SHW WS9

*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 03 Dec 2009 11:54:20 -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/Dec/03/t1259866671szocf0f1yp5ygh1.htm/, Retrieved Thu, 03 Dec 2009 19:57:55 +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/Dec/03/t1259866671szocf0f1yp5ygh1.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 «

1.59 1.26 1.13 1.92 2.61 2.26 2.41 2.26 2.03 2.86 2.55 2.27 2.26 2.57 3.07 2.76 2.51 2.87 3.14 3.11 3.16 2.47 2.57 2.89 2.63 2.38 1.69 1.96 2.19 1.87 1.6 1.63 1.22 1.21 1.49 1.64 1.66 1.77 1.82 1.78 1.28 1.29 1.37 1.12 1.51 2.24 2.94 3.09 3.46 3.64 4.39 4.15 5.21 5.8 5.91 5.39 5.46 4.72 3.14 2.63

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 0.888966488320276 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 2.26 1.93469425938856 0.325305740611437 14 2.57 2.52078854176534 0.0492114582346606 15 3.07 3.03420164067502 0.0357983593249784 16 2.76 2.78222736468926 -0.0222273646892632 17 2.51 2.57835260397630 -0.0683526039763032 18 2.87 2.90961127396768 -0.0396112739676839 19 3.14 3.19612999117814 -0.0561299911781408 20 3.11 2.89790720766739 0.212092792332605 21 3.16 2.66095729753223 0.499042702467769 22 2.47 4.23348483147476 -1.76348483147476 23 2.57 2.40525201288053 0.164747987119474 24 2.89 2.30334674674196 0.586653253258037 25 2.63 2.8464304290902 -0.2164304290902 26 2.38 2.95696193075564 -0.576961930755638 27 1.69 2.89239067395073 -1.20239067395073 28 1.96 1.67412754061246 0.285872459387537 29 2.19 1.81151962604167 0.378480373958327 30 1.87 2.49460661561066 -0.624606615610657 31 1.6 2.17618175811147 -0.576181758111474 32 1.63 1.57479023769102 0.0552097623089802 33 1.22 1.43800469373072 -0.218004693730717 34 1.21 1.58134542110573 -0.371345421105732 35 1.49 1.25591593674353 0.234084063256472 36 1.64 1.36484532354974 0.275154676450262 37 1.66 1.59302168861610 0.0669783113839038 38 1.77 1.82930579339221 -0.0593057933922083 39 1.82 2.01601796141711 -0.196017961417114 40 1.78 1.84932255172931 -0.0693225517293077 41 1.28 1.68923463784740 -0.409234637847403 42 1.29 1.47814694140706 -0.188146941407060 43 1.37 1.48525488635487 -0.115254886354868 44 1.12 1.37408714745063 -0.254087147450625 45 1.51 1.00769512144109 0.502304878558914 46 2.24 1.81153135781857 0.428468642181429 47 2.94 2.26787632094682 0.672123679053183 48 3.09 2.62537908394678 0.464620916053222 49 3.46 2.92176232499024 0.53823767500976 50 3.64 3.67694736369968 -0.0369473636996784 51 4.39 4.03955325347355 0.350446746526447 52 4.15 4.32232514268676 -0.172325142686762 53 5.21 3.75249973923036 1.45750026076964 54 5.8 5.57276717316195 0.227232826838049 55 5.91 6.37556886689363 -0.465568866893626 56 5.39 5.64135319843935 -0.251353198439354 57 5.46 4.86698354118025 0.593016458819752 58 4.72 6.45703392550234 -1.73703392550234 59 3.14 5.03095591214422 -1.89095591214422 60 2.63 3.03471010365082 -0.404710103650824 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 2.58062800055381 1.36225236851070 3.79900363259691 62 2.75295883243842 1.08922390814993 4.41669375672691 63 3.09686438962256 0.981270518214004 5.21245826103111 64 3.05196134635758 0.732711312332134 5.37121138038303 65 2.86201824786779 0.4581515401765 5.26588495555908 66 3.09988366620187 0.330621930310382 5.86914540209336 67 3.40606501472994 0.235105566147667 6.57702446331222 68 3.25853623848574 0.0813760710131928 6.43569640595828 69 2.99856143897777 -0.0816123929101518 6.07873527086569 70 3.43295465304555 -0.187862690392194 7.0537719964833 71 3.44533392960542 -0.289989914068904 7.18065777327974 72 3.26869252487611 -17.1231856882811 23.6605707380333

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259866671szocf0f1yp5ygh1/1ahxf1259866457.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259866671szocf0f1yp5ygh1/1ahxf1259866457.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259866671szocf0f1yp5ygh1/2jge81259866457.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259866671szocf0f1yp5ygh1/2jge81259866457.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259866671szocf0f1yp5ygh1/3yb9y1259866457.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259866671szocf0f1yp5ygh1/3yb9y1259866457.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