exponentiële smoothing - prijsindex ijzererts - Karen de maere

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 24 May 2008 11:10:53 -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/24/t1211649117kazyfr7t17iqj1n.htm/, Retrieved Sat, 24 May 2008 19:12:01 +0200

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

229,7 231,5 226,4 242,1 228,3 209,9 209,3 220,8 239,6 241,1 241,9 240,8 179,9 190,8 174,2 170 170,3 159,3 147,9 154,2 164,5 173,9 163,6 149,7 128,2 124,7 125,1 120,9 117,5 114 113,4 118,9 121,7 121,9 120,3 115,6 105,7 105,1 104,6 105 104,9 105,1 103,9 101,9 99 97 95,8 94,7 97,6 97,9 99,3 99,7 99,7 100 99,1 98,2 98,1 98,6 100,2 101,9 97,5 97,1 98,1 98,5 98,3 99,3 100,9 100,4 101,7 102 103,2 103,1

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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.72476947564924 beta 0.0542023038794262 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 179.9 209.963722222222 -30.0637222222223 14 190.8 198.354490712747 -7.55449071274671 15 174.2 175.833324517067 -1.63332451706680 16 170 169.964475033511 0.0355249664891630 17 170.3 169.939885617436 0.360114382564149 18 159.3 159.860528832139 -0.560528832139084 19 147.9 147.583564700591 0.316435299408568 20 154.2 152.612961635955 1.58703836404527 21 164.5 162.517265048299 1.98273495170139 22 173.9 171.177914043199 2.72208595680084 23 163.6 160.935523647130 2.66447635287039 24 149.7 146.997717991587 2.70228200841314 25 128.2 106.560682276992 21.6393177230075 26 124.7 139.572563048663 -14.8725630486633 27 125.1 114.042782182654 11.0572178173459 28 120.9 118.995121323968 1.90487867603244 29 117.5 121.652307942916 -4.152307942916 30 114 109.10941790218 4.89058209782003 31 113.4 102.299084098525 11.1009159014746 32 118.9 117.192575779593 1.70742422040669 33 121.7 128.995891871199 -7.29589187119883 34 121.9 132.473517036474 -10.5735170364740 35 120.3 113.395066412244 6.90493358775596 36 115.6 103.523645762583 12.0763542374170 37 105.7 76.443580197618 29.2564198023820 38 105.1 106.577029999478 -1.47702999947767 39 104.6 100.068932290961 4.53106770903867 40 105 99.6922820234182 5.30771797658178 41 104.9 105.202265868580 -0.302265868580420 42 105.1 100.143539718704 4.95646028129627 43 103.9 97.2977053586868 6.60229464131319 44 101.9 108.376112918518 -6.47611291851804 45 99 113.479535063656 -14.4795350636563 46 97 112.275640310766 -15.2756403107663 47 95.8 95.842186246003 -0.0421862460029701 48 94.7 83.3284749896605 11.3715250103395 49 97.6 61.4077975096935 36.1922024903065 50 97.9 89.32352223331 8.57647776669005 51 99.3 93.3646705655525 5.93532943444754 52 99.7 95.8838680626283 3.81613193737174 53 99.7 100.374485223279 -0.67448522327885 54 100 98.0844536144312 1.91554638556885 55 99.1 94.9592875557885 4.1407124442115 56 98.2 102.028983297469 -3.82898329746858 57 98.1 108.327113211137 -10.227113211137 58 98.6 111.632119530416 -13.0321195304159 59 100.2 102.751535239396 -2.55153523939578 60 101.9 93.1960713011047 8.70392869889528 61 97.5 77.7041603358503 19.7958396641497 62 97.1 87.0222445998843 10.0777554001157 63 98.1 92.3701581732485 5.72984182675145 64 98.5 95.0946939534148 3.40530604658520 65 98.3 98.9730004435915 -0.673000443591505 66 99.3 98.318357354632 0.98164264536797 67 100.9 96.0135289937885 4.88647100621154 68 100.4 102.344289750442 -1.94428975044234 69 101.7 109.235531509680 -7.53553150968033 70 102 114.813131437624 -12.8131314376242 71 103.2 110.078283218645 -6.87828321864468 72 103.1 101.417242408286 1.68275759171392 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 84.5460832458085 64.034527826971 105.057638664646 74 76.7210203455006 50.9075886056059 102.534452085395 75 73.051296175538 42.4269899708937 103.675602380182 76 70.2412324729777 35.0763766647834 105.406088281172 77 69.6532261869454 30.1084581384381 109.197994235453 78 69.0924233643858 25.2653600376298 112.919486691142 79 66.2629571164142 18.2115883028516 114.314325929977 80 66.0922567764204 13.8480711059262 118.336442446915 81 71.8502976140078 15.4262538407205 128.274341387295 82 80.7294089253272 20.1250696065826 141.333748244072 83 86.710476707247 21.9154677690395 151.505485645454 84 85.4569711141797 16.4533987850128 154.460543443347

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211649117kazyfr7t17iqj1n/13hp31211649047.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211649117kazyfr7t17iqj1n/13hp31211649047.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211649117kazyfr7t17iqj1n/25jth1211649047.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211649117kazyfr7t17iqj1n/25jth1211649047.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211649117kazyfr7t17iqj1n/3sy7m1211649047.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211649117kazyfr7t17iqj1n/3sy7m1211649047.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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