exponential smoothing

*Unverified author*

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 12:06:01 -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/t12596943910xgpwghmlm1htuf.htm/, Retrieved Tue, 01 Dec 2009 20:06:35 +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/t12596943910xgpwghmlm1htuf.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 «

7291 6820 8031 7862 7357 7213 7079 7012 7319 8148 7599 6908 7878 7407 7911 7323 7179 6758 6934 6696 7688 8296 7697 7907 7592 7710 9011 8225 7733 8062 7859 8221 8330 8868 9053 8811 8120 7953 8878 8601 8361 9116 9310 9891 10147 10317 10682 10276 10614 9413 11068 9772 10350 10541 10049 10714 10759 11684 11462 10485 11056 10184 11082 10554 11315 10847 11104 11026 11073 12073 12328 11172

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 0.327366976611456 beta 0.0426741524472546 gamma 0.625912584003787 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 7878 7988.59029958755 -110.590299587550 14 7407 7488.2790801246 -81.279080124601 15 7911 7957.03397465224 -46.0339746522377 16 7323 7320.39988730651 2.60011269348706 17 7179 7157.77597266192 21.2240273380803 18 6758 6694.42051623206 63.5794837679405 19 6934 7045.18551378264 -111.185513782641 20 6696 6887.3713435908 -191.371343590807 21 7688 7092.25811729323 595.741882706774 22 8296 8137.65718544235 158.342814557647 23 7697 7665.89759711354 31.102402886464 24 7907 7001.03249965228 905.967500347724 25 7592 8313.8716567144 -721.8716567144 26 7710 7626.19133568407 83.8086643159295 27 9011 8192.96861575676 818.03138424324 28 8225 7843.02108207557 381.978917924434 29 7733 7827.77997673001 -94.7799767300121 30 8062 7330.61346112378 731.38653887622 31 7859 7894.26749917752 -35.2674991775248 32 8221 7743.35388905604 477.646110943964 33 8330 8644.94391775863 -314.943917758626 34 8868 9336.47248048307 -468.472480483069 35 9053 8570.00870177085 482.991298229152 36 8811 8396.0938741835 414.906125816506 37 8120 8915.39275819 -795.392758189999 38 7953 8554.9567097821 -601.956709782096 39 8878 9285.32389313345 -407.323893133447 40 8601 8315.66645620527 285.333543794732 41 8361 8053.8759117906 307.124088209405 42 9116 8022.83409647932 1093.16590352068 43 9310 8388.98157355441 921.01842644559 44 9891 8789.83347775561 1101.16652224439 45 10147 9640.70611858565 506.293881414345 46 10317 10695.2006147717 -378.200614771651 47 10682 10359.0748719003 322.925128099738 48 10276 10075.7969468298 200.203053170177 49 10614 10015.1052583161 598.894741683946 50 9413 10232.1749382142 -819.17493821419 51 11068 11257.6606109571 -189.660610957097 52 9772 10570.8562371889 -798.856237188917 53 10350 9927.91389587363 422.086104126372 54 10541 10324.4336543782 216.566345621834 55 10049 10328.6378459917 -279.637845991676 56 10714 10421.4859564639 292.514043536137 57 10759 10771.2971297291 -12.2971297291479 58 11684 11308.5917572169 375.40824278306 59 11462 11518.4855746003 -56.4855746003213 60 10485 11014.4682379027 -529.468237902713 61 11056 10864.7626485383 191.237351461694 62 10184 10296.9951938175 -112.995193817542 63 11082 11909.7085981216 -827.708598121644 64 10554 10689.2533019295 -135.253301929491 65 11315 10774.1326579238 540.867342076201 66 10847 11125.3832385839 -278.383238583918 67 11104 10728.8365580329 375.163441967126 68 11026 11299.9780402019 -273.978040201899 69 11073 11329.2175760589 -256.217576058913 70 12073 11962.4872741234 110.512725876644 71 12328 11880.2484368985 447.75156310145 72 11172 11292.4070319556 -120.407031955603 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 11590.8575216106 10900.3619127246 12281.3531304966 74 10782.2288339019 10032.7721662918 11531.6855015120 75 12188.3363145687 11340.7220168244 13035.9506123130 76 11478.7523584966 10588.1116369936 12369.3930799996 77 11926.2237523265 10952.7057488215 12899.7417558315 78 11738.7274116542 10709.7968571295 12767.6579661790 79 11703.5545918015 10612.3932662784 12794.7159173246 80 11882.9295313902 10716.3255212149 13049.5335415656 81 12015.2793557698 10775.2274279979 13255.3312835417 82 12956.6264585984 11578.1553862945 14335.0975309023 83 12979.2913692166 11533.8707929497 14424.7119454835 84 11938.9725026859 10703.1314317884 13174.8135735835

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t12596943910xgpwghmlm1htuf/1stf51259694359.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t12596943910xgpwghmlm1htuf/1stf51259694359.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t12596943910xgpwghmlm1htuf/275c31259694359.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t12596943910xgpwghmlm1htuf/275c31259694359.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t12596943910xgpwghmlm1htuf/3fuyw1259694359.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t12596943910xgpwghmlm1htuf/3fuyw1259694359.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

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