exponential smoothing - Bisocoop - Evy Heynen

R Software Module: rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Tue, 27 May 2008 06:03:46 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/27/t1211889904lzvqkz7bn9spdy7.htm/, Retrieved Tue, 27 May 2008 14:05:04 +0200

User-defined keywords:

exponential smoothing - Bisocoop - Evy Heynen

Dataseries X:

» Textbox « » Textfile « » CSV «

5,44 5,44 5,44 5,44 5,49 5,49 5,49 5,49 5,49 5,49 5,6 5,6 5,6 5,6 5,6 5,6 5,6 5,67 5,67 5,67 5,67 5,67 5,67 5,67 5,67 5,67 5,82 5,82 5,95 5,95 5,95 5,95 5,95 5,95 6,02 6,02 6,05 6,05 6,05 6,12 6,12 6,12 6,12 6,12 6,12 6,12 6,12 6,17 6,17 6,17 6,17 6,17 6,28 6,27 6,28 6,28 6,27 6,27 6,28 6,59 6,59 6,59 6,59 6,59 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,63 6,79 6,79 6,79

Text written by user:

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 3 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.91195083019207 beta 0.0325127367673738 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 5.44 5.44 0 4 5.44 5.44 0 5 5.49 5.44 0.0499999999999998 6 5.49 5.48708004237394 0.00291995762605524 7 5.49 5.49131197781358 -0.00131197781358239 8 5.49 5.49164569605087 -0.00164569605087017 9 5.49 5.49162628474826 -0.00162628474825599 10 5.49 5.49157635622828 -0.00157635622827712 11 5.6 5.49152522107412 0.108474778925875 12 5.6 5.59505158905772 0.0049484109422826 13 5.6 5.60431372028188 -0.00431372028188459 14 5.6 5.6050013413659 -0.00500134136589558 15 5.6 5.60491359597353 -0.00491359597352936 16 5.6 5.60476018185902 -0.00476018185902127 17 5.6 5.60460553439919 -0.00460553439919398 18 5.67 5.60445536364419 0.065544636355809 19 5.67 5.67022209894834 -0.000222098948337468 20 5.67 5.67600622015519 -0.00600622015518759 21 5.67 5.67633742269409 -0.00633742269408888 22 5.67 5.67617868011024 -0.0061786801102448 23 5.67 5.67598150498544 -0.00598150498544481 24 5.67 5.67578679215318 -0.00578679215318001 25 5.67 5.67559806936257 -0.00559806936257168 26 5.67 5.67541546962416 -0.00541546962416195 27 5.82 5.67523882310082 0.144761176899185 28 5.82 5.81630806544742 0.00369193455258365 29 5.95 5.82883856104477 0.121161438955226 30 5.95 5.95208790746389 -0.00208790746389109 31 5.95 5.96287800360307 -0.0128780036030669 32 5.95 5.96344622958082 -0.0134462295808184 33 5.95 5.96309758046691 -0.0130975804669085 34 5.95 5.96267853871462 -0.0126785387146153 35 6.02 5.96226572354415 0.0577342764558484 36 6.02 6.02777775591951 -0.00777775591951091 37 6.05 6.03331542538513 0.0166845746148745 38 6.05 6.06165623541576 -0.0116562354157601 39 6.05 6.06380601262907 -0.0138060126290656 40 6.12 6.06358595021485 0.056414049785146 41 6.12 6.12907580956677 -0.00907580956677112 42 6.12 6.134573039403 -0.0145730394029986 43 6.12 6.1346249750561 -0.0146249750561012 44 6.12 6.13419591718401 -0.0141959171840087 45 6.12 6.13373722980466 -0.0137372298046632 46 6.12 6.13328953366053 -0.0132895336605294 47 6.12 6.13285607948394 -0.0128560794839432 48 6.17 6.1324367312246 0.0375632687753944 49 6.17 6.17911110103665 -0.00911110103665358 50 6.17 6.18295059624667 -0.0129505962466743 51 6.17 6.18290467520981 -0.0129046752098096 52 6.17 6.18251800805758 -0.0125180080575849 53 6.28 6.18211280318054 0.0978871968194639 54 6.27 6.28529407362649 -0.0152940736264933 55 6.28 6.28480612097965 -0.00480612097965416 56 6.28 6.29374016388599 -0.0137401638859860 57 6.27 6.29411940285017 -0.0241194028501743 58 6.27 6.28431814551275 -0.0143181455127532 59 6.28 6.28303061967915 -0.00303061967915053 60 6.59 6.29194690447444 0.298053095525558 61 6.59 6.5842740127427 0.00572598725729812 62 6.59 6.61018294755924 -0.0201829475592383 63 6.59 6.61186578301641 -0.0218657830164117 64 6.59 6.61136563443691 -0.0213656344369131 65 6.63 6.61068810533931 0.0193118946606905 66 6.63 6.64767908068296 -0.0176790806829583 67 6.63 6.65041192030449 -0.020411920304487 68 6.63 6.6500473307745 -0.0200473307744948 69 6.63 6.64942082526504 -0.0194208252650405 70 6.63 6.64878983417022 -0.0187898341702208 71 6.63 6.6481771570202 -0.0181771570202010 72 6.63 6.64758425828591 -0.0175842582859076 73 6.63 6.64701068048242 -0.0170106804824197 74 6.63 6.64645581046264 -0.016455810462638 75 6.63 6.64591903955336 -0.0159190395533590 76 6.63 6.64539977752247 -0.0153997775224735 77 6.63 6.64489745326199 -0.0148974532619865 78 6.63 6.64441151428113 -0.0144115142811287 79 6.63 6.64394142610972 -0.0139414261097217 80 6.63 6.64348667171134 -0.0134866717113376 81 6.63 6.64304675091471 -0.0130467509147101 82 6.79 6.64262117986363 0.147378820136373 83 6.79 6.79286562608137 -0.00286562608137153 84 6.79 6.80600955897625 -0.0160095589762461 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 6.80669218765525 6.71167166030342 6.90171271500708 86 6.82197474693365 6.69146025095177 6.95248924291554 87 6.83725730621205 6.67740972064516 6.99710489177895 88 6.85253986549045 6.66653871897092 7.03854101200999 89 6.86782242476886 6.6576191032339 7.07802574630381 90 6.88310498404726 6.6500081044399 7.11620186365461 91 6.89838754332566 6.64332194737134 7.15345313927997 92 6.91367010260406 6.6373112411707 7.19002896403742 93 6.92895266188246 6.63180401813626 7.22610130562866 94 6.94423522116086 6.6266763733235 7.26179406899823 95 6.95951778043926 6.62183596066007 7.29719960021845 96 6.97480033971766 6.61721208455978 7.33238859487555

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211889904lzvqkz7bn9spdy7/16gjk1211889819.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211889904lzvqkz7bn9spdy7/16gjk1211889819.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211889904lzvqkz7bn9spdy7/29rrr1211889819.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211889904lzvqkz7bn9spdy7/29rrr1211889819.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211889904lzvqkz7bn9spdy7/3gxti1211889819.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211889904lzvqkz7bn9spdy7/3gxti1211889819.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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