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inschrijving 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: Tue, 21 Dec 2010 22:14:17 +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/Dec/21/t129296957808rxaduic3uko8l.htm/, Retrieved Tue, 21 Dec 2010 23:12:58 +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/Dec/21/t129296957808rxaduic3uko8l.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:
KDGP2W101
 
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 Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Framework
error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.56278376127218
beta0
gammaFALSE


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
343129396903439
43786341625.413355015-3762.41335501503
53595339507.988215619-3554.98821561899
62913337507.2985763547-8374.29857635465
72469332794.3793255375-8101.37932553751
82220528235.0545972188-6030.05459721883
92172524841.4377903194-3116.43779031941
102719223087.55720891274104.44279108731
112179025397.4709608073-3607.47096080729
121325323367.244884804-10114.244884804
133770217675.112106106120026.8878938939
143036428945.9194016081418.080598392
153260929743.99213455822865.00786544185
163021231356.3720371459-1144.37203714590
172996530712.3380377862-747.338037786223
182835230291.7483259391-1939.74832593912
192581429200.0894671457-3386.08946714569
202241427294.4533008213-4880.45330082133
212050624547.8134354719-4041.81343547187
222880622273.14646789666532.85353210342
232222825949.730350534-3721.73035053399
241397123855.2009454196-9884.20094541964
253684518292.533160186318552.4668398137
263533828733.56022917416604.43977082593
273502232450.43168449512571.56831550493
283477733897.6685734633879.3314265367
292688734392.5420210945-7505.54202109446
302397030168.5448520765-6198.54485207652
312278026680.1044658106-3900.10446581058
321735124485.1890051873-7134.18900518728
332138220470.1832832213911.816716778656
342456120983.33892468093577.66107531911
351740922996.7884812061-5587.78848120605
361151419852.0718625595-8338.07186255954
373151415159.540417990516354.4595820095
382707124363.56469512772707.43530487232
392946225887.26531940483574.73468059518
402610527899.0679485003-1794.06794850028
412239726889.3956404654-4492.39564046543
422384324361.1483248015-518.148324801547
432170524069.5428616729-2364.54286167285
441808922738.8165362913-4649.81653629132
452076420121.9752967717642.02470322829
462531620483.29637408424832.70362591582
471770423203.0634977908-5499.06349779079
481554820108.2798590295-4560.27985902954
492802917541.828407511110487.1715924889
502938323443.83828143885939.16171856122
513643826786.30205221449651.69794778559
523203432218.1209259322-184.120925932169
532267932114.5006587071-9435.50065870715
542431926804.3541085138-2485.3541085138
551800425405.6371752311-7401.63717523114
561753721240.1159661826-3703.11596618256
572036619156.06243430731209.93756569273
582278219836.99564843232945.00435156767
591916921494.3962743705-2325.39627437052
601380720185.7010126320-6378.70101263197
612974316595.871664712313147.1283352877
622559123994.86199917361596.13800082644
632909624893.14254678814202.85745321188
642648227258.4424723975-776.44247239752
652240526821.4732573702-4416.47325737017
662704424335.95382602942708.04617397061
671797025859.9982375153-7889.9982375153
681873021419.6353529756-2689.63535297557
691968419905.9522525774-221.95225257735
701978519781.04112904903.95887095096259
711847919783.2691173332-1304.26911733321
721069819049.2476377693-8351.24763776928


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7314349.30108087011752.9524469086626945.6497148315
7414349.3010808701-104.84054104158928803.4427027817
7514349.3010808701-1749.6560637482330448.2582254884
7614349.3010808701-3241.3393924678531939.941554208
7714349.3010808701-4616.0579555471433314.6601172873
7814349.3010808701-5897.6506526178434596.252814358
7914349.3010808701-7102.8145634240135801.4167251642
8014349.3010808701-8243.7836295926536942.3857913328
8114349.3010808701-9329.8392720253938028.4414337655
8214349.3010808701-10368.221023299339066.8231850394
8314349.3010808701-11364.705026465240063.3071882054
8414349.3010808701-12323.987452905741022.5896146459
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/21/t129296957808rxaduic3uko8l/1cc9a1292969652.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t129296957808rxaduic3uko8l/1cc9a1292969652.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t129296957808rxaduic3uko8l/2xdtq1292969653.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t129296957808rxaduic3uko8l/2xdtq1292969653.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t129296957808rxaduic3uko8l/3xdtq1292969653.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t129296957808rxaduic3uko8l/3xdtq1292969653.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')
 




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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