Isabelle Regnard, oef 10, Exponential Smoothing, Koffie, thee, cacao

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 18 May 2011 12:41:55 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/18/t13057223327n8yflk0g48y1s9.htm/, Retrieved Wed, 18 May 2011 14:38:55 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

106,42 106,22 106,32 105,81 105,92 107,54 107,34 107,24 107,74 105,71 105,41 106,22 106,32 106,12 106,22 105,92 105,71 105,71 105,92 105,71 105,41 104,49 101,35 99,72 99,01 97,89 95,86 94,95 95,35 95,15 95,46 95,56 95,05 94,64 93,63 93,12 93,53 97,18 96,27 95,15 97,08 101,95 103,07 103,68 102,87 102,56 103,38 103,27 102,89 102,69 101,54 102,9 101,53 101,96 101,99 101,11 101,75 101,71 104,11 103,57 103,32 103,64 103,68 103,79 103,01 101,54 101,9 103,68 104,62 104,11 105,04 104,83 105,05 104,68 107,32 109,9 109,77 110,69 110,54 110,89 110,95 109,73 110,85 110,39 110,58 110,4 111,07 110,86 111,38 111,44 110,36 110,06 108,34 107,94 107,39 107,1 107,61 107,74 106,9 106,71 106,6 108,21 110,54 110,91 109,51 110,27 111,39 112,13 111,64

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 'Gwilym Jenkins' @ www.wessa.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.0295881156175766 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 106.32 106.02 0.299999999999997 4 105.81 106.128876434685 -0.318876434685265 5 105.92 105.609441481868 0.310558518131913 6 107.54 105.728630323209 1.81136967679141 7 107.34 107.402225338632 -0.0622253386316771 8 107.24 107.200384208118 0.039615791882099 9 107.74 107.101556364748 0.638443635251619 10 105.71 107.620446708844 -1.91044670884351 11 105.41 105.533920190741 -0.123920190741032 12 106.22 105.23025362581 0.989746374189963 13 106.32 106.069538355962 0.250461644038353 14 106.12 106.176949044043 -0.0569490440432077 15 106.22 105.975264029144 0.24473597085624 16 105.92 106.082505305345 -0.162505305345235 17 105.71 105.777697079582 -0.0676970795822172 18 105.71 105.565694050565 0.144305949435449 19 105.92 105.569963791681 0.350036208319253 20 105.71 105.790320703483 -0.0803207034828546 21 105.41 105.577944165222 -0.167944165221712 22 104.49 105.272975013844 -0.782975013843838 23 101.35 104.329808258609 -2.97980825860854 24 99.72 101.101641347335 -1.38164134733462 25 99.01 99.4307611834077 -0.420761183407663 26 97.89 98.7083116528656 -0.818311652865617 27 95.86 97.5640993530694 -1.70409935306941 28 94.95 95.483678264387 -0.53367826438695 29 95.35 94.5578877301977 0.792112269802303 30 95.15 94.9813248396187 0.168675160381312 31 95.46 94.786315619766 0.673684380234107 32 95.56 95.116248671098 0.44375132890201 33 95.05 95.229378436723 -0.179378436723013 34 94.64 94.714070966798 -0.0740709667979473 35 93.63 94.3018793464684 -0.67187934646843 36 93.12 93.271999702684 -0.151999702684037 37 93.53 92.7575023179072 0.77249768209279 38 97.18 93.1903590686393 3.98964093136074 39 96.27 96.958405025789 -0.688405025788995 40 95.15 96.0280364182942 -0.878036418294215 41 97.08 94.8820569752333 2.1979430247667 42 101.95 96.877089967571 5.07291003242906 43 103.07 101.897187816128 1.17281218387198 44 103.68 103.051889118622 0.628110881377893 45 102.87 103.680473736001 -0.810473736000986 46 102.56 102.846493345395 -0.286493345395172 47 103.38 102.528016547168 0.85198345283203 48 103.27 103.373225132075 -0.103225132074613 49 102.89 103.260170894932 -0.370170894932144 50 102.69 102.869218235695 -0.179218235694634 51 101.54 102.663915505816 -1.12391550581611 52 102.9 101.480660963886 1.41933903611435 53 101.53 102.882656531387 -1.35265653138674 54 101.96 101.472633973545 0.487366026454794 55 101.99 101.917054215884 0.0729457841159729 56 101.11 101.949212544178 -0.839212544178253 57 101.75 101.044381826393 0.70561817360661 58 101.71 101.705259738496 0.00474026150406814 59 104.11 101.665399993901 2.44460000609864 60 103.57 104.137731101521 -0.56773110152055 61 103.32 103.580933008049 -0.260933008049065 62 103.64 103.323212492038 0.31678750796155 63 103.68 103.65258563745 0.0274143625497771 64 103.79 103.693396776779 0.0966032232210665 65 103.01 103.806255084117 -0.796255084116638 66 101.54 103.002695396627 -1.46269539662671 67 101.9 101.489416996118 0.410583003881982 68 103.68 101.861565373508 1.8184346264925 69 104.62 103.695369427479 0.92463057252084 70 104.11 104.662727503762 -0.552727503762455 71 105.04 104.136373338476 0.903626661523901 72 104.83 105.093109948612 -0.26310994861241 73 105.05 104.875325021033 0.174674978967275 74 104.68 105.100493324506 -0.420493324505898 75 107.32 104.718051719404 2.60194828059598 76 109.9 107.435038465961 2.46496153403878 77 109.77 110.087972032823 -0.317972032823263 78 110.69 109.948563839553 0.74143616044708 79 110.54 110.890501538391 -0.350501538391271 80 110.89 110.730130858349 0.159869141650773 81 110.95 111.084861084996 -0.134861084996075 82 109.73 111.140870799621 -1.41087079962089 83 110.85 109.87912579128 0.970874208719735 84 110.39 111.027852129618 -0.637852129617968 85 110.58 110.54897928706 0.0310207129400766 86 110.4 110.739897131501 -0.339897131500919 87 111.07 110.549840215876 0.52015978412399 88 110.86 111.235230763708 -0.375230763708259 89 111.38 111.014128392488 0.365871607511593 90 111.44 111.544953843913 -0.104953843912639 91 110.36 111.601848457444 -1.24184845744445 92 110.06 110.485104501706 -0.425104501706073 93 108.34 110.17252646056 -1.83252646056003 94 107.94 108.398305455773 -0.458305455772731 95 107.39 107.984745060959 -0.594745060959141 96 107.1 107.417147675333 -0.317147675332521 97 107.61 107.117763873247 0.492236126753085 98 107.74 107.642328212676 0.0976717873235486 99 106.9 107.775218136812 -0.875218136812336 100 106.71 106.90932208139 -0.199322081389752 101 106.6 106.7134245166 -0.113424516600446 102 108.21 106.600068498889 1.60993150111059 103 110.54 108.257703338281 2.28229666171937 104 110.91 110.655232195781 0.254767804218787 105 109.51 111.032770295028 -1.52277029502805 106 110.27 109.58771439148 0.682285608520218 107 111.39 110.367901936949 1.02209806305113 108 112.13 111.518143892611 0.611856107389059 109 111.64 112.276247561858 -0.636247561857672 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 110 111.767422195436 109.553005633928 113.981838756944 111 111.894844390872 108.71651883852 115.073169943224 112 112.022266586308 108.072212956841 115.972320215776 113 112.149688781744 107.521974698767 116.777402864722 114 112.27711097718 107.028417707404 117.525804246956 115 112.404533172616 106.572668998615 118.236397346617 116 112.531955368052 106.143692725182 118.920218010922 117 112.659377563488 105.734412116629 119.584343010347 118 112.786799758924 105.339990634824 120.233608883025 119 112.91422195436 104.95696460555 120.871479303171 120 113.041644149796 104.582763169281 121.500525130312 121 113.169066345232 104.215423468622 122.122709221842

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/18/t13057223327n8yflk0g48y1s9/1u4q51305722512.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057223327n8yflk0g48y1s9/1u4q51305722512.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057223327n8yflk0g48y1s9/2uugm1305722512.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057223327n8yflk0g48y1s9/2uugm1305722512.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057223327n8yflk0g48y1s9/3qpkz1305722512.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057223327n8yflk0g48y1s9/3qpkz1305722512.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=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) 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