Home » date » 2009 » Jun » 03 »

opdracht 10 - inschrijvingen wagens- Birgit Teugels

*Unverified author*
R Software Module: rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Wed, 03 Jun 2009 07:19:13 -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/Jun/03/t12440353846clngotg6vacnnt.htm/, Retrieved Wed, 03 Jun 2009 15:23:04 +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/Jun/03/t12440353846clngotg6vacnnt.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 «
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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.225645293268414
beta0.000987392360328418
gamma0.443424096464601


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133770241487.9961256583-3785.99612565827
143036432384.3135659263-2020.31356592626
153260934048.9003449235-1439.90034492352
163021230953.1156725606-741.115672560583
172996530167.1395456752-202.139545675152
182835228194.2073966200157.792603380043
192581422076.43666590613737.56333409386
202241420801.71448943241612.28551056765
212050621128.5686532066-622.568653206636
222880626754.33510888112051.66489111885
232222822075.9028005779152.09719942206
241397113470.7919101912500.208089808842
253684537059.3137240151-214.313724015083
263533829795.39583259385542.60416740621
273502233348.54129285661673.45870714344
283477731163.6755808983613.32441910198
292688731542.0050931576-4655.0050931576
302397028668.5927624311-4698.59276243109
312278022752.574744840727.4252551592508
321735120061.652401461-2710.65240146099
332138218709.35389209042672.64610790961
342456125499.2125262368-938.212526236843
351740920022.3003500512-2613.30035005117
361151411945.8020671156-431.802067115581
373151431811.4261592257-297.426159225743
382707127135.3806512935-64.3806512935298
392946227863.14396409921598.85603590077
402610526585.9642618321-480.964261832112
412239723768.4658044660-1371.46580446604
422384321869.55173426421973.44826573577
432170519509.00931905272195.99068094733
441808916761.20592048311327.79407951686
452076418040.65011360032723.34988639968
462531623196.74519867042119.25480132960
471770418102.2740810686-398.274081068615
481554811461.24841949954086.75158050045
492802933585.7321923070-5556.73219230705
502938327714.33593642431668.66406357568
513643829460.60678135436977.39321864572
523203428524.46033210153509.53966789855
532267925984.4778564577-3305.47785645768
542431924768.9290462077-449.929046207748
551800421739.111569185-3735.11156918499
561753717326.7906944692210.209305530821
572036618791.38806959711574.61193040290
582278223365.1325770413-583.132577041317
591916917096.73422453732072.26577546265
601380712536.81758758111270.18241241892
612974329375.9445157708367.055484229182
622559127375.9606757846-1784.96067578459
632909629846.2377203062-750.237720306224
642648226330.5427575007151.457242499258
652240521404.03647799641000.96352200358
662704422063.41261627184980.58738372821
671797019291.7487681354-1321.74876813540
681873016844.38845099571885.61154900430
691968419126.6572632209557.342736779075
701978522649.0312084711-2864.03120847110
711847916986.41544496441492.58455503558
721069812281.3703145687-1583.37031456868


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7326500.469400026423700.500890167429300.4379098855
7423936.429930691820958.012913894326914.8469474893
7526838.754287560223558.733455948530118.7751191718
7624044.394515092420689.163127062227399.6259031225
7719771.041334130616444.482929762423097.5997384987
7821290.888961754417665.054642664324916.7232808446
7916074.261585842912658.628759715319489.8944119704
8015127.007409125711599.807198068518654.2076201830
8116276.306596022612432.098804288920120.5143877562
8218074.023874609013808.728215261922339.3195339562
8315011.181302335311004.409162770919017.9534418996
849844.603480536377800.629960171711888.5770009010
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t12440353846clngotg6vacnnt/1e35n1244035148.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t12440353846clngotg6vacnnt/1e35n1244035148.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t12440353846clngotg6vacnnt/2eoyk1244035148.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t12440353846clngotg6vacnnt/2eoyk1244035148.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t12440353846clngotg6vacnnt/3jq4y1244035148.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t12440353846clngotg6vacnnt/3jq4y1244035148.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')
 




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Software written by Ed van Stee & Patrick Wessa


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