0.09514796765286 54 1.89 1.88267969991618 0.00732030008382045 55 1.92 1.91139462841568 0.00860537158431862 56 1.9 1.91858390889326 -0.0185839088932596 57 1.91 1.90606019119196 0.00393980880803646 58 1.95 1.92222906532821 0.0277709346717872 59 2.04 1.94120775348521 0.0987922465147866 60 1.99 2.03767155075633 -0.0476715507563259 61 1.94 1.96332079647982 -0.0233207964798199 62 1.93 1.92842559151925 0.0015744084807523 63 1.89 1.92521187971164 -0.0352118797116436 64 1.87 1.89163494147564 -0.0216349414756434 65 1.89 1.87031026467300 0.0196897353270027 66 1.9 1.90109131606675 -0.00109131606674695 67 1.93 1.92285296472611 0.00714703527389493 68 1.94 1.92498325249749 0.0150167475025058 69 1.88 1.94465840485279 -0.0646584048527863 70 1.89 1.90479394954258 -0.0147939495425775 71 1.92 1.89622173853625 0.0237782614637523 72 1.91 1.908197432131 0.00180256786899835 73 1.89 1.88101863887289 0.00898136112710701 74 1.89 1.87770056699217 0.0122994330078319 75 1.98 1.87877049671953 0.101229503280466 76 2.02 1.96454948482091 0.0554505151790892 77 2.02 2.01556692275763 0.00443307724236952 78 1.99 2.03107582509615 -0.0410758250961469 79 1.97 2.02072255554663 -0.050722555546628 80 1.96 1.97399330259088 -0.0139933025908829 81 1.95 1.95733292253833 -0.00733292253833495 82 1.98 1.97460655088350 0.00539344911649775 83 2 1.98917786518788 0.0108221348121205 84 2 1.98647687891938 0.0135231210806217 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 1.96910501833384 1.90253842599635 2.03567161067134 86 1.95805385650021 1.8701427623546 2.04596495064581 87 1.96028693518841 1.85557187623896 2.06500199413787 88 1.95240578969947 1.83316713818783 2.07164444121111 89 1.94871277989035 1.81613752380699 2.08128803597372 90 1.95381770933240 1.80801916642693 2.09961625223786 91 1.97693884249067 1.82013084938968 2.13374683559165 92 1.97899130086745 1.81228675731074 2.14569584442416 93 1.97527063031295 1.79700803223875 2.15353322838716 94 2.00095021236857 1.81280579798834 2.18909462674880 95 2.01173134939429 1.81605383343224 2.20740886535634 96 2 NA NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/16/t1232106818p0sze147chxti43/13kbe1232106777.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/16/t1232106818p0sze147chxti43/13kbe1232106777.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/16/t1232106818p0sze147chxti43/28jj11232106777.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/16/t1232106818p0sze147chxti43/28jj11232106777.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/16/t1232106818p0sze147chxti43/32e1e1232106777.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/16/t1232106818p0sze147chxti43/32e1e1232106777.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