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inschrijvingen nieuwe personenwagens

*Unverified author*
R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Wed, 02 Jun 2010 08:45:25 +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/Jun/02/t1275468425fcwjldby5x4le33.htm/, Retrieved Wed, 02 Jun 2010 10:47:07 +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/2010/Jun/02/t1275468425fcwjldby5x4le33.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:
KDGP2W61
 
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 Server184.73.236.201 @ 184.73.236.201


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.225679028753732
beta0.00094149628696139
gamma0.443442884267825


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133770241487.9961256583-3785.99612565827
143036432384.2423306432-2020.24233064318
153260934048.8239474283-1439.82394742829
163021230953.0817784316-741.081778431551
172996530167.1615625239-202.161562523925
182835228194.2876712464157.712328753587
192581422076.54434447373737.45565552631
202241420801.92075326921612.07924673078
212050621128.7820231174-622.782023117405
222880626754.5259191592051.47408084105
232222822076.0673310009151.932668999121
241397113470.8643970099500.1356029901
253684537059.4733194599-214.473319459903
263533829795.48397041035542.51602958971
273502233348.72441949681673.27558050316
283477731163.74413083673613.25586916331
292688731542.0186569803-4655.01865698035
302397028668.3449958561-4698.34499585611
312278022752.225994223627.7740057763804
321735120061.35455277-2710.35455277003
332138218709.04253007082672.95746992922
342456125498.9960342699-937.996034269905
351740920022.1189854628-2613.11898546284
361151411945.6711210855-431.671121085454
373151431811.142739522-297.142739522031
382707127135.223971572-64.2239715719661
392946227863.02418044031598.97581955968
402610526585.9480635963-480.948063596261
412239723768.4474504715-1371.44745047153
422384321869.56385517591973.43614482408
432170519509.10820626882195.89179373124
441808916761.2809759651327.71902403496
452076418040.74222789362723.25777210641
462531623196.82850721342119.17149278664
471770418102.3007276661-398.300727666137
481554811461.22353787174086.77646212826
492802933585.8002125576-5556.8002125576
502938327714.04861898681668.9513810132
513643829460.21037802946977.78962197057
523203428524.13301245923509.86698754081
532267925984.1070779241-3305.10707792409
542431924768.3603312277-449.360331227745
551800421738.5190502831-3734.51905028314
561753717326.1475284391210.852471560949
572036618790.72385674411575.27614325593
582278223364.3485694361-582.348569436119
591916917096.1467294062072.85327059405
601380712536.44630626261270.55369373736
612974329375.0615334862367.938466513806
622559127375.1673515005-1784.16735150052
632909629845.1799392579-749.179939257865
642648226329.5061513023152.493848697704
652240521403.18892294651001.81107705352
662704422062.65158253634981.3484174637
671797019291.1739870894-1321.17398708937
681873016843.79259252391886.2074074761
691968419125.9670976035558.032902396455
701978522648.0790967245-2863.07909672453
711847916985.57738857371493.42261142634
721069812280.7803828348-1582.78038283481


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7326498.981865143423698.880672300829299.083057986
7423934.863394318520956.288363419126913.4384252178
7526836.693618630423556.492578439430116.8946588213
7624042.23331480820686.841609152927397.6250204631
7719769.007584472216442.31068039923095.7044885454
7821288.45675620117662.497386310724914.4161260914
7916072.176615045812656.443904693519487.9093253982
8015124.888989784911597.600805588718652.1771739811
8116273.780768290912429.524494834220118.0370417475
8218070.92652369313805.659849372122336.193198014
8315008.434190426611001.710892847819015.1574880055
849842.625886158257798.833920993911886.4178513226
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Jun/02/t1275468425fcwjldby5x4le33/16y0x1275468322.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jun/02/t1275468425fcwjldby5x4le33/16y0x1275468322.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Jun/02/t1275468425fcwjldby5x4le33/2h8zi1275468322.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jun/02/t1275468425fcwjldby5x4le33/2h8zi1275468322.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Jun/02/t1275468425fcwjldby5x4le33/3h8zi1275468322.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jun/02/t1275468425fcwjldby5x4le33/3h8zi1275468322.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')
 




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


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