Home » date » 2010 » Dec » 18 »

Inschrijvingen nieuwe personenwagens (Opgave 10)

*Unverified author*
R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Sat, 18 Dec 2010 10:12:18 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/18/t1292667805ukxqjlzj50t4420.htm/, Retrieved Sat, 18 Dec 2010 11:23:29 +0100
 
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/2010/Dec/18/t1292667805ukxqjlzj50t4420.htm/},
    year = {2010},
}
@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 = {2010},
    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:
KDGP2W101
 
Dataseries X:
» Textbox « » Textfile « » CSV «
41086 39690 43129 37863 35953 29133 24693 22205 21725 27192 21790 13253 37702 30364 32609 30212 29965 28352 25814 22414 20506 28806 22228 13971 36845 35338 35022 34777 26887 23970 22780 17351 21382 24561 17409 11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.298636157942104
beta0
gamma0.619823384572421


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133770240443.7037927351-2741.70379273505
143036431996.9844990975-1632.98449909746
153260933561.8688755481-952.868875548083
163021230629.3187021052-417.318702105218
172996529937.661508177927.3384918221163
182835228050.1283635797301.871636420328
192581421460.41407584544353.58592415464
202241420567.60484274581846.39515725418
212050621231.3911251245-725.391125124541
222880627004.35736641881801.64263358119
232222822474.1539270696-246.153927069619
241397113911.154390600659.8456093993864
253684536937.4508845106-92.4508845106393
263533829763.87864848695574.12135151311
273502233776.72645318581245.27354681423
283477731733.43637477143043.56362522861
292688732268.625918055-5381.62591805498
302397028885.125941827-4915.12594182699
312278022498.7957065518281.204293448154
321735119299.8958110955-1948.89581109546
332138217712.25964895233669.74035104774
342456125896.3275057667-1335.32750576675
351740919539.0897330241-2130.08973302409
361151410546.5034875310967.496512468986
373151433777.6507675658-2263.65076756578
382707128419.0617148974-1348.06171489740
392946228482.8512423471979.148757652936
402610527141.8424180499-1036.84241804993
412239722795.8623690159-398.862369015857
422384321103.19342257482739.80657742525
432170519261.86039184262443.13960815737
441808915739.11962067762349.88037932239
452076417877.79658642182886.20341357817
462531623652.0603232371663.93967676299
471770417845.0117837314-141.011783731421
481554810793.02412561804754.97587438204
492802933750.5998184451-5721.59981844506
502938327757.3685858631625.63141413698
513643829720.89932135666717.10067864336
523203429217.05528114562816.94471885435
532267926299.2991943212-3620.29919432120
542431925009.0402640972-690.040264097213
551800422014.4633779833-4010.46337798333
561753716523.90159468371013.09840531626
572036618496.51839448371869.48160551635
582278223435.8076546138-653.80765461384
591916916151.94437088833017.05562911168
601380712171.46196030601635.53803969404
612974329643.065818910899.9341810891783
622559128582.3560614190-2991.35606141904
632909631380.4596230663-2284.45962306634
642648226492.9417291983-10.9417291983009
652240519932.26681422652472.7331857735
662704421735.45483827575308.54516172428
671797019088.8124414929-1118.81244149294
681873016645.65355471782084.34644528216
691968419310.4721229259373.527877074121
701978522706.0868861345-2921.08688613454
711847916340.93600907532138.06399092471
721069811497.3792233808-799.379223380776


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7327574.268409722922373.729642367332774.8071770786
7425139.863710774419712.375660964730567.351760584
7529138.597582397723493.276547161334783.9186176342
7625921.649520785820066.594213537131776.7048280344
7720443.949608899714386.417461977426501.4817558221
7822741.479127294716488.022581427028994.9356731623
7915715.40130852279271.9750591494522158.8275578959
8014998.84298067808370.8896848883521626.7962764677
8116297.47036048959489.990066634323104.9506543446
8218149.295628629811166.902699892325131.6885573674
8314855.8096387137702.7799259730422008.8393514530
848096.77929900556777.08961081535515416.4689871958
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/18/t1292667805ukxqjlzj50t4420/1h01v1292667135.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/18/t1292667805ukxqjlzj50t4420/1h01v1292667135.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/18/t1292667805ukxqjlzj50t4420/2h01v1292667135.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/18/t1292667805ukxqjlzj50t4420/2h01v1292667135.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/18/t1292667805ukxqjlzj50t4420/3ss0g1292667135.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/18/t1292667805ukxqjlzj50t4420/3ss0g1292667135.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=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

Creative Commons License

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