BBWS9-exponentialsmoothing

*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 13:49:49 -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/t1259700621deuj08qfr65otfk.htm/, Retrieved Tue, 01 Dec 2009 21:50:26 +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/t1259700621deuj08qfr65otfk.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 «

96,8 114,1 110,3 103,9 101,6 94,6 95,9 104,7 102,8 98,1 113,9 80,9 95,7 113,2 105,9 108,8 102,3 99 100,7 115,5 100,7 109,9 114,6 85,4 100,5 114,8 116,5 112,9 102 106 105,3 118,8 106,1 109,3 117,2 92,5 104,2 112,5 122,4 113,3 100 110,7 112,8 109,8 117,3 109,1 115,9 96 99,8 116,8 115,7 99,4 94,3 91 93,2 103,1 94,1 91,8 102,7 82,6

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 0.0710539545448988 beta 1 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 95.7 94.9307408679596 0.769259132040403 14 113.2 112.025059303842 1.17494069615817 15 105.9 104.943690583731 0.95630941626851 16 108.8 107.979165423207 0.820834576792578 17 102.3 101.608929935168 0.691070064832232 18 99 98.7381909309036 0.261809069096373 19 100.7 98.7907127330063 1.90928726699369 20 115.5 108.874381400642 6.62561859935799 21 100.7 108.827552568900 -8.12755256890016 22 109.9 103.904266171705 5.9957338282954 23 114.6 122.072013488954 -7.47201348895449 24 85.4 86.63302976268 -1.23302976267991 25 100.5 103.234098631968 -2.73409863196801 26 114.8 121.704799347454 -6.9047993474544 27 116.5 112.704800658295 3.7951993417046 28 112.9 115.575414354338 -2.6754143543384 29 102 107.804475187270 -5.80447518727048 30 106 102.856201277533 3.14379872246657 31 105.3 103.854371509038 1.44562849096170 32 118.8 117.717745018480 1.08225498151964 33 106.1 102.013924982102 4.08607501789824 34 109.3 110.769289825928 -1.46928982592766 35 117.2 114.889686085588 2.31031391441218 36 92.5 85.571448738844 6.92855126115603 37 104.2 101.852371825963 2.34762817403677 38 112.5 117.848943691905 -5.3489436919053 39 122.4 119.871484376355 2.52851562364518 40 113.3 117.349409047939 -4.04940904793922 41 100 106.820060208653 -6.82006020865268 42 110.7 110.868186541988 -0.168186541988007 43 112.8 110.365035156504 2.43496484349618 44 109.8 125.096029511562 -15.2960295115624 45 117.3 109.813446603974 7.48655339602567 46 109.1 113.362930794477 -4.26293079447697 47 115.9 120.403668412532 -4.50366841253233 48 96 93.3376189175815 2.66238108241853 49 99.8 103.802893517563 -4.00289351756275 50 116.8 110.173887100328 6.6261128996722 51 115.7 119.001102352076 -3.30110235207604 52 99.4 108.732376562866 -9.3323765628663 53 94.3 94.1805915535665 0.119408446433539 54 91 102.959047167137 -11.9590471671372 55 93.2 101.691910201205 -8.49191020120477 56 103.1 96.3722431741136 6.72775682588636 57 94.1 101.298479898548 -7.19847989854793 58 91.8 91.486938169151 0.313061830848923 59 102.7 95.074310706052 7.62568929394794 60 82.6 77.7006342195378 4.89936578046223 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 80.150439456161 69.537756073401 90.763122838921 62 92.2353310628805 81.4758782581014 102.994783867660 63 89.9801253631593 78.939930538606 101.020320187713 64 76.566323343031 65.2710987356703 87.8615479503915 65 71.9155140219512 60.1641694913526 83.6668585525498 66 69.2569079712413 56.849928060996 81.6638878814866 67 71.2023490591717 57.6458810273444 84.758817090999 68 78.6917249273386 62.9888196959605 94.3946301587168 69 72.1159488329979 55.4338739221895 88.7980237438063 70 70.6390240027075 52.229458915883 89.048589089532 71 78.9152347002952 56.4714948771408 101.358974523450 72 63.093825753476 43.8900541255342 82.2975973814179

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259700621deuj08qfr65otfk/1lvyg1259700587.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259700621deuj08qfr65otfk/1lvyg1259700587.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259700621deuj08qfr65otfk/2sq441259700587.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259700621deuj08qfr65otfk/2sq441259700587.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259700621deuj08qfr65otfk/3end21259700587.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259700621deuj08qfr65otfk/3end21259700587.ps (open in new window)

Parameters (Session):

par1 = FALSE ; par2 = 0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

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