Opgave 10, oefening 1, stap 1, Sara Vandenberghe

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 04 Jul 2009 10:12:31 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jul/04/t1246724012akhcjz19dg5jdtk.htm/, Retrieved Sat, 04 Jul 2009 18:13:32 +0200

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/Jul/04/t1246724012akhcjz19dg5jdtk.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 «

9.26 9.29 9.28 9.31 9.27 9.27 9.28 9.25 9.32 9.33 9.31 9.3 9.29 9.33 9.35 9.35 9.37 9.37 9.35 9.33 9.34 9.37 9.33 9.31 9.26 9.27 9.29 9.27 9.29 9.31 9.33 9.35 9.34 9.35 9.38 9.43 9.47 9.5 9.55 9.58 9.61 9.57 9.61 9.65 9.62 9.63 9.62 9.63 9.65 9.72 9.75 9.77 9.78 9.82 9.84 9.9 9.94 9.96 10.03 10.03 10.12 10.12 10.05 10.14 10.17 10.2 10.2 10.35 10.43 10.52 10.57 10.57 10.57 10.65 10.57 10.61 10.63 10.71 10.72 10.77 10.79 10.82 10.9 10.83 10.92 10.91 10.88 10.87 11 10.99 11.03 11.04 10.99 10.9 11 10.99 10.92 10.98 11.15 11.19 11.33 11.38 11.4 11.45 11.56 11.61 11.82 11.77 11.85 11.82 11.92 11.86 11.87 11.94 11.86 11.92 11.83 11.91 11.93 11.99 11.96 12.12 11.85 12.01 12.1 12.21 12.31 12.31 12.39 12.35 12.41 12.51

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.796863822577094 beta 0.0468032585328228 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 9.28 9.32 -0.0399999999999991 4 9.31 9.31663361415677 -0.00663361415677244 5 9.27 9.33960828797938 -0.0696082879793831 6 9.27 9.3098046240713 -0.0398046240712997 7 9.28 9.30226587547783 -0.022265875477828 8 9.25 9.3078726969698 -0.0578726969697936 9 9.32 9.282947320686 0.0370526793140051 10 9.33 9.3350464527953 -0.00504645279530003 11 9.31 9.35341009795203 -0.0434100979520338 12 9.3 9.3395841268297 -0.0395841268296913 13 9.29 9.32733061107319 -0.0373306110731892 14 9.33 9.31548056461478 0.0145194353852176 15 9.35 9.34548945867752 0.00451054132247819 16 9.35 9.36769085151072 -0.0176908515107250 17 9.37 9.37154096270876 -0.00154096270875748 18 9.37 9.3882028645585 -0.0182028645585071 19 9.35 9.39090860878503 -0.0409086087850277 20 9.33 9.37399524661972 -0.0439952466197244 21 9.34 9.35298141547763 -0.0129814154776309 22 9.37 9.3561972317917 0.0138027682082935 23 9.33 9.38127118070931 -0.0512711807093105 24 9.31 9.3525778530357 -0.0425778530356951 25 9.26 9.32922394759101 -0.0692239475910146 26 9.27 9.28205496925066 -0.0120549692506593 27 9.29 9.27999228151791 0.0100077184820861 28 9.27 9.29588379757039 -0.0258837975703887 29 9.29 9.28220930539741 0.00779069460258519 30 9.31 9.2956593581516 0.0143406418483938 31 9.33 9.31486367295308 0.0151363270469229 32 9.35 9.33526656228545 0.0147334377145487 33 9.34 9.35589789937695 -0.0158978993769541 34 9.35 9.35152730685384 -0.00152730685383595 35 9.38 9.35855115745453 0.0214488425454693 36 9.43 9.3846838225396 0.0453161774604087 37 9.47 9.43152560751611 0.0384743924838880 38 9.5 9.47435035571448 0.0256496442855205 39 9.55 9.5079121506461 0.0420878493538925 40 9.58 9.55614265750597 0.0238573424940292 41 9.61 9.59073571221689 0.0192642877831144 42 9.57 9.62238720527064 -0.0523872052706356 43 9.61 9.5949883917146 0.0150116082853984 44 9.65 9.6218571246591 0.0281428753408957 45 9.62 9.66023930097633 -0.0402393009763298 46 9.63 9.64262943701015 -0.0126294370101476 47 9.62 9.64654984953122 -0.0265498495312162 48 9.63 9.63838739041673 -0.00838739041673264 49 9.65 9.64438512326698 0.00561487673301997 50 9.72 9.66175016769455 0.0582498323054477 51 9.75 9.72323057948552 0.0267694205144799 52 9.77 9.76062377758323 0.0093762224167655 53 9.78 9.78450665929435 -0.0045066592943499 54 9.82 9.79715869524713 0.0228413047528733 55 9.84 9.83245521964093 0.00754478035907091 56 9.9 9.85584388593079 0.0441561140692137 57 9.94 9.91005363818748 0.0299463618125184 58 9.96 9.95405702716777 0.00594297283223533 59 10.03 9.97915463191625 0.0508453680837455 60 10.03 10.0419296508618 -0.0119296508617524 61 10.12 10.054236602095 0.065763397905009 62 10.12 10.1309070332374 -0.0109070332374390 63 10.05 10.1460747847545 -0.09607478475451 64 10.14 10.0897922480221 0.0502077519779505 65 10.17 10.1519495121428 0.0180504878572290 66 10.2 10.1891550236619 0.0108449763380918 67 10.2 10.2210231960517 -0.0210231960516882 68 10.35 10.2267126973630 0.123287302637022 69 10.43 10.3519961157767 0.0780038842232642 70 10.52 10.4441040353925 0.0758959646074704 71 10.57 10.5373628326262 0.0326371673737729 72 10.57 10.5973674893702 -0.0273674893702189 73 10.57 10.6085359129155 -0.0385359129154814 74 10.65 10.6093673951757 0.0406326048243368 75 10.57 10.6748008315678 -0.104800831567776 76 10.61 10.6204349905888 -0.0104349905887720 77 10.63 10.6408766928057 -0.0108766928057378 78 10.71 10.6605607632905 0.0494392367095315 79 10.72 10.7301522929775 -0.0101522929774944 80 10.77 10.7518788503979 0.0181211496021429 81 10.79 10.7968113345469 -0.00681133454688698 82 10.82 10.8216219897395 -0.00162198973949046 83 10.9 10.8505073526289 0.0494926473710606 84 10.83 10.9219699896770 -0.0919699896770165 85 10.92 10.8772760725125 0.0427239274874882 86 10.91 10.9415082891165 -0.0315082891165481 87 10.88 10.9454124102493 -0.0654124102493316 88 10.87 10.9198599541075 -0.0498599541075304 89 11 10.9048411195691 0.0951588804309438 90 10.99 11.0089315766759 -0.0189315766759321 91 11.03 11.0214014072707 0.00859859272929064 92 11.04 11.0561297254907 -0.0161297254907353 93 10.99 11.0705513701330 -0.0805513701329836 94 10.9 11.0306335070855 -0.130633507085461 95 11 10.9459349167193 0.0540650832807472 96 10.99 11.0104323529006 -0.0204323529006025 97 10.92 11.0148034358867 -0.0948034358867478 98 10.98 10.956375121183 0.0236248788170048 99 11.15 10.9931991553461 0.156800844653912 100 11.19 11.1419943153488 0.0480056846512067 101 11.33 11.2058849598158 0.124115040184229 102 11.38 11.3350533688995 0.0449466311004816 103 11.4 11.4028116585140 -0.0028116585140463 104 11.45 11.4324082317869 0.0175917682130962 105 11.56 11.4789196571576 0.0810803428423856 106 11.61 11.5790467889536 0.0309532110463522 107 11.82 11.6403838483879 0.179616151612080 108 11.77 11.8268839592059 -0.056883959205857 109 11.85 11.8228041535748 0.0271958464252169 110 11.82 11.8867387947487 -0.0667387947487281 111 11.92 11.8733312403746 0.0466687596253887 112 11.86 11.9520346131103 -0.0920346131102896 113 11.87 11.9167777793567 -0.0467777793567006 114 11.94 11.9158398633430 0.0241601366570414 115 11.86 11.9723308784422 -0.112330878442163 116 11.92 11.9158676688856 0.00413233111438949 117 11.83 11.9523638963778 -0.122363896377792 118 11.91 11.8834961942065 0.0265038057935403 119 11.93 11.9342442595087 -0.00424425950869356 120 11.99 11.9603320108038 0.0296679891962022 121 11.96 12.0145496983228 -0.0545496983228375 122 12.12 11.9996228815160 0.120377118483965 123 11.85 12.1285784803860 -0.278578480385983 124 12.01 11.9292309818655 0.0807690181344665 125 12.1 12.0192468516945 0.0807531483054973 126 12.21 12.1122618305975 0.0977381694025485 127 12.31 12.2224567838539 0.0875432161460559 128 12.31 12.3277927440258 -0.0177927440257886 129 12.39 12.3485266932794 0.0414733067205599 130 12.35 12.4180343954074 -0.068034395407432 131 12.41 12.3977419726128 0.0122580273872064 132 12.51 12.4418888499962 0.0681111500037979 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 133 12.5330833215999 12.4160261649205 12.6501404782793 134 12.5700024818514 12.4175662713761 12.7224386923268 135 12.606921642103 12.4235017450026 12.7903415392034 136 12.6438408023545 12.4318061860312 12.8558754186779 137 12.6807599626061 12.4415479702433 12.9199719549688 138 12.7176791228576 12.4522133540860 12.9831448916292 139 12.7545982831092 12.4634868109164 13.0457097553019 140 12.7915174433607 12.4751601433450 13.1078747433765 141 12.8284366036123 12.4870887606319 13.1697844465926 142 12.8653557638638 12.4991683329362 13.2315431947915 143 12.9022749241154 12.5113213275284 13.2932285207023 144 12.9391940843669 12.5234887684558 13.3548994002781

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jul/04/t1246724012akhcjz19dg5jdtk/1jm3r1246723946.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jul/04/t1246724012akhcjz19dg5jdtk/1jm3r1246723946.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jul/04/t1246724012akhcjz19dg5jdtk/24dqs1246723946.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jul/04/t1246724012akhcjz19dg5jdtk/24dqs1246723946.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jul/04/t1246724012akhcjz19dg5jdtk/34fvv1246723946.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jul/04/t1246724012akhcjz19dg5jdtk/34fvv1246723946.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; 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