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Opdracht 10_Opgave 1_Evelien Verbist

*Unverified author*
R Software Module: rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Sat, 17 Jan 2009 02:21:14 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jan/17/t1232184372a0f81pyzy43kuv5.htm/, Retrieved Sat, 17 Jan 2009 10:26:15 +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/2009/Jan/17/t1232184372a0f81pyzy43kuv5.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'Gwilym Jenkins' @ 72.249.127.135


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.225645293268359
beta0.000987392360344324
gamma0.443424096464966


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133770241487.9961256583-3785.99612565827
143036432384.3135659264-2020.31356592642
153260934048.9003449238-1439.90034492376
163021230953.1156725608-741.115672560802
172996530167.1395456753-202.139545675338
182835228194.2073966201157.792603379919
192581422076.43666590623737.56333409381
202241420801.71448943221612.28551056781
212050621128.5686532064-622.568653206425
222880626754.3351088812051.66489111902
232222822075.9028005777152.097199422253
241397113470.7919101911500.208089808935
253684537059.3137240137-214.313724013737
263533829795.39583259325542.60416740679
273502233348.5412928561673.45870714403
283477731163.67558089773613.32441910227
292688731542.0050931574-4655.00509315741
302397028668.5927624313-4698.59276243134
312278022752.574744842227.4252551577847
321735120061.6524014616-2710.65240146157
332138218709.35389209042672.64610790962
342456125499.2125262374-938.212526237432
351740920022.3003500512-2613.30035005118
361151411945.8020671158-431.802067115779
373151431811.4261592252-297.426159225179
382707127135.3806512947-64.3806512946976
392946227863.14396409931598.85603590074
402610526585.9642618326-480.964261832625
412239723768.4658044645-1371.46580446454
422384321869.55173426311973.44826573692
432170519509.00931905342195.99068094658
441808916761.20592048261327.79407951737
452076418040.6501136012723.349886399
462531623196.74519867022119.25480132980
471770418102.2740810676-398.274081067633
481554811461.24841949954086.75158050051
492802933585.732192306-5556.732192306
502938327714.3359364251668.66406357501
513643829460.60678135486977.39321864521
523203428524.46033210133509.53966789867
532267925984.4778564559-3305.47785645586
542431924768.9290462075-449.929046207497
551800421739.1115691862-3735.11156918616
561753717326.7906944695210.209305530538
572036618791.38806959851574.61193040150
582278223365.1325770419-583.132577041892
591916917096.73422453672072.26577546332
601380712536.81758758221270.18241241785
612974329375.9445157682367.055484231823
622559127375.9606757853-1784.96067578530
632909629846.2377203085-750.237720308509
642648226330.5427575017151.457242498342
652240521404.03647799451000.96352200549
662704422063.41261627144980.58738372855
671797019291.7487681347-1321.74876813473
681873016844.38845099601885.61154900405
691968419126.6572632223557.342736777737
701978522649.0312084714-2864.03120847137
711847916986.41544496481492.58455503518
721069812281.3703145697-1583.37031456974


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7326500.469400025523700.500890165229300.4379098858
7423936.429930691720958.012913893226914.8469474903
7526838.754287561423558.733455948830118.7751191740
7624044.394515093420689.163127062427399.6259031244
7719771.041334130316444.482929761323097.5997384992
7821290.888961755817665.054642664924916.7232808467
7916074.261585842412658.628759714219489.8944119707
8015127.007409126511599.807198068518654.2076201845
8116276.306596023712432.098804289420120.5143877580
8218074.023874609113808.728215261622339.3195339565
8315011.181302336411004.409162771419017.9534419013
849844.603480536957800.6299601726111888.5770009013
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/17/t1232184372a0f81pyzy43kuv5/1kttg1232184070.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/17/t1232184372a0f81pyzy43kuv5/1kttg1232184070.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/17/t1232184372a0f81pyzy43kuv5/2fznm1232184070.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/17/t1232184372a0f81pyzy43kuv5/2fznm1232184070.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/17/t1232184372a0f81pyzy43kuv5/3sc0n1232184070.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/17/t1232184372a0f81pyzy43kuv5/3sc0n1232184070.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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