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Opgave 10 oefening 2

*Unverified author*
R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Sun, 06 Jun 2010 18:49:12 +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/06/t1275850173lguz0w4xau2xvtx.htm/, Retrieved Sun, 06 Jun 2010 20:49:34 +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/06/t1275850173lguz0w4xau2xvtx.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:
KDGP2W62
 
Dataseries X:
» Textbox « » Textfile « » CSV «
22577.0 22792.0 23932.0 22321.0 21102.0 22824.0 23129.0 23604.0 24746.0 26911.0 27909.0 28922.0 29800.0 30506.0 30771.0 31976.0 33749.0 34371.0 33246.0 35072.0 35762.0 36179.0 37433.0 38298.0 37559.0 37511.0 39364.0 40084.0 42712.0 41938.0 40799.0 38568.0 41134.0 43955.0 43607.0 45082.0 46464.0 46496.0 46774.0 47890.0 45740.0 42660.0 39190.0 39010.0 41150.0 42530.0 44710.0 46620.0 44560.0 46120.0 48060.0 51970.0 57720.0 63490.0 65370.0 64260.0 58700.0 58630.0 59803.0 59266.0 60570.0 63062.0 63846.0 64726.0 63460.0 65220.0 66659.0 66871.0 65672.0 67182.0 68292.0 68318.0 69530.0 70500.0 72044.0 73811.0 76018.0 77818.0 79455.0 81408.0 81815.0
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0311447030224647
gammaFALSE


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
32393223007925
42232124175.8088502958-1854.80885029578
52110222507.0413794899-1405.04137948988
62282421244.28178299141579.71821700861
72312923015.4816377193113.518362280698
82360423324.0171334001279.982866599868
92474623807.7371166318938.262883368236
102691124978.95903549131932.04096450873
112790927204.1318775581704.868122441872
122892228224.0847859016697.915214098415
132980029258.8211479795541.178852020461
143050630153.6760026078352.323997392246
153077130870.6490288742-99.6490288742243
163197631132.5454894635843.454510536543
173374932363.81462970711385.18537029292
183437134179.9558166959191.04418330409
193324634807.9058310491-1561.90583104909
203507233634.2607377921437.73926220799
213576235505.0387001372256.961299862785
223617936203.0416835097-24.0416835097058
233743336619.2929124166813.70708758336
243829837898.6355780067399.364421993305
253755938776.0736643274-1217.07366432741
263751137999.1682664955-488.168266495471
273936437935.96441081051428.03558918952
284008439833.4401551413250.559844858697
294271240561.24376709882150.75623290122
304193843256.2284312462-1318.2284312462
314079942441.1725982393-1642.17259823927
323856841251.0276203555-2683.02762035548
334113438936.46552191842197.53447808156
344395541570.90708061992384.09291938008
354360744466.158946572-859.158946571966
364508244091.4006963319990.59930366811
374646445597.2526174589866.747382541107
384649647006.2472072836-510.247207283639
394677447022.3557095447-248.355709544747
404789047292.620744727597.379255272957
414574048427.2259442243-2687.22594422429
424266046193.5330902372-3533.53309023717
433919043003.4822515217-3813.48225152168
443901039414.7124793166-404.7124793166
454115039222.10782933881927.8921706612
464253041422.15145845341107.84854154663
474471042836.65507227371873.34492772628
484662045074.99984370641545.00015629361
494456047033.1184147438-2473.11841474382
504612044896.09387617721223.90612382277
514806046494.21206893111565.78793106893
525197048482.97806904043487.02193095963
535772052501.58033151295218.41966848707
546349058414.10646233455075.89353766546
556537064342.19365913881027.80634086121
566426066254.2043823895-1994.20438238951
575870065082.0954791339-6382.0954791339
585863059323.3270107753-693.327010775254
595980359231.7335469272571.266453072793
605926660422.5254709549-1156.52547095485
616057059849.505828624720.494171375947
626306261175.9454056211886.05459437903
636384663726.686015847119.313984152941
646472664514.40201445211.59798555007
656346065400.99217087-1940.99217087004
666522064074.54054613941145.45945386063
676665965870.2155406541788.784459345872
686687167333.7819983892-462.781998389197
696567267531.3687904852-1859.36879048521
706718266274.4593016963907.540698303681
716829267812.7243872258479.275612774218
726831868937.6512838515-619.651283851548
736953068944.3524286385585.647571361493
747050070174.5922483244325.407751675622
757204471154.7269761115889.273023888469
767381172726.42312034641084.57687965357
777601874527.20194516831490.79805483173
787781876780.63240785251037.36759214754
797945578612.940913435842.059086564972
808140880276.16659361351131.83340638653
818181582264.4172089263-449.417208926272


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8282657.42024342179199.521185098786115.3193017435
8383499.840486842278532.896900243988466.7840734405
8484342.260730263378164.592512090390519.9289484363
8585184.680973684377941.792703747692427.569243621
8686027.101217105477806.31884847194247.8835857399
8786869.521460526577728.827945921996010.214975131
8887711.941703947677692.177607605297731.70580029
8988554.361947368777685.3857703499423.3381243974
9089396.782190789877700.9544634141101092.609918165
9190239.202434210877733.5197918933102744.885076528
9291081.62267763277779.1050199977104384.140335266
9391924.04292105377834.6775768833106013.408265223
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Jun/06/t1275850173lguz0w4xau2xvtx/1aax51275850149.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jun/06/t1275850173lguz0w4xau2xvtx/1aax51275850149.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Jun/06/t1275850173lguz0w4xau2xvtx/2aax51275850149.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jun/06/t1275850173lguz0w4xau2xvtx/2aax51275850149.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Jun/06/t1275850173lguz0w4xau2xvtx/3l1fq1275850149.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jun/06/t1275850173lguz0w4xau2xvtx/3l1fq1275850149.ps (open in new window)


 
Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
 
Parameters (R input):
par1 = 12 ; par2 = Double ; 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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