Opgave 10 - Robbert Van Hees

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 18 Aug 2009 06:28:25 -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/Aug/18/t1250598570gtugqkd9gsy8r0f.htm/, Retrieved Tue, 18 Aug 2009 14:29:34 +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/Aug/18/t1250598570gtugqkd9gsy8r0f.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 «

12.11 11.42 11.71 12.04 12.21 12 12.36 12.32 12.96 12.79 13.19 12.34 13.25 12.54 12.77 12.96 13 13.61 13.8 14.16 14.27 14.69 15.01 15.09 15.14 14.2 13.83 14.31 14.04 14.9 14.92 15.36 15.5 15.65 16.18 15.44 15.58 15.24 15.33 16.07 15.82 15.87 15.72 17.07 16.83 17.52 17.76 17.36 17.95 16.71 17.14 16.72 17.26 17.24 17.69 18.13 18.08 18.18 18.18 17.64 17.89 16.82 16.61 16.66 17.02 16.91 17.18 18.06 17.58 17.48 17.54 17.44 17.79 16.79 16.19 16.62 16.39 16.54 17.26 18 17.29 18.16 17.82 17.48 18.31 17.04 17.03 16.97 17.11 17.12 17.69 18.5 18.27 18.45 18.35 18.03 18.49 18.07 17.8 17.88 18.12 18.68 18.8 19.64 19.56 19.3 20.07 19.82 20.29 19.36 18.74 18.87 18.87 18.91 19.31 20.06 20.72 20.42 20.58 20.58 21.18 19.87 19.83 19.48 19.49 19.4 19.89 20.44 20.07 19.75 19.54 19.07

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 5 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.459863297921987 beta 0.146965751748968 gamma 0.668062732641707 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 13.25 12.653919734621 0.596080265378989 14 12.54 12.2569966494964 0.283003350503645 15 12.77 12.6590897031678 0.110910296832230 16 12.96 12.9483127697628 0.0116872302372268 17 13 13.0220852317476 -0.0220852317476012 18 13.61 13.6147159025095 -0.00471590250949383 19 13.8 13.8609842107814 -0.0609842107813989 20 14.16 13.8605075801446 0.299492419855431 21 14.27 14.8243506935806 -0.554350693580581 22 14.69 14.4491988086156 0.240801191384367 23 15.01 15.1167772122287 -0.106777212228696 24 15.09 14.1521778767687 0.937822123231348 25 15.14 16.0103777873678 -0.87037778736779 26 14.2 14.6735890306251 -0.473589030625059 27 13.83 14.6445012348439 -0.814501234843888 28 14.31 14.3853483127609 -0.0753483127608661 29 14.04 14.2990182191282 -0.259018219128231 30 14.9 14.7131055352171 0.186894464782881 31 14.92 14.9292764810236 -0.00927648102361367 32 15.36 14.9816541140753 0.3783458859247 33 15.5 15.5982526686552 -0.0982526686552312 34 15.65 15.6543455758710 -0.00434557587102091 35 16.18 16.0177218598778 0.162278140122247 36 15.44 15.4314241465585 0.00857585344152056 37 15.58 16.0895502007709 -0.509550200770947 38 15.24 14.9236134216439 0.316386578356092 39 15.33 15.0755570300789 0.254442969921053 40 16.07 15.6248007149800 0.445199285020028 41 15.82 15.748602725672 0.0713972743280014 42 15.87 16.6352319471215 -0.765231947121494 43 15.72 16.3611111036762 -0.641111103676197 44 17.07 16.2474982617157 0.822501738284338 45 16.83 16.917836124607 -0.0878361246069908 46 17.52 17.0236490021358 0.496350997864212 47 17.76 17.7528673668786 0.00713263312136547 48 17.36 16.9884055360909 0.371594463909055 49 17.95 17.7195593582415 0.230440641758491 50 16.71 17.1946888973513 -0.48468889735134 51 17.14 16.9886613300307 0.151338669969302 52 16.72 17.6423396096089 -0.922339609608947 53 17.26 16.9237821574691 0.336217842530939 54 17.24 17.6221348011800 -0.382134801180047 55 17.69 17.5574053086713 0.132594691328741 56 18.13 18.4378311485022 -0.307831148502228 57 18.08 18.2148297569720 -0.134829756972028 58 18.18 18.4900082689929 -0.31000826899286 59 18.18 18.5890863468764 -0.409086346876393 60 17.64 17.6202364179753 0.0197635820246767 61 17.89 18.0030216263282 -0.113021626328223 62 16.82 16.9021048390842 -0.0821048390841916 63 16.61 16.9817522037394 -0.37175220373943 64 16.66 16.8337121745102 -0.173712174510214 65 17.02 16.7959765021331 0.224023497866892 66 16.91 17.0542823246001 -0.144282324600134 67 17.18 17.1703520047632 0.00964799523681137 68 18.06 17.6965530542373 0.363446945762703 69 17.58 17.7695492764780 -0.189549276478036 70 17.48 17.8694792625431 -0.389479262543137 71 17.54 17.8026563417840 -0.262656341783977 72 17.44 17.0011431127419 0.438856887258133 73 17.79 17.4736788419357 0.316321158064323 74 16.79 16.5809548350985 0.209045164901493 75 16.19 16.6907879978106 -0.500787997810566 76 16.62 16.5463949705615 0.073605029438454 77 16.39 16.7740268297144 -0.384026829714369 78 16.54 16.5876713347055 -0.0476713347055444 79 17.26 16.77298659296 0.487013407040003 80 18 17.6455421345448 0.354457865455206 81 17.29 17.5241602188327 -0.234160218832717 82 18.16 17.5321505711483 0.627849428851711 83 17.82 18.0540695375838 -0.234069537583849 84 17.48 17.5823081803749 -0.102308180374898 85 18.31 17.8000254158002 0.509974584199846 86 17.04 16.9855631712916 0.0544368287083898 87 17.03 16.7972232028239 0.232776797176061 88 16.97 17.2957964015063 -0.325796401506281 89 17.11 17.2340747384349 -0.124074738434860 90 17.12 17.3728886947149 -0.252888694714855 91 17.69 17.7388732154873 -0.0488732154873048 92 18.5 18.3653024655593 0.134697534440697 93 18.27 17.9305064814485 0.339493518551457 94 18.45 18.5827839427230 -0.132783942722952 95 18.35 18.4428550695268 -0.0928550695268093 96 18.03 18.0850429512244 -0.0550429512244115 97 18.49 18.5733969603524 -0.083396960352406 98 18.07 17.2763988455062 0.793601154493786 99 17.8 17.5109047825453 0.289095217454715 100 17.88 17.8677390700958 0.0122609299041692 101 18.12 18.093145156335 0.0268548436649958 102 18.68 18.3245029063218 0.355497093678242 103 18.8 19.1932883024889 -0.393288302488916 104 19.64 19.8673950560483 -0.227395056048291 105 19.56 19.3697587398674 0.190241260132566 106 19.3 19.8544358722569 -0.554435872256892 107 20.07 19.5525813239502 0.517418676049843 108 19.82 19.5271298648397 0.292870135160292 109 20.29 20.2975602736362 -0.00756027363622636 110 19.36 19.3420123035072 0.0179876964928205 111 18.74 19.0419942751055 -0.301994275105546 112 18.87 19.0247659626135 -0.154765962613478 113 18.87 19.1707321350768 -0.300732135076778 114 18.91 19.3426550929002 -0.43265509290018 115 19.31 19.4930379739120 -0.183037973912040 116 20.06 20.2638669442370 -0.203866944236960 117 20.72 19.8396260745132 0.880373925486779 118 20.42 20.3382199175224 0.081780082477632 119 20.58 20.7368883577538 -0.15688835775385 120 20.58 20.2689537763939 0.311046223606109 121 21.18 20.9176303002009 0.262369699799141 122 19.87 20.0406803843038 -0.170680384303758 123 19.83 19.4930507727502 0.336949227249828 124 19.48 19.8416369217171 -0.361636921717107 125 19.49 19.8436897697541 -0.353689769754098 126 19.4 19.9475753366679 -0.547575336667904 127 19.89 20.1393742194867 -0.249374219486661 128 20.44 20.8851028594458 -0.445102859445761 129 20.07 20.7039113347433 -0.633911334743274 130 19.75 20.0860800097087 -0.336080009708688 131 19.54 20.0380452364186 -0.498045236418633 132 19.07 19.4085519085413 -0.338551908541341 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 133 19.4830364281475 18.891837303645 20.0742355526500 134 18.1911958431426 17.500343871551 18.8820478147342 135 17.7164085421561 16.9132205040403 18.5195965802719 136 17.4334754083866 16.508098326319 18.3588524904541 137 17.3768703641924 16.3143342284591 18.4394064999258 138 17.3610177910097 16.1510846499415 18.5709509320780 139 17.6913643405494 16.3034768885111 19.0792517925878 140 18.2401416855529 16.6438731301956 19.8364102409103 141 18.0735224924664 16.312890146758 19.8341548381748 142 17.7914169944171 15.8727040699339 19.7101299189004 143 17.7674355955275 15.6599021563648 19.8749690346902 144 17.4220739435082 12.6421985779019 22.2019493091146

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250598570gtugqkd9gsy8r0f/1erki1250598500.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250598570gtugqkd9gsy8r0f/1erki1250598500.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250598570gtugqkd9gsy8r0f/2o1h71250598500.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250598570gtugqkd9gsy8r0f/2o1h71250598500.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250598570gtugqkd9gsy8r0f/3m0ty1250598500.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/18/t1250598570gtugqkd9gsy8r0f/3m0ty1250598500.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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