Exponential Smoothing

*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: Tue, 01 Dec 2009 13:26:53 -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/01/t1259699260tgythzvmbd9np8b.htm/, Retrieved Tue, 01 Dec 2009 21:27:45 +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/01/t1259699260tgythzvmbd9np8b.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 «

105.7 105.7 111.1 82.4 60 107.3 99.3 113.5 108.9 100.2 103.9 138.7 120.2 100.2 143.2 70.9 85.2 133 136.6 117.9 106.3 122.3 125.5 148.4 126.3 99.6 140.4 80.3 92.6 138.5 110.9 119.6 105 109 129.4 148.6 101.4 134.8 143.7 81.6 90.3 141.5 140.7 140.2 100.2 125.7 119.6 134.7 109 116.3 146.9 97.4 89.4 132.1 139.8 129 112.5 121.9 121.7 123.1

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 0.196498523917098 beta 0.0899638888814172 gamma 0.583891170761644 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 120.2 110.836266892128 9.36373310787225 14 100.2 93.7737425390607 6.42625746093925 15 143.2 137.733968961221 5.46603103877948 16 70.9 69.2677650721188 1.63223492788116 17 85.2 83.563859402248 1.63614059775202 18 133 131.471213139645 1.52878686035532 19 136.6 112.802431551073 23.7975684489271 20 117.9 136.202701952687 -18.3027019526874 21 106.3 127.870142486416 -21.5701424864163 22 122.3 114.292139737955 8.00786026204501 23 125.5 121.150889303946 4.34911069605408 24 148.4 161.952468839141 -13.5524688391415 25 126.3 141.820088080406 -15.5200880804060 26 99.6 114.330930031326 -14.7309300313257 27 140.4 158.468316777822 -18.0683167778224 28 80.3 76.103667450336 4.19633254966406 29 92.6 91.5099997783892 1.09000022161084 30 138.5 142.155019193663 -3.65501919366267 31 110.9 130.82261788252 -19.9226178825200 32 119.6 124.011853083112 -4.41185308311196 33 105 115.229242095174 -10.2292420951737 34 109 116.476607663784 -7.47660766378387 35 129.4 116.966482707007 12.4335172929932 36 148.6 148.050329870125 0.549670129875324 37 101.4 128.964019288729 -27.5640192887285 38 134.8 99.6220205129872 35.1779794870128 39 143.7 152.162179437852 -8.46217943785194 40 81.6 80.0212821933726 1.57871780662735 41 90.3 93.4181970405116 -3.11819704051156 42 141.5 140.783350177299 0.716649822701498 43 140.7 121.849978681189 18.8500213188111 44 140.2 130.47529005527 9.72470994472985 45 100.2 121.107034884099 -20.9070348840991 46 125.7 122.147022453900 3.55297754609956 47 119.6 135.697013378742 -16.0970133787416 48 134.7 156.956073049891 -22.2560730498909 49 109 118.415772442545 -9.41577244254475 50 116.3 121.236254667216 -4.93625466721626 51 146.9 143.849462541121 3.05053745887881 52 97.4 79.1900307188684 18.2099692811316 53 89.4 93.7095433342137 -4.30954333421366 54 132.1 143.192577388638 -11.0925773886379 55 139.8 129.768647719405 10.031352280595 56 129 131.705789881828 -2.70578988182803 57 112.5 105.636187052539 6.86381294746096 58 121.9 123.320922692383 -1.4209226923831 59 121.7 126.117611532921 -4.41761153292131 60 123.1 146.348068519575 -23.2480685195753 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 113.459640628880 96.3315883874954 130.587692870264 62 120.273009022562 102.174500466326 138.371517578797 63 148.220115600902 128.207138399329 168.233092802475 64 88.7826108260244 70.0979528260481 107.467268826001 65 88.7979231027091 69.0910776021049 108.504768603313 66 134.411176744043 109.622097010197 159.200256477890 67 132.811807301196 106.660707089634 158.962907512757 68 126.588181350545 99.6337017801938 153.542660920897 69 105.767533360297 80.1108516189914 131.424215101604 70 117.283993882002 88.3337441384241 146.234243625581 71 118.460753727227 87.6312341444537 149.290273310000 72 129.548212502931 -45.6960479819908 304.792472987854

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259699260tgythzvmbd9np8b/1laj61259699211.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259699260tgythzvmbd9np8b/1laj61259699211.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259699260tgythzvmbd9np8b/2zy3f1259699211.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259699260tgythzvmbd9np8b/2zy3f1259699211.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259699260tgythzvmbd9np8b/38d4s1259699211.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259699260tgythzvmbd9np8b/38d4s1259699211.ps (open in new window)

Parameters (Session):

par1 = 12 ;

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