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*The author of this computation has been verified*
R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Tue, 30 Nov 2010 14:24:01 +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/Nov/30/t1291126938nkcb8ckmkd7f7yl.htm/, Retrieved Tue, 30 Nov 2010 15:22:22 +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/Nov/30/t1291126938nkcb8ckmkd7f7yl.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:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
1483509 8036554 4623093 5528662 4221032 8061847 7640066 2935533 8161548 2543967 13163450 3348436 3997440 2322911 2019457 3047748 5728767 2605173 5646743 13121544 3453409 1878333 4247362 23022552 7646203 9016602 3606568 3173510 17568772 10805045 31056269 15623385 6663443 35435745 2823250 5197089 4120632 8832767 3695374 8385805 3777904 5199532 5297275 14847382 5900158 4416718 3926429 4876884 2795297 3385527 3877941 3556729 4982836 2976325 2295026 2218752 4146062 3302091 3864505 5454794 1749836 6684048 2809918 4092664 5070470 9814477 6665318 3912554 6188129 3627991 3308767 3820332 4932979 5567917 5020814 3803273 3999984 4883104 13731747 47531824 8415570 22178158 61211654 18223748 17678085 49299580 25899948 34121754 9859231 29740892 21085212 43003866 59549247 18026465 4680597 5564728 11792347 10371624 3728446 5732978 4067638 2395508 5018801 22068888 7678580 15510095 6471239 14349204 35151574 8210488 50226 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.104061953379148
beta0
gamma0.180728414306662


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1339974405199021.44239531-1201581.44239531
1423229112710388.04568667-387477.045686666
1520194572188600.03733354-169143.037333538
1630477483370649.73002083-322901.730020828
1757287676706464.15203651-977697.152036509
1826051732696659.60610524-91486.6061052391
1956467436689257.50563639-1042514.50563639
20131215442543939.4428424110577604.5571576
21345340910652204.8960617-7198795.89606166
2218783333170839.09062063-1292506.09062063
23424736215619609.4785574-11372247.4785574
24230225523736211.2482941219286340.7517059
2576462036959067.78349364687135.216506358
2690166023830250.374266335186351.62573367
2736065683643446.09048391-36878.0904839062
2831735105668291.65335616-2494781.65335616
291756877210843731.53230816725040.4676919
30108050454836166.248925635968878.75107437
313105626913420816.446625517635452.5533745
32156233858984106.563293936639278.43670607
33666344317062807.7366147-10399364.7366147
34354357455431412.0469582130004332.9530418
35282325041610461.9740206-38787211.9740206
36519708917379597.4889591-12182508.4889591
37412063212903743.9853599-8783111.98535986
3888327677696654.136083831136112.86391617
3936953745472322.95565903-1776948.95565903
4083858057653175.18675683732629.813243168
41377790418387562.0408045-14609658.0408045
4251995327617909.68655863-2418377.68655863
43529727518288955.056674-12991680.056674
44148473829330478.816275955516903.18372405
45590015814056479.1963001-8156321.19630013
4644167187863054.93052828-3446336.93052828
47392642919321981.1694767-15395552.1694767
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4927952976582319.38187541-3787022.38187541
5033855274593973.52435223-1208446.52435223
5138779412877246.471396761000694.52860324
5235567294614727.67698048-1057998.67698048
5349828369033260.32442357-4050424.32442357
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1351002504213317162.8669739-3292120.86697389
1361063979612534119.4539978-1894323.45399780
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1381076437811057292.6580037-292914.658003664
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347566618811397668.9806309-5731480.98063094
348687555615260164.9270090-8384608.92700902
349709876613622539.8214543-6523773.82145427
3503608330911408330.046802424674978.9531976
351102003309307980.46299397892349.53700603
35277849768703613.7734752-918637.773475198


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
35310395306.43030715124527.0251658915666085.8354484
3547730191.533086422238216.29940713222166.7667658
35511023687.84160294586369.6880564117461005.9951493
35612084884.50724245043806.3354287119125962.6790560
35713597343.96996455775891.4019045721418796.5380245
35812283981.08315824609466.0154934719958496.1508229
35910023435.51118192837821.7953181517209049.2270457
36014031868.35577554890214.5881655623173522.1233855
36113479465.74115324319303.9725895822639627.5097167
36216649040.61787785644454.8496115427653626.3861440
3638751362.027304961328755.5032612916173968.5513486
3647837458.921086212772531.5392494912902386.3029229
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291126938nkcb8ckmkd7f7yl/1stf31291127035.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291126938nkcb8ckmkd7f7yl/1stf31291127035.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/30/t1291126938nkcb8ckmkd7f7yl/2stf31291127035.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291126938nkcb8ckmkd7f7yl/2stf31291127035.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/30/t1291126938nkcb8ckmkd7f7yl/33kf61291127035.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291126938nkcb8ckmkd7f7yl/33kf61291127035.ps (open in new window)


 
Parameters (Session):
par1 = 12 ;
 
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

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Software written by Ed van Stee & Patrick Wessa


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