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Goudprijs-Exponential-Nina Van Geel

*Unverified author*
R Software Module: rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Fri, 05 Jun 2009 09:45:02 -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/05/t1244216793lobv0kl0pkwae4t.htm/, Retrieved Fri, 05 Jun 2009 17:46:37 +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/05/t1244216793lobv0kl0pkwae4t.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 «
9721 9897 9828 9924 10371 10846 10413 10709 10662 10570 10297 10635 10872 10296 10383 10431 10574 10653 10805 10872 10625 10407 10463 10556 10646 10702 11353 11346 11451 11964 12574 13031 13812 14544 14931 14886 16005 17064 15168 16050 15839 15137 14954 15648 15305 15579 16348 15928 16171 15937 15713 15594 15683 16438 17032 17696 17745 19394 20148 20108 18584 18441 18391 19178 18079 18483 19644 19195 19650 20830 23595 22937
 
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
alpha0.784666830625502
beta0.0378641310094148
gamma1


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131087210741.6474358974130.352564102563
141029610265.303347394030.6966526059896
151038310392.5495905495-9.54959054953906
161043110462.5155496928-31.5155496927582
171057410600.8508660457-26.8508660456828
181065310674.5486461629-21.5486461629444
191080510647.0583430597157.941656940338
201087211025.8506887781-153.850688778106
211062510837.2522401850-212.252240185027
221040710547.0218628396-140.021862839627
231046310142.9747819922320.025218007779
241055610749.5862347794-193.58623477943
251064610866.6264595966-220.626459596553
261070210078.5323568813623.467643118718
271135310664.9624480266688.037551973386
281134611301.020186069344.9798139306604
291145111526.1043572766-75.1043572765575
301196411587.3683400464376.631659953608
311257411947.0847311115626.915268888459
321303112676.7770273560354.222972644035
331381212939.4177222090872.582277791016
341454413613.3522118249930.647788175129
351493114277.6754710051653.324528994903
361488615174.3088032397-288.308803239657
371600515347.4769841290657.523015871013
381706415592.56583641971471.43416358034
391516817045.8316060251-1877.83160602512
401605015641.3918566917408.608143308275
411583916248.0752671819-409.075267181917
421513716256.7648398332-1119.76483983325
431495415563.9516028764-609.951602876434
441564815295.3962878081352.603712191883
451530515699.3387386149-394.338738614941
461557915384.9769985834194.023001416555
471634815383.0039047665964.996095233517
481592816302.1162564163-374.116256416339
491617116589.7593055656-418.759305565622
501593716111.7462231936-174.746223193579
511571315449.3506519834263.649348016603
521559416178.4810701130-584.481070112979
531568315761.2153280806-78.2153280806397
541643815817.6841453827620.315854617282
551703216592.9327386944439.067261305561
561769617378.8434581587317.156541841337
571774517617.1426840708127.857315929232
581939417877.75196930351516.24803069650
592014819157.1126501077990.887349892266
602010819886.7665234069221.233476593101
611858420728.2167249392-2144.21672493916
621844118993.8430463573-552.843046357306
631839118162.9395133201228.060486679875
641917818714.2275167589463.772483241082
651807919292.3653460815-1213.36534608155
661848318638.6683680733-155.668368073348
671964418773.0758289109870.924171089078
681919519891.5064846986-696.506484698646
691965019283.4464530862366.55354691379
702083020027.2020641329802.797935867071
712359520609.30015610352985.69984389645
722293722773.4381660234163.561833976615


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7323093.514934282221591.338555947324595.6913126171
7423481.258255137321543.968518754825418.5479915197
7523365.677844896421050.329461584325681.0262282085
7623895.366206360621233.833279615826556.8991331053
7723841.269974929420853.656632628726828.8833172302
7824496.283975368321196.124913561527796.4430371752
7925107.389882250121504.142683011228710.6370814891
8025312.530843162621412.936129841029212.1255564841
8125608.217572794821417.110405287629799.3247403019
8226275.707227758721796.533724622530754.8807308949
8326791.494450133422026.657550359531556.3313499074
8426010.012445362820961.112631684831058.9122590408
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244216793lobv0kl0pkwae4t/1du851244216700.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244216793lobv0kl0pkwae4t/1du851244216700.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244216793lobv0kl0pkwae4t/2olt61244216700.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244216793lobv0kl0pkwae4t/2olt61244216700.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244216793lobv0kl0pkwae4t/3kz9x1244216700.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244216793lobv0kl0pkwae4t/3kz9x1244216700.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')
 




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