Home » date » 2010 » Dec » 24 »

Aantal personenwagens

*Unverified author*
R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Fri, 24 Dec 2010 12:11:55 +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/24/t1293192624otuah2g554qakhk.htm/, Retrieved Fri, 24 Dec 2010 13:10:24 +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/24/t1293192624otuah2g554qakhk.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 time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.225679028753479
beta0.000941496286975265
gamma0.443442884267471


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133770241487.9961256583-3785.99612565827
143036432384.2423306439-2020.24233064395
153260934048.8239474295-1439.82394742945
163021230953.0817784327-741.081778432705
172996530167.161562525-202.161562524972
182835228194.2876712472157.71232875279
192581422076.54434447413737.45565552587
202241420801.92075326871612.07924673134
212050621128.7820231166-622.782023116553
222880626754.52591915832051.47408084169
232222822076.067331151.932668999951
241397113470.8643970095500.135602990518
253684537059.4733194593-214.473319459285
263533829795.48397040955542.51602959046
273502233348.72441949451673.27558050553
283477731163.74413083453613.25586916551
292688731542.0186569777-4655.01865697772
302397028668.3449958553-4698.34499585533
312278022752.225994223727.7740057763112
321735120061.3545527706-2710.35455277064
332138218709.04253007232672.95746992771
342456125498.99603427-937.996034270021
351740920022.1189854634-2613.1189854634
361151411945.6711210861-431.671121086054
373151431811.1427395242-297.142739524152
382707127135.2239715725-64.2239715724645
392946227863.02418044141598.97581955856
402610526585.9480635964-480.948063596363
412239723768.4474504728-1371.44745047278
422384321869.56385517681973.43614482318
432170519509.10820626772195.89179373227
441808916761.28097596471327.71902403535
452076418040.74222789212723.25777210785
462531623196.82850721182119.17149278816
471770418102.3007276653-398.30072766529
481554811461.2235378714086.77646212899
492802933585.8002125536-5556.80021255356
502938327714.04861898481668.95138101521
513643829460.21037802766977.78962197236
523203428524.13301245673509.86698754333
532267925984.1070779225-3305.10707792255
542431924768.3603312266-449.360331226591
551800421738.5190502818-3734.51905028182
561753717326.1475284397210.852471560305
572036618790.7238567441575.276143256
582278223364.3485694364-582.34856943641
591916917096.14672940692072.85327059313
601380712536.44630626191270.55369373807
612974329375.0615334871367.938466512893
622559127375.1673514991-1784.16735149907
632909629845.1799392567-749.179939256737
642648226329.5061513026152.493848697366
652240521403.18892294811001.81107705188
662704422062.65158253614981.34841746389
671797019291.1739870883-1321.17398708832
681873016843.7925925231886.20740747698
691968419125.9670976018558.032902398219
701978522648.0790967238-2863.07909672385
711847916985.57738857391493.42261142614
721069812280.7803828343-1582.78038283435


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7326498.981865145723698.880672305229299.0830579861
7423934.863394319820956.288363422826913.4384252168
7526836.693618631223556.49257844330116.8946588194
7624042.233314809120686.841609156927397.6250204613
7719769.00758447416442.310680403623095.7044885444
7821288.456756201917662.497386314824914.416126089
7916072.176615047512656.443904698119487.909325397
8015124.888989785711597.600805592618652.1771739788
8116273.780768291712429.524494838620118.0370417449
8218070.92652369513805.65984937822336.1931980121
8315008.434190427611001.710892852419015.1574880027
849842.625886159177798.83392099711886.4178513213
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293192624otuah2g554qakhk/1p7rw1293192711.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293192624otuah2g554qakhk/1p7rw1293192711.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/24/t1293192624otuah2g554qakhk/20yrh1293192711.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293192624otuah2g554qakhk/20yrh1293192711.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/24/t1293192624otuah2g554qakhk/30yrh1293192711.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293192624otuah2g554qakhk/30yrh1293192711.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=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')
 




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Software written by Ed van Stee & Patrick Wessa


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