Exponential Smoothing Overlijdens België

*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: Fri, 03 Dec 2010 19:14:24 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/03/t129140374334uubz0imogt6pp.htm/, Retrieved Fri, 03 Dec 2010 20:15:46 +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/2010/Dec/03/t129140374334uubz0imogt6pp.htm/}, year = {2010}, } @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 = {2010}, 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 «

12008 9169 8788 8417 8247 8197 8236 8253 7733 8366 8626 8863 10102 8463 9114 8563 8872 8301 8301 8278 7736 7973 8268 9476 11100 8962 9173 8738 8459 8078 8411 8291 7810 8616 8312 9692 9911 8915 9452 9112 8472 8230 8384 8625 8221 8649 8625 10443 10357 8586 8892 8329 8101 7922 8120 7838 7735 8406 8209 9451 10041 9411 10405 8467 8464 8102 7627 7513 7510 8291 8064 9383 9706 8579 9474 8318 8213 8059 9111 7708 7680 8014 8007 8718 9486 9113 9025 8476 7952 7759 7835 7600 7651 8319 8812 8630

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 0.0618419834147308 beta 0 gamma 0.322340313497252 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 10102 10040.4337606838 61.5662393162402 14 8463 8403.52843507176 59.4715649282425 15 9114 9059.07690397433 54.9230960256718 16 8563 8529.76075320513 33.2392467948721 17 8872 8874.1452968581 -2.14529685809612 18 8301 8294.42492348267 6.57507651732703 19 8301 8164.41050195957 136.589498040431 20 8278 8300.72809680264 -22.7280968026425 21 7736 7797.19317558775 -61.1931755877531 22 7973 8408.77949760859 -435.77949760859 23 8268 8611.7423251823 -343.742325182295 24 9476 8799.14691404673 676.853085953275 25 11100 10093.6184900840 1006.38150991604 26 8962 8514.50897235092 447.491027649075 27 9173 9192.6778494662 -19.6778494661939 28 8738 8652.19089891796 85.8091010820353 29 8459 8989.12596304143 -530.125963041428 30 8078 8379.39131259644 -301.391312596435 31 8411 8269.64879929562 141.351200704379 32 8291 8358.08224692338 -67.082246923379 33 7810 7840.17230073919 -30.1723007391902 34 8616 8340.39980801158 275.600191988422 35 8312 8615.1883734454 -303.188373445406 36 9692 9113.73522726881 578.264772731187 37 9911 10501.7613282095 -590.761328209517 38 8915 8654.86941101666 260.130588983337 39 9452 9180.17680584806 271.823194151941 40 9112 8689.61676050825 422.383239491748 41 8472 8861.103686033 -389.103686032995 42 8230 8329.26089772807 -99.260897728067 43 8384 8365.90658871498 18.0934112850191 44 8625 8383.68597391713 241.314026082870 45 8221 7896.00965962521 324.990340374787 46 8649 8510.66861110863 138.331388891374 47 8625 8601.93898023799 23.0610197620117 48 10443 9387.21859523958 1055.78140476042 49 10357 10451.2545903467 -94.2545903467144 50 8586 8892.3825826454 -306.382582645396 51 8892 9386.19159501558 -494.191595015576 52 8329 8893.78995931962 -564.789959319616 53 8101 8758.82950000134 -657.829500001344 54 7922 8298.01841584362 -376.018415843619 55 8120 8353.0375376632 -233.037537663193 56 7838 8422.78977342329 -584.78977342329 57 7735 7909.32979364573 -174.329793645733 58 8406 8436.66298295507 -30.6629829550675 59 8209 8482.623936501 -273.623936501006 60 9451 9561.85696016096 -110.856960160962 61 10041 10205.9677681594 -164.967768159438 62 9411 8578.57390800513 832.42609199487 63 10405 9086.01450733354 1318.98549266646 64 8467 8684.39395953467 -217.393959534669 65 8464 8542.78142865477 -78.781428654771 66 8102 8203.00123047686 -101.001230476862 67 7627 8318.266257289 -691.266257289006 68 7513 8253.30868108957 -740.308681089573 69 7510 7854.35672547885 -344.356725478853 70 8291 8414.62083907508 -123.620839075076 71 8064 8381.3602080626 -317.360208062602 72 9383 9507.11022847005 -124.110228470046 73 9706 10134.0379869939 -428.037986993937 74 8579 8791.99337919066 -212.993379190664 75 9474 9381.92171962309 92.0782803769125 76 8318 8439.81620253703 -121.816202537029 77 8213 8346.03167141113 -133.031671411134 78 8059 7996.17712591597 62.8228740840332 79 9111 7943.07358653374 1167.92641346626 80 7708 7978.26144211615 -270.261442116152 81 7680 7728.11644621713 -48.1164462171328 82 8014 8373.45253564256 -359.452535642564 83 8007 8267.01962824298 -260.019628242977 84 8718 9454.75568599356 -736.755685993556 85 9486 9951.88661121125 -465.886611211248 86 9113 8672.53218116372 440.467818836281 87 9025 9395.12740395928 -370.127403959275 88 8476 8359.7551637003 116.244836299706 89 7952 8277.30117263641 -325.301172636413 90 7759 7974.78391873713 -215.783918737132 91 7835 8238.64088847943 -403.640888479433 92 7600 7741.72305384134 -141.723053841341 93 7651 7566.70513958672 84.294860413278 94 8319 8126.07985893804 192.920141061962 95 8812 8083.87589607805 728.124103921947 96 8630 9188.55280672682 -558.552806726819 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 9778.61662528438 8954.4143856884 10602.8188648804 98 8802.16070029986 7976.38391244333 9627.93748815638 99 9252.3875396821 8425.03920012356 10079.7358792406 100 8386.98666844296 7558.06975669734 9215.90358018858 101 8163.81763789416 7333.33511659372 8994.3001591946 102 7914.53634473787 7082.49115979107 8746.58152968467 103 8134.92871718823 7301.32379793644 8968.53363644002 104 7742.17839945442 6907.01665882665 8577.3401400822 105 7644.27412703949 6807.55846170506 8480.98979237392 106 8231.28483785532 7393.01812837458 9069.55154733605 107 8338.99928026366 7499.18439123675 9178.81416929058 108 9009.54854237078 8168.18832258444 9850.90876215713

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/03/t129140374334uubz0imogt6pp/1slr51291403661.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t129140374334uubz0imogt6pp/1slr51291403661.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t129140374334uubz0imogt6pp/2slr51291403661.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t129140374334uubz0imogt6pp/2slr51291403661.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t129140374334uubz0imogt6pp/3yrjj1291403661.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/03/t129140374334uubz0imogt6pp/3yrjj1291403661.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) 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