opgave10(oefening2)

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 11:07:54 -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/t1211908131dfni1imvxw6txbw.htm/, Retrieved Tue, 27 May 2008 19:08:51 +0200

User-defined keywords:

Inleiding tot kwantitatief onderzoek

Dataseries X:

» Textbox « » Textfile « » CSV «

107,5 107,5 113,3 107,8 104,5 105,1 104,2 106,6 103,8 107,7 106,4 110 113,2 113,9 112 113,9 113,1 111,7 110,7 113,5 114 112,7 112,2 115,8 118,4 118,8 123,9 118 120,2 118,7 119,8 124,8 121,3 120,2 118,3 129,6 130,2 127,19 133,1 129,12 123,28 123,36 124,13 126,96 127,14 123,7 123,67 130,19 134,01 124,96 129,96 128,32 132,38 126,25 128,91 131,42 129,44 126,86 126,71 131,63 132,78 126,61 132,84 123,14 128,13 125,49 126,48 130,86 127,32 126,56 126,64 129,26 126,47 135,38 135,5 132,22 122,62 125,16 128,5 133,86 128,87 125,07 125,25 132,16 130,24

Text written by user:

Kara Van den Acker

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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.209409698147397 beta 0.108381287029044 gamma 0.300287584116774 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 113.2 109.775928064425 3.42407193557545 14 113.9 111.283225694997 2.61677430500343 15 112 109.972664929298 2.02733507070204 16 113.9 112.40022142809 1.49977857191004 17 113.1 112.265228799386 0.834771200614057 18 111.7 111.368909961890 0.331090038109721 19 110.7 110.787274521677 -0.0872745216767044 20 113.5 113.958962582679 -0.458962582679035 21 114 114.461425076549 -0.461425076549176 22 112.7 113.178410302636 -0.478410302635695 23 112.2 112.877345775629 -0.677345775628766 24 115.8 116.524038337809 -0.724038337808935 25 118.4 121.764793423966 -3.36479342396572 26 118.8 121.673020616404 -2.87302061640438 27 123.9 118.764508189771 5.13549181022938 28 118 121.777885565704 -3.77788556570430 29 120.2 120.135047442862 0.0649525571383265 30 118.7 118.664268023442 0.0357319765576989 31 119.8 117.656939022347 2.14306097765316 32 124.8 121.242502118245 3.55749788175487 33 121.3 122.544992746328 -1.24499274632808 34 120.2 120.912761006353 -0.71276100635258 35 118.3 120.397980217044 -2.09798021704368 36 129.6 123.851446643917 5.74855335608321 37 130.2 130.187002469882 0.0129975301183265 38 127.19 131.061621092611 -3.87162109261138 39 133.1 129.868056158550 3.23194384145026 40 129.12 130.362799559793 -1.24279955979347 41 123.28 130.244471314226 -6.96447131422588 42 123.36 127.113206928932 -3.75320692893187 43 124.13 125.623117572303 -1.49311757230296 44 126.96 128.733258718716 -1.77325871871643 45 127.14 127.398746033049 -0.258746033049405 46 123.7 125.720577032665 -2.02057703266482 47 123.67 124.228710615527 -0.558710615527261 48 130.19 129.755932675317 0.434067324682786 49 134.01 133.269575901468 0.740424098532287 50 124.96 132.938970192895 -7.9789701928952 51 129.96 132.072407311814 -2.11240731181402 52 128.32 129.764534108095 -1.44453410809507 53 132.38 127.621555102042 4.75844489795772 54 126.25 127.341780942959 -1.09178094295946 55 128.91 126.654411068459 2.255588931541 56 131.42 130.330925027620 1.08907497238025 57 129.44 129.799105801815 -0.359105801815161 58 126.86 127.498202352423 -0.638202352422951 59 126.71 126.517963087675 0.192036912324724 60 131.63 132.463297611215 -0.833297611214817 61 132.78 135.719117079147 -2.93911707914731 62 126.61 132.290671591549 -5.6806715915494 63 132.84 133.170367078481 -0.330367078480549 64 123.14 131.254569897908 -8.11456989790811 65 128.13 128.916188809941 -0.786188809941109 66 125.49 125.729692385253 -0.239692385253207 67 126.48 125.652798144893 0.827201855107106 68 130.86 128.314450099391 2.54554990060947 69 127.32 127.401647275270 -0.0816472752695745 70 126.56 124.787447682793 1.77255231720679 71 126.64 124.231009814799 2.40899018520055 72 129.26 130.064637612067 -0.804637612066955 73 126.47 132.521887934877 -6.05188793487736 74 135.38 127.545468544750 7.83453145524955 75 135.5 132.496843374830 3.00315662517031 76 132.22 129.462322533542 2.75767746645801 77 122.62 131.469291974559 -8.84929197455872 78 125.16 126.821957640582 -1.66195764058216 79 128.5 126.791198046367 1.7088019536328 80 133.86 130.180891816246 3.67910818375356 81 128.87 128.992825158372 -0.122825158372166 82 125.07 126.913764603838 -1.84376460383797 83 125.25 125.791821816828 -0.54182181682782 84 132.16 130.238648392060 1.92135160793961 85 130.24 132.060014233799 -1.82001423379899 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 86 131.375554384317 128.674459266286 134.076649502349 87 133.497534448056 130.443377559773 136.551691336338 88 129.673844622614 126.288270108523 133.059419136705 89 128.160094092738 124.408137655013 131.912050530463 90 127.093142655933 122.954097234358 131.232188077509 91 128.284521302000 123.692535223561 132.876507380438 92 131.826550842537 126.690006781396 136.963094903677 93 128.910182569821 123.400144902906 134.420220236735 94 126.396098367387 120.500339684379 132.291857050395 95 125.958437923751 119.592311489528 132.324564357975 96 131.121477066829 124.01415631411 138.228797819549 97 131.609939131289 40.0240179663676 223.19586029621

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211908131dfni1imvxw6txbw/1u3rr1211908064.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211908131dfni1imvxw6txbw/1u3rr1211908064.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211908131dfni1imvxw6txbw/2eyjf1211908064.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211908131dfni1imvxw6txbw/2eyjf1211908064.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211908131dfni1imvxw6txbw/3eepl1211908064.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211908131dfni1imvxw6txbw/3eepl1211908064.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