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: Fri, 04 Dec 2009 06:28:30 -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/04/t1259933368bswh2541go9y3og.htm/, Retrieved Fri, 04 Dec 2009 14:29:32 +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/04/t1259933368bswh2541go9y3og.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 «

5594 5585 5710 5511 5403 5826 5884 5965 5960 6064 6046 5954 5952 5960 5983 5996 6021 6094 6202 6276 6306 6342 6345 6328 6191 6261 6253 6198 6247 6293 6381 6448 6470 6516 6532 6526 6533 6498 6507 6464 6453 6468 6497 6808 6793 6907 6792 6757 6734 6654 6589 6469 6521 6448 6410 6528 6445 6458 6215 6167

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 0.59512425238397 beta 0.241357167807255 gamma 0.812552195322275 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 5952 5749.65534450099 202.344655499006 14 5960 5911.24101041888 48.7589895811234 15 5983 6002.01512275132 -19.0151227513152 16 5996 6040.97366911689 -44.9736691168873 17 6021 6071.981422266 -50.9814222659961 18 6094 6136.4592164406 -42.4592164405967 19 6202 6278.27614189613 -76.2761418961327 20 6276 6319.24273569651 -43.2427356965136 21 6306 6286.53836661607 19.4616333839258 22 6342 6404.10743769132 -62.1074376913193 23 6345 6320.40735301381 24.5926469861906 24 6328 6224.39089273991 103.609107260093 25 6191 6368.77173543585 -177.771735435846 26 6261 6204.51436266217 56.4856373378261 27 6253 6232.36133722416 20.6386627758429 28 6198 6247.24943893843 -49.2494389384347 29 6247 6234.8574029844 12.1425970155988 30 6293 6311.42053795636 -18.4205379563582 31 6381 6432.94724172827 -51.9472417282723 32 6448 6477.39136024148 -29.3913602414814 33 6470 6451.37644628614 18.6235537138627 34 6516 6520.64288345998 -4.64288345998193 35 6532 6484.82030479844 47.1796952015557 36 6526 6414.64098934762 111.359010652383 37 6533 6459.5754975784 73.4245024216043 38 6498 6548.63686574423 -50.636865744229 39 6507 6510.42969602792 -3.42969602792073 40 6464 6493.70919961818 -29.7091996181771 41 6453 6524.45815370116 -71.4581537011618 42 6468 6541.14356032191 -73.1435603219106 43 6497 6612.77564821377 -115.775648213775 44 6808 6609.45989989865 198.540100101353 45 6793 6748.7041393727 44.2958606272987 46 6907 6845.14706608877 61.8529339112338 47 6792 6891.5565931881 -99.5565931880992 48 6757 6756.35029806862 0.649701931378331 49 6734 6710.34538286687 23.6546171331274 50 6654 6710.65600682782 -56.6560068278213 51 6589 6665.73934906081 -76.7393490608147 52 6469 6567.49733204843 -98.4973320484341 53 6521 6505.27850366499 15.7214963350125 54 6448 6547.62319574845 -99.6231957484451 55 6410 6559.15089808502 -149.150898085023 56 6528 6601.28872337265 -73.2887233726478 57 6445 6454.90272938832 -9.90272938832004 58 6458 6439.09488420521 18.9051157947924 59 6215 6323.33499546291 -108.334995462912 60 6167 6132.03410561018 34.9658943898166 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 6036.06943597542 5896.3535856075 6175.78528634335 62 5916.56706099519 5738.34734457363 6094.78677741674 63 5824.97431609994 5603.24022901897 6046.70840318091 64 5706.75937032207 5438.48925260581 5975.02948803834 65 5683.54284048762 5361.42768651193 6005.65799446331 66 5623.72188611979 5245.65421450379 6001.78955773578 67 5627.28541398857 5185.49608225556 6069.07474572157 68 5738.36373043759 5219.37138247084 6257.35607840434 69 5650.41205039918 5066.68447496298 6234.13962583538 70 5635.03937340683 4976.39441350906 6293.6843333046 71 5470.07697768457 4751.56447356188 6188.58948180725 72 5396.68259965547 4618.1206281845 6175.24457112644

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259933368bswh2541go9y3og/1en9n1259933308.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259933368bswh2541go9y3og/1en9n1259933308.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259933368bswh2541go9y3og/2jl081259933308.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259933368bswh2541go9y3og/2jl081259933308.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259933368bswh2541go9y3og/3lmj61259933308.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259933368bswh2541go9y3og/3lmj61259933308.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