Kristof Nollekens - Exp Smoothing - 10 oef2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 05 Jun 2009 10:52:18 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/05/t1244220841rlkfni4yxf3gbrr.htm/, Retrieved Fri, 05 Jun 2009 18:54:05 +0200

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/Jun/05/t1244220841rlkfni4yxf3gbrr.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 «

155 176 180 181 208 183 185 205 180 196 183 147 128 158 186 165 191 168 171 169 157 175 156 129 89 138 146 151 156 129 146 141 137 155 147 128 92 136 159 131 134 148 146 144 161 140 141 139 94 136 164 141 159 162 154 166 156 147 161 135 98 150 173 144 167 161 156 175 163 159 167 148 119 150 161 136 166 155 140 141

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 0.3969420535359 beta 0.0141114199930199 gamma 0.748470071977163 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 128 132.711239909822 -4.71123990982153 14 158 162.035845855414 -4.03584585541398 15 186 189.872729176268 -3.87272917626845 16 165 167.325171462959 -2.32517146295910 17 191 193.090291447698 -2.09029144769787 18 168 169.380749569493 -1.38074956949299 19 171 166.774396501205 4.22560349879512 20 169 186.777689862744 -17.7776898627438 21 157 156.534747806337 0.465252193663417 22 175 169.184439823387 5.81556017661254 23 156 159.642212085019 -3.64221208501897 24 129 126.631551486938 2.36844851306249 25 89 108.830295004100 -19.8302950041004 26 138 125.106364265537 12.8936357344631 27 146 153.961101046977 -7.96110104697655 28 151 133.902275236164 17.0977247638365 29 156 163.126103617622 -7.12610361762194 30 129 141.027605450006 -12.0276054500063 31 146 136.140747444941 9.85925255505938 32 141 146.248096189310 -5.24809618931027 33 137 131.271768777750 5.72823122224952 34 155 145.858081541908 9.14191845809154 35 147 135.375101306355 11.6248986936453 36 128 114.087791333242 13.9122086667578 37 92 92.2353524910681 -0.235352491068141 38 136 131.168645094079 4.83135490592053 39 159 147.241885864638 11.7581141353619 40 131 146.173778234449 -15.1737782344485 41 134 151.040510383096 -17.0405103830955 42 148 124.345875484610 23.6541245153904 43 146 143.971765071542 2.02823492845809 44 144 144.413956293347 -0.413956293347411 45 161 136.467013630232 24.5329863697678 46 140 161.582316185765 -21.5823161857653 47 141 140.160193470417 0.839806529582859 48 139 116.277663083602 22.7223369163978 49 94 91.848941326368 2.15105867363202 50 136 134.546400716189 1.45359928381100 51 164 152.486690360291 11.5133096397090 52 141 139.120640030229 1.87935996977117 53 159 150.461714255734 8.53828574426637 54 162 151.949611720761 10.0503882792389 55 154 156.979452763920 -2.97945276392025 56 166 154.717299411202 11.2827005887980 57 156 162.851672916130 -6.85167291613024 58 147 154.32957591457 -7.32957591457014 59 161 148.949120545191 12.0508794548088 60 135 137.762111693425 -2.76211169342454 61 98 93.7205973380399 4.27940266196015 62 150 137.964534977068 12.0354650229324 63 173 166.013248273733 6.98675172626656 64 144 145.910747362506 -1.91074736250616 65 167 159.402501000478 7.59749899952249 66 161 161.341465694832 -0.341465694831726 67 156 156.534217737577 -0.534217737576796 68 175 161.833419625711 13.1665803742893 69 163 162.641897115592 0.35810288440814 70 159 156.775253184924 2.22474681507646 71 167 164.560784749759 2.43921525024095 72 148 142.226560399564 5.77343960043552 73 119 102.288675977653 16.7113240223466 74 150 160.756366135467 -10.7563661354669 75 161 178.968330529485 -17.9683305294851 76 136 145.093550740936 -9.0935507409362 77 166 159.693641972541 6.3063580274586 78 155 157.718226366012 -2.71822636601217 79 140 152.069585565496 -12.0695855654961 80 141 158.102515288249 -17.1025152882493 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 81 142.136324689947 124.722436441939 159.550212937954 82 137.371135600819 118.188185783879 156.554085417759 83 143.141605675039 121.884313834243 164.398897515835 84 124.117359846772 102.392175413404 145.842544280141 85 92.0418734606554 71.1085742980996 112.975172623211 86 122.651450473787 96.6429781166018 148.659922830972 87 137.486923677882 107.826741531098 167.147105824666 88 118.012501193463 89.772109282876 146.252893104049 89 139.307014715856 105.863473255490 172.750556176223 90 131.770352833650 98.2106089764762 165.330096690825 91 123.887319052283 90.3695367839728 157.405101320592 92 130.841112342868 93.385530154248 168.296694531489

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244220841rlkfni4yxf3gbrr/1e38g1244220736.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244220841rlkfni4yxf3gbrr/1e38g1244220736.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244220841rlkfni4yxf3gbrr/2hdap1244220736.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244220841rlkfni4yxf3gbrr/2hdap1244220736.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244220841rlkfni4yxf3gbrr/3pc0g1244220736.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244220841rlkfni4yxf3gbrr/3pc0g1244220736.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