*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 10:51:35 -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/t1259862719c9l0dhvblrdtm1n.htm/, Retrieved Thu, 03 Dec 2009 18:52:03 +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/t1259862719c9l0dhvblrdtm1n.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 «

115.47 103.34 102.60 100.69 105.67 123.61 113.08 106.46 123.38 109.87 95.74 123.06 123.39 120.28 115.33 110.4 114.49 132.03 123.16 118.82 128.32 112.24 104.53 132.57 122.52 131.8 124.55 120.96 122.6 145.52 118.57 134.25 136.7 121.37 111.63 134.42 137.65 137.86 119.77 130.69 128.28 147.45 128.42 136.9 143.95 135.64 122.48 136.83 153.04 142.71 123.46 144.37 146.15 147.61 158.51 147.4 165.05 154.64 126.2 157.36 154.15 123.21 113.07 110.45 113.57 122.44 114.93 111.85 126.04 121.34

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 0.558149525043339 beta 0 gamma 0.210439498485435 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 123.39 118.324142628205 5.06585737179483 14 120.28 117.878205915142 2.40179408485788 15 115.33 114.319490210457 1.01050978954348 16 110.4 110.420479837141 -0.0204798371409112 17 114.49 114.805606426700 -0.315606426700157 18 132.03 132.178508250469 -0.148508250469234 19 123.16 122.573425841937 0.586574158062803 20 118.82 116.016545997262 2.80345400273828 21 128.32 134.036599918303 -5.71659991830336 22 112.24 117.172439789972 -4.93243978997194 23 104.53 100.288874931493 4.24112506850672 24 132.57 130.029280941729 2.54071905827124 25 122.52 132.249143709074 -9.72914370907434 26 131.8 123.297672126277 8.50232787372252 27 124.55 123.014600959619 1.53539904038105 28 120.96 119.31269297798 1.64730702201990 29 122.6 124.601252316458 -2.00125231645791 30 145.52 141.048848942491 4.47115105750910 31 118.57 134.090577197526 -15.5205771975257 32 134.25 118.749630152202 15.5003698477983 33 136.7 143.064243217082 -6.36424321708157 34 121.37 125.911514687526 -4.54151468752563 35 111.63 110.0991281657 1.53087183430006 36 134.42 138.168699121546 -3.74869912154617 37 137.65 135.737240017102 1.91275998289802 38 137.86 134.978904587097 2.88109541290305 39 119.77 130.910540695208 -11.1405406952082 40 130.69 120.143968487292 10.5460315127081 41 128.28 130.060093438373 -1.78009343837269 42 147.45 147.232951926130 0.217048073869762 43 128.42 136.041367904197 -7.62136790419717 44 136.9 127.993775051947 8.9062249480534 45 143.95 146.594836496423 -2.64483649642332 46 135.64 131.687575449830 3.95242455017018 47 122.48 121.180704534332 1.29929546566818 48 136.83 148.630112000102 -11.8001120001017 49 153.04 142.231178897901 10.8088211020988 50 142.71 146.528214288553 -3.81821428855315 51 123.46 137.416862989954 -13.9568629899545 52 144.37 127.094839871366 17.2751601286337 53 146.15 139.620707246508 6.52929275349192 54 147.61 161.617145485194 -14.0071454851938 55 158.51 141.757496778861 16.7525032211392 56 147.4 148.850950253000 -1.45095025300023 57 165.05 160.597109330442 4.4528906695584 58 154.64 150.264873084438 4.37512691556196 59 126.2 139.747237942662 -13.5472379426617 60 157.36 157.692040353663 -0.332040353663331 61 154.15 159.796247726105 -5.64624772610517 62 123.21 153.548831671235 -30.3388316712351 63 113.07 128.692290509669 -15.6222905096693 64 110.45 120.344750532434 -9.89475053243387 65 113.57 116.706564421809 -3.13656442180904 66 122.44 131.398473696496 -8.9584736964959 67 114.93 117.216856779711 -2.28685677971127 68 111.85 111.990892577709 -0.140892577709209 69 126.04 125.017215338995 1.02278466100462 70 121.34 112.763236362479 8.57676363752145 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 71 102.924271231338 86.1005462509806 119.747996211696 72 129.659244039039 110.392362704154 148.926125373924 73 131.454649736528 110.021317971952 152.887981501104 74 126.062698762572 102.662640970160 149.462756554983 75 119.508147179691 94.2943077488146 144.721986610568 76 120.412743890928 93.5071182151721 147.318369566683 77 122.925703106227 94.4285508421546 151.422855370299 78 138.826946942014 108.822569239426 168.831324644602 79 130.26584343449 98.826414758425 161.705272110555 80 126.515825001723 93.7040486152604 159.327601388185 81 139.728988847396 105.600003163771 173.85797453102 82 127.606533156748 92.2093205835683 163.003745729928

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862719c9l0dhvblrdtm1n/1t2761259862690.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862719c9l0dhvblrdtm1n/1t2761259862690.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862719c9l0dhvblrdtm1n/2py1x1259862690.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862719c9l0dhvblrdtm1n/2py1x1259862690.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862719c9l0dhvblrdtm1n/3jlmb1259862690.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/03/t1259862719c9l0dhvblrdtm1n/3jlmb1259862690.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=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