WS 9

*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 08:14:53 -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/03/t1259853350gm59rvhos0uutti.htm/, Retrieved Thu, 03 Dec 2009 16:15:55 +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/t1259853350gm59rvhos0uutti.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:

WS 9 link 11

Dataseries X:

» Textbox « » Textfile « » CSV «

162 161 149 139 135 130 127 122 117 112 113 149 157 157 147 137 132 125 123 117 114 111 112 144 150 149 134 123 116 117 111 105 102 95 93 124 130 124 115 106 105 105 101 95 93 84 87 116 120 117 109 105 107 109 109 108 107 99 103 131 137

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.837256207348513 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 157 158.906178603059 -1.90617860305909 14 157 157.431844504105 -0.431844504104788 15 147 147.132924301797 -0.132924301797033 16 137 136.909521451706 0.0904785482941293 17 132 131.795644965744 0.20435503425594 18 125 124.946407783027 0.0535922169731577 19 123 123.978412132794 -0.978412132794162 20 117 118.392756452051 -1.39275645205112 21 114 112.393465096920 1.6065349030804 22 111 108.784773901927 2.21522609807320 23 112 111.570279367648 0.429720632352101 24 144 147.652982354818 -3.65298235481836 25 150 152.164591695020 -2.16459169502025 26 149 150.684660732368 -1.68466073236763 27 134 139.857094564603 -5.85709456460339 28 123 125.679901575758 -2.67990157575771 29 116 118.749874893847 -2.74987489384704 30 117 110.202101708307 6.79789829169296 31 111 114.779133267667 -3.77913326766672 32 105 107.203544782240 -2.20354478224027 33 102 101.419260975123 0.580739024877204 34 95 97.5360567028293 -2.53605670282933 35 93 95.930342754738 -2.93034275473806 36 124 122.676377901057 1.32362209894310 37 130 130.451363345676 -0.451363345676242 38 124 130.384226756879 -6.38422675687943 39 115 116.488835101663 -1.48883510166277 40 106 107.665375326701 -1.66537532670129 41 105 102.167570671125 2.83242932887478 42 105 100.236132388576 4.76386761142398 43 101 101.654950790650 -0.654950790650176 44 95 97.2941041902427 -2.29410419024268 45 93 92.1843726317706 0.8156273682294 46 84 88.3983956037706 -4.39839560377061 47 87 85.0840810496644 1.91591895033561 48 116 114.528763116401 1.47123688359866 49 120 121.693115513950 -1.69311551394961 50 117 119.604682370739 -2.60468237073938 51 109 110.063161084503 -1.06316108450297 52 105 101.935071882057 3.06492811794340 53 107 101.163223109654 5.83677689034555 54 109 101.994307920580 7.00569207941987 55 109 104.320596202825 4.67940379717521 56 108 103.876450472356 4.12354952764403 57 107 104.327885318669 2.67211468133128 58 99 100.469523285408 -1.46952328540777 59 103 100.923390417182 2.07660958281848 60 131 135.481192586871 -4.48119258687078 61 137 137.92127557445 -0.921275574449965 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 62 136.250293428768 130.250961460929 142.249625396608 63 128.018483184182 120.378422752515 135.658543615849 64 120.341758085133 111.495253126718 129.188263043548 65 117.023275329465 107.017206971342 127.029343687588 66 112.752794770666 101.828422999044 123.677166542287 67 108.680407768387 96.960780387749 120.400035149024 68 104.218745004152 91.8512903084259 116.586199699877 69 101.077596396723 88.0246107745957 114.13058201885 70 94.6673400490953 81.3753571888381 107.959322909352 71 96.8140992380954 82.3106694200394 111.317529056151 72 126.621291845258 107.152381317610 146.090202372906 73 133.154775984433 100.420396587777 165.889155381090

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259853350gm59rvhos0uutti/1mryo1259853291.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259853350gm59rvhos0uutti/1mryo1259853291.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259853350gm59rvhos0uutti/2fjym1259853291.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259853350gm59rvhos0uutti/2fjym1259853291.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259853350gm59rvhos0uutti/3ttxn1259853291.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259853350gm59rvhos0uutti/3ttxn1259853291.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